![4 1 Introduction to Systems Approaches to Nuclear Fusion
Controlled nuclear fusion research has been advancing steadily over decades. As
physics and technical capabilities have increased, so have the complexities of the
machines used to produce the plasmas. The results of these experiments have
become so impressive that near energy-breakeven fusion conditions (where fusion
output equals heating input) have been obtained in both magnetic and inertial
confinement experiments. However, the next generations of machines beyond
these, leading to a fusion reactor, will become yet more complex and more internally
coupled, so that systems approaches will be required to design, construct and
operate them.
The word system stands for connectivity between elements, often dynamic in
nature. Logical structures and sets of procedures have been developed to deal with
this complexity. It is the goal of this monograph to describe systems approaches and
apply them to machines of increasing complexity, including potential fusion
reactors.
1.1.1.2 Experiencing Fusion Research
An introduction to fusion research should not neglect to mention the excitement of
actually participating in experiments. I was fortunate enough to participate in the
high power fusion experiments on the world’s largest operating magnetic confine-
ment machine, the Joint European Torus (JET). On 9 November 1991, high energy
tritium was injected into a deuterium plasma, resulting in the world’s first controlled
release of fusion energy and a power production of 1.7 megawatts [1]. The exper-
iments were led by Paul Rebut, the director and inspiration for these experiments.
Almost exactly 6 years later, we carried out maximum fusion power experiments.
I had been scientific secretary to Alan Gibson for planning the experimental cam-
paign. The need to limit vacuum vessel radioactivity meant we were allowed only
two attempts at the highest fusion power. The control room was packed with
operators, diagnostic physicists, directors, TV reporters and cameramen.
The plasma discharge in JET was ready to be started, the klaxon sounded, the
machine countdown began. The computers controlled the pre-programmed
sequences. Suddenly, the plasma viewing camera inside JET, which was sensitive
to fusion-produced neutrons, showed a white haze characteristic of a giant neutron
flux. The measurement of the total neutron power was 16 megawatts [2], ten times
greater than in our first experiments. The fusion power was nearly equal to the
plasma loss power.
In February 2022, JET operation was extended to 5 s of fusion power production
of over 11 megawatts [3] in nearly steady-state conditions. The highest amount of
controlled fusion energy of 59 megajoules was produced, paving the way for
successful operation of ITER, a proto-reactor designed to follow on from JET.](https://image.slidesharecdn.com/24419585-250512020537-3ff2e172/85/Systems-Approaches-To-Nuclear-Fusion-Reactors-Frederick-B-Marcus-32-320.jpg)
![1.1 Fusion Physics and Systems Approaches 5
1.1.1.3 Types of Systems Approaches
The approaches used are systems engineering [4], systems architecture [5] and
systems emergent properties [6, 7]. These procedures are best described using
relevant examples from fusion research. Therefore, a brief introduction is provided
of essential plasma physics and engineering concepts for fusion machines.
A system comprises parts or elements that have relationships with each other. In
this context, systems thinking [4] is a way of understanding these relationships and
connections. Systems engineering [4] involves developing the relationships between
elements and the problem solving process. Forward engineering is applied to
designing a new machine. Reverse engineering is the process of studying an existing
machine. Systems architecture [5] describes the physical layout and relationships
between form and function of elements to optimize machine design and its imple-
mentation. Systems modelling [6] uses mathematics or computations of the interac-
tions of the components of the system. Systems complexity [7] leads to systems
emergent properties, particularly performance and metrics, robustness and fragility,
which can be optimized or used for mitigation.
The analysis of systems involves choices of the correct levels of detail and
simplification. In an ideal world with infinite resources, the dictum of Max Planck
might be achieved: “The goal is nothing other than the coherence and completeness
of the system not only in respect of all details, but also in respect of all physicists of
all places, all times, all peoples, and all cultures [8].” This monograph demonstrates
that by breaking down a system into component parts which are analysed at an
appropriate level, successful machine designs can be efficiently produced without
needing infinite resources.
1.1.2 Detailed Monograph Organization
The overall strategy of this monograph is to start by developing the formalisms and
then analysing many of the relevant tokamak (toroidal magnetic chamber) experi-
ments using both systems reverse and forward engineering with the aim of demon-
strating ever increasing levels of complexity. Next, systems approaches are shown to
be essential for the proto-reactor ITER [9, 10] and the European Union (EU) funded
consortium (EUROfusion)-sponsored demonstration fusion reactor (DEMO) [11–
14] using systems codes [15, 16]. An EU DEMO case study examines how the
designers used a methodology which is consistent with that developed in this book
and the best principles of systems engineering. The monograph then goes on to
explore stellarator, linear, reversed field and inertial confinement devices and their
possibilities for fusion reactors. A synthesis and comparison of various concepts is
developed.](https://image.slidesharecdn.com/24419585-250512020537-3ff2e172/85/Systems-Approaches-To-Nuclear-Fusion-Reactors-Frederick-B-Marcus-33-320.jpg)
![6 1 Introduction to Systems Approaches to Nuclear Fusion
1.1.2.1 Part I – Introductory Systems and Plasma Fundamentals
This Chap. 1 presents a basic overview of plasma and tokamak physics [17–25]
followed by the development of systems formalisms applied to experiments, with
applications summarized in checklists.
Chapter 2 creates the design space for tokamaks and different views of interacting
system elements. Medium plasma current experiments are examined to classify
machine elements and plasma operational scenarios.
1.1.2.2 Part II – High-Current Tokamaks
Chapter 3 examines Doublet III [26] and its upgrade DIII-D [27] with its flexible
shaping system to serve as a case study of systems reverse engineering. Other
machines reviewed are Asdex-U, Alcator C-Mod, MAST-U and NSTX-U [28–31].
Chapter 4 discusses TCV [32] as a case study for design and operation, chosen for
its maximum flexibility plasma shaping system [33].
Chapter 5 studies JET [34] in depth, including forward engineering of the first
high power d-t (deuterium–tritium) fusion experiments [2]. Further d-t experiments
were conducted under EUROfusion management [35] and obtained a record fusion
energy production. Experiments using d-t on TFTR [36] are summarized.
Chapter 6 makes a case study of the superconducting and long-pulse Tore Supra
and WEST and reviews EAST, KSTAR, SST-1, JT-60U and JT-60SA [37–43].
1.1.2.3 Part III – Prototype Tokamak Fusion Reactors
Chapter 7 analyses the role of research, innovation and prototyping in systems
integration of the design and construction of ITER [20] with the aim of achieving
sustained fusion power.
Chapter 8 considers concepts for tokamak fusion reactors, highlighting the EU
DEMO [44] as a case study in the advantages of systems engineering for designing
fusion reactors. This is followed by analysis of other fusion reactor concepts and
designs, some based on ITER, others exploring compact machines with high mag-
netic field and/or low aspect ratio.
1.1.2.4 Part IV – Helical, Linear and Inertial Fusion Reactor Concepts
Using the systems formalism already developed for tokamaks, Chap. 9 explores in
detail the stellarator, helias, heliotron/torsatron and other concepts, which are con-
sidered in terms of robustness and fragilities. A case study is made of the W7-X [45]](https://image.slidesharecdn.com/24419585-250512020537-3ff2e172/85/Systems-Approaches-To-Nuclear-Fusion-Reactors-Frederick-B-Marcus-34-320.jpg)
![helias. Reactor concepts are considered based on W7-X and on the LHD torsatron/
heliotron [46].
1.1 Fusion Physics and Systems Approaches 7
Chapter 10 analyses linear magnetic traps and their toroidal versions and makes a
forward engineering case study of MFTF-B [47]. Geometries include simple and
tandem mirrors, field reversed configurations and reversed field pinches [48]. Poten-
tial reactor developments are examined.
Chapter 11 investigates inertial fusion concepts such as direct-drive and indirect-
drive laser implosion, laser shock and fast ignition and linear z-pinch compression.
The laser powered National Ignition Facility (NIF) [49] which has had the very
impressive recent result of energy breakeven, is presented as a case study in forward
engineering. Reactor concepts are examined including HiPER [50].
1.1.2.5 Part V – Synthesis and Conclusions
Chapter 12 provides a synthesis of the conclusions presented in this monograph
relating to the advantages of using systems approaches. Comparisons are made of
various concepts.
1.1.3 A Simplified Description of Plasmas
The following basic description of plasmas [21, 22, 24] provides background for
reading this monograph and clarifies the examples used when discussing systems
definitions. Readers who are familiar with plasmas and tokamaks can jump to
Sect. 1.2.
• Plasma: A plasma is an electrically conducting collection of ions and electrons
(ionized atoms) that provide charge (quasi-) neutrality. The ions in fusion reactors
are mostly deuterium and tritium.
• Density and temperature: A plasma is locally characterized by density per cubic
metre (m3
) for electrons and hydrogen isotope ions as ne and ni, impurity ions
with charge Z as nz. A collection of ions and electrons interact and collide with
each other via the Coulomb force, establishing a Maxwellian distribution of
energies characterized by a temperature T, where 1 keV (kilo electron volt) is
equivalent to 11.6 million degrees Kelvin, since they are related by the
Boltzmann constant. A Maxwellian velocity distribution is proportional to E
times exp(-E/T), where the particle energy is E = mv2
/2. Electron and ion
temperatures are defined as Te and Ti. A singly charged particle has an energy
of 1 keV when accelerated through a potential of 1 kV (kilovolt). The most
probable particle energy in kV equals the temperature in keV in a Maxwellian
distribution. Fast electrons or ions created or injected externally or by resonant
electromagnetic fields, will deposit energy and heat via Coulomb collisions.](https://image.slidesharecdn.com/24419585-250512020537-3ff2e172/85/Systems-Approaches-To-Nuclear-Fusion-Reactors-Frederick-B-Marcus-35-320.jpg)
![h i
1.1 Fusion Physics and Systems Approaches 9
but is nearly half of the maximum at 20 keV. The reaction rate per unit volume is
ndnt σv . The He4
(α-particle) ion deposits heat in the plasma.
• Radioactivity: Fusion product alpha particles and neutrons deposit their energy
in structures surrounding the plasma and generate energy as heat, which could be
processed into electricity. The neutrons also induce radioactivity into the struc-
ture, and can be used to breed tritium. Tritium itself is radioactive.
• Fusion gain Q: An important metric is Q, the energy gain of a plasma, defined by
the total fusion power (or energy) produced by the plasma, divided by the heating
power (or energy) applied to it. Therefore, Q = 1 is referred to as the breakeven
condition. The ignition condition Q = infinity(1) occurs when no external
heating is required, i.e. when contained alpha particles heat the plasma and
maintain a fusion burn.
1.1.4 Tokamak Magnetic Field Coils and Geometry
In this chapter, examples of systems concepts are applied to the nuclear fusion
concept called the tokamak, an acronym for (toroidal chamber magnetized).
In early 1969, Lev Artsimovich was in charge of the T-3 tokamak, which had
reported record results [51]. He presented four lectures at the Massachusetts Institute
of Technology (MIT) in April 1969 (which I attended). MIT soon proposed its own
high magnetic field version of a tokamak based on Bitter magnet technology
[52]. Many other tokamaks were constructed around this period [53]. Tokamaks
are currently the most investigated fusion concept, shown schematically in Fig. 1.1.
The main elements of a tokamak are:
• Vacuum chamber: The torus-shaped vacuum chamber is surrounded by
poloidally wrapped coils which produce a toroidal magnetic field pointed along
the axis of the inside of the vacuum vessel, so that plasma particles flow along the
directions of the field inside the torus and are contained.
• Toroidal magnetic field and its gradient: The toroidal field is stronger than the
poloidal field and provides particle confinement. However, because of the toroi-
dal geometry, the toroidal magnetic field is stronger nearer the inner part of the
torus than the outer part, decreasing with the major radius (R) as 1/R. This
magnetic gradient causes electrons and ions to drift upwards and downwards
producing an electric field,. Without confining fields, the particles would escape
and hit the walls of the vessel.
• Plasma current: In order to stop particles drifting out, an electrical current is
induced in the plasma, which creates a magnetic field circling around the plasma
current, the so-called poloidal field. The individual plasma particles follow the
combined toroidal and poloidal field, and spiral around the plasma. Since parti-
cles are then drifting upwards half the time and downwards half the time, the drift
is cancelled and the particles are confined.](https://image.slidesharecdn.com/24419585-250512020537-3ff2e172/85/Systems-Approaches-To-Nuclear-Fusion-Reactors-Frederick-B-Marcus-37-320.jpg)
![Poloidal magnetic field
Plasma electric current
(secondary transformer circuit)
Toroidal magnetic field
Toroidal field coils
Inner poloidal field coils
(primary transformer circuit)
Outer poloidal field coils
(for plasma positioning and shaping)
Resulting helical magnetic field
10 1 Introduction to Systems Approaches to Nuclear Fusion
Fig. 1.1 Schematic of a tokamak chamber and magnetic profile. (From [54], Fig. 1)
• Poloidal field coils: These are fields that are symmetric around the torus and
generated by coils that are wound in the toroidal direction. They can be wired to
produce special multipole fields (see below) or they can produce a superposition
of these fields by individual coil current control to provide plasma positioning and
shaping and confinement.
• Transformer: The plasma current itself is generated by transformer action either
by a coil with changing current or a coil plus an iron core going through the hole
in the vacuum vessel torus. A magnetic flux change in this primary winding
creates a one-turn voltage that acts on the plasma to ionize the gas and create a
flowing current which ohmically heats the plasma by collision with the acceler-
ated electrons.
• Vertical field: As the plasma current and pressure from ohmic and external
heating increase, the toroidal plasma expands radially outwards. A vertical
magnetic field perpendicular to the plasma current, generated by external coils,
produces a radially inward force which holds the plasma in place.
• Shaping field: Although the simplest plasma shape is a circular torus, it is often
desirable to further shape the plasma with additional coils in the toroidal direction
to generate shaping poloidal magnetic fields.
• Horizontal field: Vertically elongated plasmas can be up-down unstable. A
horizontal field can raise or lower the plasma and be used with feedback for
positional stability.
• Plasma exhaust: At the same time as the plasma is being heated, particles and
energy are also escaping in the form of electromagnetic radiation, energetic ions,](https://image.slidesharecdn.com/24419585-250512020537-3ff2e172/85/Systems-Approaches-To-Nuclear-Fusion-Reactors-Frederick-B-Marcus-38-320.jpg)
![1.1 Fusion Physics and Systems Approaches 11
electrons and fusion products. Some power is going either to a plasma limiter
structure and the walls, or to a magnetic configuration that removes plasma
energy (divertor). The plasma escape needs to be controlled to avoid damaging
surrounding structures.
1.1.5 Plasma Current and MHD Fluid Equilibrium
There are essential physics elements [21] that are central to tokamak design. Current
in the ionized plasma flows along the toroidal magnetic field Btor, which creates a
poloidal magnetic field Bpol (see Fig. 1.1) that is perpendicular to the plasma current.
Closed surfaces of constant poloidal magnetic flux are formed on which there is a
force equilibrium between magnetic fields and the plasma pressure. Magnetic field
lines lie on a flux surface, so particles following field lines will stay on that surface.
The shape of these nested flux surfaces can be calculated by using Magneto-Hydro-
Dynamic (MHD) fluid equations developed by Grad and Shafranov [21], which
describe the force balance in equilibrium conditions.
The so called safety factor (q) is defined as the number of times a magnetic field
line goes around toroidally for each time it goes around poloidally on a flux surface,
and it is a function of minor radius. q may be non-integral and is calculated in a
circular plasma with major radius R and minor radius r by the formula:
q =
rBtor
RBpol
ð1:1Þ
It is valid in the large aspect ratio A = R/r regime. In a tokamak, the lowest value of q
at the plasma edge r = a is kept above 2 and often 3, otherwise resonant instabilities
may occur.
The current in MA in a plasma with toroidal field Btor and vertical elongation κ is
approximately given by:
IMA =
5aκBtor
R
a q
ð1:2Þ
The number of volt-seconds of magnetic flux required from the primary transformer
and ohmic heating coil is given by LIplasma, where L is the plasma self inductance.
Additional voltage used to sustain plasma resistance is calculated as resistivity times
plasma circumference divided by cross section. As an example, the self inductance
of an unshielded current loop of major radius R and cross section a, for uniform
current, is given by.](https://image.slidesharecdn.com/24419585-250512020537-3ff2e172/85/Systems-Approaches-To-Nuclear-Fusion-Reactors-Frederick-B-Marcus-39-320.jpg)
![12 1 Introduction to Systems Approaches to Nuclear Fusion
Lcircular = μ0 R In
8R
r
- 2
ð1:3Þ
For an aspect ratio of 3, L becomes 1.5 microhenries times R. Hence to produce a
plasma current of 1 MA at R = 0.8 m requires about 1.2 volt-seconds for the
magnetic energy of an unshielded plasma, and less if nearby shaping coils reduce
the effective inductance. The resistive losses in forming the plasma need to be added
into the volt-second flux requirement from the ohmic heating transformer coil.
1.1.6 Plasma Pressure and Confinement Time
Plasma stability requirements limit the ratio beta (β) of the plasma pressure
(nT) integrated over particle species and space to the magnetic field pressure,
β = nT=
Btor
2
2μ0
ð1:4Þ
The Troyon Limit [21] in a tokamak on β was determined from computation and
experiment to be:
β %
ð Þlimit 2:8 x IMA=aBtor ð1:5Þ
The Lawson criteria is the value of plasma density (n) times energy confinement (τ)
at which a fusion reactor reaches energy breakeven, and is approximately equal to an
nτ product of 1020
m-3
s-1
for deuterium and tritium at 10 or more keV temperature.
Combining the above formulas (with MKS units), the Lawson criteria for plasma
self-ignition becomes
τ Btor2
κ
R
a q
17 ð1:6Þ
Using suggested reactor parameters of Btor = 5 Tesla, elongation κ = 2, Aspect ratio
R/a = 3, and q = 2, an energy confinement time of about 2 seconds is required,
which is the confinement time estimated for the so-called L-mode confinement in
ITER. With divertor plasmas, enhanced confinement modes become possible with
even higher confinement times.
Wesson [21] notes that for a parabolic radial distribution of deuterium and tritium
total ion density with peak density values ni(0), ion temperature Ti(0) and global
energy confinement time τE, the triple product for plasma ignition by self-heating
from fusion product alpha particles is:](https://image.slidesharecdn.com/24419585-250512020537-3ff2e172/85/Systems-Approaches-To-Nuclear-Fusion-Reactors-Frederick-B-Marcus-40-320.jpg)
![1.1 Fusion Physics and Systems Approaches 13
ni 0
ð ÞTi 0
ð ÞτE 5 × 1021
m- 3
keVs ð1:7Þ
A group of scientists developed a scaling law of energy confinement time for the
ITER project (see Chap. 7), the ITER ELMy H-mode confinement time [55, 56]. It is
valid operating in a high confinement mode (H-mode) when the plasma has Edge
Localized Mode (ELM) instabilities and is given by:
τH98ðy,2Þ = 0:144I0:93
B0:15
n0:41
20 P- 0:69
R1:97
κ0:78
a ε0:58
M0:19
ð1:8Þ
Various tokamak designs have taken different approaches to maximizing the figures
of merit, either by emphasizing an increase in the toroidal field or an increase in
elongation, or a reduction in the aspect ratio as in spherical tokamak design. JET (see
Chap. 5) tried to optimize all three of these, with R/a = 2.4, Btor = 3.5 tesla and
elongation κ = 1.7. Ignition in JET would have required a confinement time of about
4 seconds, whereas only about 1 second was reached. Even this lower confinement
time allowed the approach to Q = 1, where the plasma loss power from auxiliary
heating equals the plasma loss power.
1.1.7 Individual Particle Effects in Toroidal Systems
In fusion reactors with spatially dependent magnetic fields, the mirror effect occurs
when a particle follows a magnetic field line. The gyroradius-averaged motion of a
particle is constrained by adiabatic invariants, meaning constants of motion where
external fields change slowly. During a time much shorter than the time to signifi-
cantly collide with other particles, the total particle energy E is constant, and the
magnetic moment involving the energy perpendicular to the field M = Eperp/B is an
adiabatic constant of the motion. As the particle moves into a higher magnetic field,
the perpendicular energy increases and conservation means the parallel energy and
velocity decreases. If the field variation is large enough, the parallel energy becomes
zero, and the particle is reflected (mirrored) back in the opposite direction. The
mirror ratio is defined as the ratio between the maximum and minimum magnetic
field along this trajectory.
In linear mirror machines, fast particles bounce back and forth between two
intense magnetic fields. In toroidal tokamaks and stellarators, particles are trapped
between the inside and outside of the spatially varying toroidal field. Since particles
drift vertically in opposite directions on one bounce and on the return bounce, the
shape of their orbits is that of a banana, hence the term banana orbits, which can have
a significant effect on plasma transport. These orbits and the rate of collision with
other particles determine the rate of transport labelled as neoclassical in a torus,
which is enhanced compared to classical losses of non-trapped particles.
Banana orbits can contribute to a current referred to as bootstrap, which is
generated by plasma pressure radial gradients.](https://image.slidesharecdn.com/24419585-250512020537-3ff2e172/85/Systems-Approaches-To-Nuclear-Fusion-Reactors-Frederick-B-Marcus-41-320.jpg)
![14 1 Introduction to Systems Approaches to Nuclear Fusion
1.1.8 Auxiliary Heating and Current Drive
Auxiliary heating methods can be chosen to preferentially heat ions or electrons, and
also to impart momentum and drive spin and plasma current. When one species is
heated, it can transfer energy to the other species by Coulomb interactions, which are
stronger at high density and weaker at high electron temperature.
• Neutral beam injection (NBI): An external source is used to inject ions into a
high voltage static electric field which accelerates them to high energy. They are
then neutralized by charge exchange with a cold gas and travel into the vacuum
vessel, where they are then ionized by the plasma, then trapped by the magnetic
field. These injected ions slow down and heat the plasma. They can contribute to
fusion via beam-plasma and beam-beam collisions.
• Electron cyclotron resonance heating (ECRH): A microwave source such as a
high power gyrotron injects microwaves into the plasma where they are resonant
with the electron cyclotron frequency at its first or higher harmonics. These waves
can heat the electrons and also induce current drive.
• Lower hybrid current drive (LHCD): Lower hybrid current drive is produced
by injecting microwaves via waveguides at a frequency intermediate between the
electron and ion cyclotron frequencies. It has proved to be relatively efficient for
current drive by interaction with electrons.
• Ion cyclotron resonance heating (ICRH): Antennas inside the vacuum vessel
are used to launch radio frequency waves resonant with the cyclotron frequency
of ions. ICRH is most efficient when heating minority helium or impurity species
of a few percent which in turn heat the main plasma.
• Alfven Wave Heating (AWH): Alfven waves are created at low radio frequency
by antennas inside the vacuum vessel. Heating seems to be accompanied by
continuous plasma density rise.
• Alpha particle heating (APH): When d-t fusion occurs, the alpha particles are
trapped by the magnetic field, if strong enough. The plasma is heated as the alphas
slow down, with heat transfer typically to electrons.
1.1.9 Elements of a Tokamak Fusion Reactor
Tokamak reactor designs were initiated during the 1970’s, including the Experimen-
tal Power Reactor (EPR) [57], based upon previous general reactor considerations
[58]. This design was superseded, but it highlighted several features illustrating the
complexity of a fusion reactor compared to existing tokamaks without neutron
production. In a reactor, plasma self-heating and ignition require confinement of
charged alpha particles from d-t fusion, while neutrons escape the plasma into the
surrounding structure. A plasma current of at least 1 MA is required for some alpha
confinement and 2.5 MA is a minimum for confining most alpha particles. Shielding
was essential to protect components against sustained 14 MeV neutrons. A breeding](https://image.slidesharecdn.com/24419585-250512020537-3ff2e172/85/Systems-Approaches-To-Nuclear-Fusion-Reactors-Frederick-B-Marcus-42-320.jpg)
![blanket with lithium-6 and lithium-7 was needed to breed tritium fuel from their
reactions with neutrons.
1.1 Fusion Physics and Systems Approaches 15
Fig. 1.2 The ARIES-AT fusion power core. (From [62], Fig. 1)
The EPR parameters were derived from systems scoping studies [59]. The nuclear
blanket and shield were sufficiently thick so as to protect the superconducting coils.
The result was a tokamak with minor radius of 2.25 m, major radius of 6.75 m,
magnetic field on axis of 4.8 T and plasma current of 7.2 MA. The poloidal
magnetics system [60] was designed both to reduce the total volt-second energy
requirements and to reduce the field time-variation at the toroidal field coils.
Reactor studies in the USA continued as a community effort that produced the
ARIES series, starting with ARIES-I, ARIES-II and ARIES-III [61]. A design
shown in Fig. 1.2 is for the ARIES-AT Advanced Tokamak fusion reactor
[62]. This particular 1000-MWe ARIES-AT design had a major radius of 5.2 m,
minor radius of 1.3 m, toroidal β of 9.2% (βN = 5.4) and on-axis toroidal field 5.6 T.
The plasma current was 13 MA and the current-drive power was 35 MW.
These concepts evolved and demonstration reactors are being designed [63].](https://image.slidesharecdn.com/24419585-250512020537-3ff2e172/85/Systems-Approaches-To-Nuclear-Fusion-Reactors-Frederick-B-Marcus-43-320.jpg)
![16 1 Introduction to Systems Approaches to Nuclear Fusion
1.2 Systems Engineering and Architecture Principles
1.2.1 Elements, Relationships and Systems Thinking
Let us begin by looking at the essentials of systems engineering [4] and how they
apply to fusion experiments and reactors. The word system stands for connectivity
and in this context refers to a fusion experiment or reactor installation.
Systems consist of elements, which have properties and functions, and can
themselves be seen as systems, with their own subsystems. Such an element could
be an ionized plasma with properties such as density and temperature, and functions
such as producing fusion products such as neutrons and alpha particles. Another
element might be the poloidal field shaping coils in a tokamak.
Elements are linked to each other through relations. For example, poloidal field
shaping coils influence the plasma shape, but a moving or disrupting plasma can
induce currents in the shaping coils. Relations can be in one direction or in both
directions and can be complex, involving several types of interactions.
Elements and relations form a construct which demonstrates an order, forming the
structure of a system. Examples of structural types include hierarchical, network
and structures with feedback.
Subsystems are found by taking a system and determining its constitutive ele-
ments at a lower level and then connecting them by means of relations. Two plasma
subsystems might be the electron temperature radial profile (determining plasma
resistivity), and the plasma current radial profile. Their steady-state relationship is
determined by Ohm’s law, where the voltage (V) is the product of current (I) and
resistance (R) as V=IR when there is a constant voltage across the plasma.
Systems have emergent properties [7] of robustness and fragility, for example in
the context of dynamic systems biology [64]. These properties and metrics allow the
designer to evaluate the stability and probable success of systems.
These elements and their relations are discussed in detail in Chap. 2 in the context
of the design space available for nuclear fusion experiments and reactors.
1.2.2 Hierarchy
A system divided into multiple levels results in a systems hierarchy. Under the
system, there is a level of subsystems of order 1 and below are subsystems of order
2, etc., and the lowest level is the element level, with relations acting as connectors.
A typical hierarchy might involve the following descending levels: tokamak;
power supplies; poloidal coil power supplies and transformer; coil #5 power supply;
solid state thyristor rectifiers. The lowest element would require a controlling
systems relationship with the power supplies.
The elements can be seen as black boxes, so only the function (the purpose) or
desired inputs and outputs (results) are of significance. For a thyristor, we do not](https://image.slidesharecdn.com/24419585-250512020537-3ff2e172/85/Systems-Approaches-To-Nuclear-Fusion-Reactors-Frederick-B-Marcus-44-320.jpg)
![1.3 Systems Engineering Process Model 19
Many models for analysing nuclear fusion plasmas and the surrounding machin-
ery have been developed and will be discussed in Chap. 2. There are also dedicated
systems engineering and architecture languages such as SysML described in OMG
Systems Modelling Language [65] and Object Process Methodology (OPM)
[66]. Examples of plasma models include the tokamak simulation code (TCS) [67]
and the analysis code TRANSP [68].
1.2.5 Agility
An agile system should be capable of being variable and modified, which can be an
important concern in a rapidly changing environment. Agile fusion experiments
have been able to incorporate new features which greatly improve their performance.
Examples include the addition of auxiliary heating of the plasma, or the installation
of divertor coils that improve plasma performance and impurity and gas control.
Some machines are designed to be highly flexible from the beginning; others have
enough flexibility to allow important upgrades. Plasma physics concepts and new
technologies are being developed that could result in machine upgrades allowing
significant improvements to the performance of ITER.
1.3 Systems Engineering Process Model
Systems engineering [4] involves systems thinking about the relationship between
elements and the problem solving process shown in Fig. 1.3.
There are four basic systems principles [4] for solving a problem:
• Proceed from the general to the detailed.
• Think in variants: consider alternative solutions to each problem.
• Use a phased approach in developing ideas.
• Develop a problem solving cycle as a general work logic.
The first stage of a project is the planning of the general objectives of the project and
of the general means to carry out the objectives. For a nuclear fusion experiment, it is
necessary to look at all of the previous knowledge and experience of related
experiments, and then assess what needs to be done to achieve the project objectives.
Important inputs are the capabilities of the group planning the experiment and the
amount of financing available to carry it out.
Proceeding from the general to the detailed involves using the hierarchical
method already discussed. It starts with a simple model using black boxes, and
evolves to a detailed treatment of more complex white boxes. General objectives and
a general solution framework need to be established. Concepts at higher levels serve
as guidance for the detailed design. In the context of nuclear fusion experiments, the
basic goals need to be decided, the approximate budget applied as a constraint and](https://image.slidesharecdn.com/24419585-250512020537-3ff2e172/85/Systems-Approaches-To-Nuclear-Fusion-Reactors-Frederick-B-Marcus-47-320.jpg)
![the overall machine parameters initially decided. Then basic choices need to be made
such as superconducting or resistive coils, with or without divertor, auxiliary
heating, etc.
20 1 Introduction to Systems Approaches to Nuclear Fusion
Fig. 1.3 Systems Engineering (SE) concepts. (From [4], Fig. 1)
Variant creation involves studying several solutions to the same problem. For
example, if the goal is creating a high current tokamak, variants might involve high
or low toroidal field, plasma aspect ratio, degree of elongation, type of divertor.
Extreme variants could be scoped for feasibility. During the detailed design of the
optimum choice, small variations can be explored for optimization. Variants can
involve different paradigms, even an entirely different fusion concept.
Dividing the development of a project into phases that proceed from one to
the next in a logical and timely fashion coincides with moving from the general to
the specific. The number of phases and approaches depend on the complexity of the
project. Phase I might involve a general specification of machine design suitable for
preliminary external evaluation for funding, and Phase II might involve a more
detailed design suitable for actual application for funding approval. Phase III might
be the production of highly specific details needed for manufacturing.
The problem-solving cycle requires a chain of logic for each problem, which
involves setting objectives and goals, searching for a solution, and selecting the most
appropriate approach. This can include prototyping, where a low cost test of a
component or concept may be made to determine its feasibility.](https://image.slidesharecdn.com/24419585-250512020537-3ff2e172/85/Systems-Approaches-To-Nuclear-Fusion-Reactors-Frederick-B-Marcus-48-320.jpg)
![1.3 Systems Engineering Process Model 21
1.3.1 Problem Solving Process, Systems Architecture
and Design
The systems engineering process model is implemented using the tools of systems
architecture and concept development. Systems architecture [5] goes beyond struc-
ture and involves the allocation of function to the elements of a structure. Systems
design involves systems architecture and concept development.
Systems architecture is defined as:
• the allocation of function to elements;
• the arrangement of these elements in a structure;
• the definition of interfaces between these elements and the system
environment; and
• creation of a defined value.
An example for a tokamak involves the architecture of the plasma, vacuum vessel,
toroidal field coils, and poloidal field shaping coils. Two different architectures
could involve having the poloidal shaping coils either inside or outside the toroidal
field coils. In the two cases, the functions assigned to each element would differ. The
plasma function would be to demonstrate the value of a complex shape while giving
the shaping coils the function of producing that configuration, made easier if inside
the toroidal field coils. The vacuum vessel would have the obvious function of
producing a vacuum for the plasma, but its conducting walls would also have the
function of stabilizing the plasma by image currents induced by plasma motion.
Each subsystem has its own architecture, but is part of the overall tokamak system.
The definition of interfaces between the systems involves different aspects, includ-
ing mechanical structure, cooling, electromagnetics, etc.
The definition of good architecture [5] is adapted here for fusion reactors:
• The experiment’s architecture should be able to make multiple and significant
contributions towards a fusion reactor.
• It should fulfil the project objectives and goals.
• It ensures compliance with regulations, especially health and safety.
• It can be operated and serviced efficiently and is sustainable.
• It is scalable and adaptable with minimal effort.
• Further machines and experiments can be developed from it.
• It is elegant.
1.3.2 Concept Development
Concept design and development involves producing a selected architectural design
in a more concrete and detailed fashion. The process includes searching for objec-
tives and possible solutions, then making a selection of the best approach.](https://image.slidesharecdn.com/24419585-250512020537-3ff2e172/85/Systems-Approaches-To-Nuclear-Fusion-Reactors-Frederick-B-Marcus-49-320.jpg)
![innovation required, risk and performance. The metrics of actual performance are an
emergent property of the entire system (see below).
1.4 Systems Emergent Properties, Robustness and Dynamics 23
Risks can be evaluated at the individual element level or at the project level. A
risk on a component might depend on whether or not the component will fail during
the lifetime of a project, and is related to the difficulty of repair or maintenance. Risk
can also involve failure of the entire project. The risk associated with each element of
a system can be quantified, and the overall risk to the system calculated as the
product of the individual risks. A typical quantification of a multi-element system in
an important final product would be risk level probabilities: high (0.90); medium
(0.95), low (0.98), very low (0.99). The project management can then decide what
level of risk is acceptable. There will often be trade-offs between total risk and total
cost, for example with machining tolerances.
1.4 Systems Emergent Properties, Robustness
and Dynamics
1.4.1 Emergent Properties of Systems
Emergent properties of systems such as robustness are revealed by analysis, com-
putational modelling and experience. Once the interactions are known, they can be
integrated into a dynamic simulation. During the design of a fusion machine, the
operation phase can be simulated and optimized. During the operations, analysis and
simulation can be incorporated for real time control.
Emergent properties of systems need to be considered during these optimizations.
In a dynamic system, robustness refers to the ability to tolerate perturbations.
Robustness includes the ability of a system to resist change without damaging the
main system functions. Perturbations can be small at an anticipated level, or large
enough to represent a danger to the system. Disruptions in tokamaks are a prime
example. Robustness therefore has two dimensions, which are resistance and
avoidance.
As in the analysis of biological organisms [64], the properties for developing a
robust system [7, Chap. 17] in fusion reactors must be optimized, including:
• systems control
• fault-tolerance
• modularity
• decoupling](https://image.slidesharecdn.com/24419585-250512020537-3ff2e172/85/Systems-Approaches-To-Nuclear-Fusion-Reactors-Frederick-B-Marcus-51-320.jpg)
![1.4 Systems Emergent Properties, Robustness and Dynamics 25
1.4.4 Fragilities
A fragility is any event that can damage or destroy a system, ranging from small
perturbations during operation to a systematic failure mode. Fragilities can occur
even in a system that is designed to be robust against many perturbations [69]. Not
all perturbations can be anticipated.
For example, a plasma experiment would be highly robust against many plasma
instabilities, but could be destroyed by a crack in a vacuum window. Several
superconducting magnets in the Large Hadron Collider at CERN were destroyed
not by a quench, but by a helium valve not designed for high pressure.
A certain level of performance is expected in systems. The goal of a new plasma
experiment may be to push performance to new records. Components would be
tested to their limits. Obviously, if operations were conducted short of the design
limits, then system fragility would be reduced. Hence the size of safety margins
affects performance and robustness.
1.4.5 Resource Demands
Resource demands can range from the quantity and complexity of components to
funding for the project. Quantification of resource demands includes metrics such as
expense per element, the cost of systems integration and of the total system itself.
Consumption of resources is also important during an experiment such as volt
seconds from a transformer or power from a motor-generator.
1.4.6 Performance
Performance is an emergent property of a system and is perhaps the most important
metric for evaluating original project goals. It can include quantification of the
progress made towards a higher level goal. Metrics of success in a tokamak can
include maximum toroidal magnetic field and plasma current. Other metrics are the
triple product of plasma density, temperature and energy confinement time achieved,
as a measure of progress towards building a fusion reactor.](https://image.slidesharecdn.com/24419585-250512020537-3ff2e172/85/Systems-Approaches-To-Nuclear-Fusion-Reactors-Frederick-B-Marcus-53-320.jpg)
![26 1 Introduction to Systems Approaches to Nuclear Fusion
1.5 Examples of Systems Engineering, Architecture,
and Emergent Properties
1.5.1 Building a House
House building is given in [4] as an example of systems engineering. A study was
presented to set goals and to develop variants and choose among them. Systems and
subsystems were then identified so as to provide assessments and choice of variants
so as to proceed to building. The goals altered strongly during the study and
illustrated some important lessons:
• Objectives direct the solution search and enable decision making.
• Thinking in variants is essential and decisions channel the next stages.
• Incremental implementation clarifies goals, since a project focus can change.
• Working in phases helps and exit possibilities are necessary.
• Use of a problem solving cycle (PSC) is essential, where systems logic is applied
to each project phase of increasing content.
1.5.2 Landing on the Moon and Returning
The design of the lunar mission spacecraft of 1969 was analysed [5] in terms of
developing systems architecture. Even very complicated systems can be
deconstructed into simpler systems and subsystems, until a level of detail is reached
that allows development of variants and optimization and decisions. The goal was to
get astronauts to the moon and back, but the choice of means was wide open. The
mission plan was divided into nine major decisions, and variants were determined
for each, including earth orbit rendezvous, launch type, lunar orbit, etc. To decide
among variants, the designers used constraints and metrics including performance,
costs, developmental and operational risk. The analysis led to a series of successful
missions. Even when one mission experienced major faults, the astronauts returned
alive.
1.5.3 Guiding an Airplane in Flight
An airplane provides an example of emergent properties [7] such as robustness, and
how systems work together to achieve optimum performance. The airplane course is
maintained by a pilot and an automatic flight controller which uses control surfaces
and negative feedback. Fault tolerance is provided by the pilot, several redundant
control surfaces and backup automatic flight controllers. Modularity comes from the
steady thrust of multiple and redundant jet engines. Decoupling is achieved by the](https://image.slidesharecdn.com/24419585-250512020537-3ff2e172/85/Systems-Approaches-To-Nuclear-Fusion-Reactors-Frederick-B-Marcus-54-320.jpg)
Systems Approaches To Nuclear Fusion Reactors Frederick B Marcus
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- 5. Springer Series in Plasma Science andTechnology Frederick B. Marcus Systems Approaches to Nuclear Fusion Reactors
- 6. Springer Series in Plasma Science and Technology Series Editors Michael Bonitz, Kiel, Germany Rudolf Neu, Garching, Germany Tomohiro Nozaki, Tokyo, Japan Jozef Ongena, Brussel, Belgium Hideaki Takabe, Faculty of Engineering, Osaka University, Osaka, Japan Zensho Yoshida, National Institute for Fusion Science, Toki, Gifu, Japan
- 7. Plasma Science and Technology covers all fundamental and applied aspects of what is referred to as the “fourth state of matter.” Bringing together contributions from physics, the space sciences, engineering and the applied sciences, the topics covered range from the fundamental properties of plasma to its broad spectrum of applica- tions in industry, energy technologies and healthcare. Contributions to the book series on all aspects of plasma research and technology development are welcome. Particular emphasis in applications will be on high- temperature plasma phenomena, which are relevant to energy generation, and on low-temperature plasmas, which are used as a tool for industrial applications. This cross-disciplinary approach offers graduate-level readers as well as researchers and professionals in academia and industry vital new ideas and techniques for plasma applications.
- 8. Frederick B. Marcus Systems Approaches to Nuclear Fusion Reactors
- 9. Frederick B. Marcus Rixensart, Belgium ISSN 2511-2007 ISSN 2511-2015 (electronic) Springer Series in Plasma Science and Technology ISBN 978-3-031-17710-1 ISBN 978-3-031-17711-8 (eBook) https://doi.org/10.1007/978-3-031-17711-8 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
- 10. Preface Motivation Major physics and engineering advances provide a strong basis for constructing nuclear fusion reactors as an inexhaustible energy source. Such machines are complex and internally interconnected, requiring systems approaches to design, construction and operation. Now is the right time to publish a monograph about applying systems approaches. Several more countries have entered the field of fusion research. Successes on toroidal magnetic confinement experiments have led to international construction projects and demonstration reactor design. Other fusion concepts such as stellarators have obtained improved plasma confinement. Laser inertial confinement has dem- onstrated a fusion burn and near energy breakeven. Private industries are making large-scale investments in innovative reactor designs. Overview Systems approaches for engineering, architecture and analysis of emergent proper- ties such as robustness are currently being applied to proto-fusion machines and demonstration reactor designs. Multi-level methodologies can deal with the complex interactions of physics and engineering in fusion power plants. The first chapter provides a basic plasma physics background, definitions of systems concepts and a logical structure for their applications. In the following chapters and in order of increasing complexity, most currently operating tokamak experiments are referenced and extensively analysed. In-depth case studies are developed of important existing tokamaks, including fusion experiments on JET, superconducting technology machines and the ITER proto-reactor under construc- tion. The final chapter on tokamaks demonstrates in detail how systems approaches v
- 11. vi Preface are currently being applied to fusion reactor design. Further chapters apply these principles to other magnetic and inertial confinement machines, including stellarators, linear machines and lasers. In the concluding chapter, a synthesis of the application of systems concepts is provided. A glossary and index are provided. Readership This monograph is structured for teaching systems approaches to students and young researchers interested in plasma physics and nuclear fusion engineering. Practising fusion physicists and engineers can learn how their findings are integrated into systems design of fusion reactors and how they can contribute most effectively. General readers with a technical background will find an accessible survey of the design and operation of almost all existing fusion experiments and concepts, includ- ing their results and future prospects as reactor concepts. Rixensart, Belgium Frederick B. Marcus
- 12. Acknowledgements I acknowledge and appreciate the help and guidance received from Springer Nature Responsible Editor Hisako Niko, Assistant Editors Nitesh Shrivastava and Malini Arumugam, and Production Assistant Sindhuja Aroumougame. I am grateful for the extremely helpful and challenging comments from reviewers Basil Duval, Gianfranco Federici and Fritz Wagner for Chaps. 4, 8 and 9, respectively. vii
- 13. Contents Part I Introductory Systems and Plasma Fundamentals 1 Introduction to Systems Approaches to Nuclear Fusion . . . . . . . . . 3 1.1 Fusion Physics and Systems Approaches . . . . . . . . . . . . . . . . . 3 1.1.1 Fusion Reactors and Systems . . . . . . . . . . . . . . . . . . 3 1.1.2 Detailed Monograph Organization . . . . . . . . . . . . . . . 5 1.1.3 A Simplified Description of Plasmas . . . . . . . . . . . . . 7 1.1.4 Tokamak Magnetic Field Coils and Geometry . . . . . . 9 1.1.5 Plasma Current and MHD Fluid Equilibrium . . . . . . . 11 1.1.6 Plasma Pressure and Confinement Time . . . . . . . . . . . 12 1.1.7 Individual Particle Effects in Toroidal Systems . . . . . . 13 1.1.8 Auxiliary Heating and Current Drive . . . . . . . . . . . . . 14 1.1.9 Elements of a Tokamak Fusion Reactor . . . . . . . . . . . 14 1.2 Systems Engineering and Architecture Principles . . . . . . . . . . . 16 1.2.1 Elements, Relationships and Systems Thinking . . . . . . 16 1.2.2 Hierarchy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.2.3 Aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 1.2.4 Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 1.2.5 Agility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 1.3 Systems Engineering Process Model . . . . . . . . . . . . . . . . . . . . 19 1.3.1 Problem Solving Process, Systems Architecture and Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 1.3.2 Concept Development . . . . . . . . . . . . . . . . . . . . . . . . 21 1.3.3 Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 1.3.4 Metrics and Risk . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 1.4 Systems Emergent Properties, Robustness and Dynamics . . . . . . 23 1.4.1 Emergent Properties of Systems . . . . . . . . . . . . . . . . 23 1.4.2 Mechanisms for Robustness . . . . . . . . . . . . . . . . . . . 24 1.4.3 Robustness Trade-Offs . . . . . . . . . . . . . . . . . . . . . . . 24 1.4.4 Fragilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 ix
- 14. x Contents 1.4.5 Resource Demands . . . . . . . . . . . . . . . . . . . . . . . . . . 25 1.4.6 Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 1.5 Examples of Systems Engineering, Architecture, and Emergent Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 1.5.1 Building a House . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 1.5.2 Landing on the Moon and Returning . . . . . . . . . . . . . 26 1.5.3 Guiding an Airplane in Flight . . . . . . . . . . . . . . . . . . 26 1.6 Systems Reverse Engineering . . . . . . . . . . . . . . . . . . . . . . . . . 27 1.6.1 Identifying Elements and Relationships in Existing Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 1.6.2 Analysing Metrics and Emergent Properties . . . . . . . . 27 1.6.3 Contributing Lessons Learned to the Design Space . . . 28 1.7 Systems Forward Engineering – From Concept to Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 1.7.1 Developing a Solution-Neutral Function . . . . . . . . . . 28 1.7.2 Developing and Implementing Concepts . . . . . . . . . . 28 1.7.3 Organization of Project Management . . . . . . . . . . . . . 29 1.8 Summary Checklists of Systems Strategies for Fusion . . . . . . . . 30 1.8.1 Systems Concepts Summary – Checklist 1.1 . . . . . . . 30 1.8.2 Analyse Existing Plasma Physics and Nuclear Fusion Machines – Checklist 1.2 . . . . . . . . . . . . . . . . . . . . . 30 1.8.3 Design, Fund, Build and Commission New Fusion Machines – Checklists 1.3A and 1.3B . . . . . . . . . . . . 30 1.8.4 Design and Carry Out Fusion Experiments on Existing Machines – Checklist 1.4 . . . . . . . . . . . . 31 1.8.5 Analyse Prototype Reactor Machines and Experiments – Checklist 1.5 . . . . . . . . . . . . . . . . 32 1.8.6 Planning and Building Next-Step Fusion Reactor Machines – Checklist 1.6 . . . . . . . . . . . . . . . . . . . . . 32 1.8.7 Designing and Building a Fusion Reactor – Checklist 1.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 1.8.8 Comparing Approaches to Diverse Concept Fusion reactors – Checklist 1.8 . . . . . . . . . . . . . . . . . . . . . . . 33 1.8.9 Detailed Checklists 1.1 to 1.8 . . . . . . . . . . . . . . . . . . 33 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 2 Systems Design Space for Tokamak Physics and Engineering . . . . . 45 2.1 Developing a Design Space . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 2.2 Detailed Views of Tokamak Design Space . . . . . . . . . . . . . . . . 46 2.2.1 The Time View . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 2.2.2 Time Scales and Design Options . . . . . . . . . . . . . . . . 47 2.2.3 Plasma View . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 2.2.4 Spatial View of Form . . . . . . . . . . . . . . . . . . . . . . . . 50 2.3 Engineering and Interface Analysis . . . . . . . . . . . . . . . . . . . . . 50 2.3.1 Engineering Aspects . . . . . . . . . . . . . . . . . . . . . . . . . 50 2.3.2 Interface Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
- 15. Contents xi 2.4 Operational Scenarios from Tokamaks with Less Than 700 kA Plasma Current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 2.4.1 Strategy for Developing a Catalogue of Operational Scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 2.4.2 TOSCA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 2.4.3 TCABR, Formerly TCA . . . . . . . . . . . . . . . . . . . . . . 56 2.4.4 Neutral Beam Heating with PLT and COMPASS . . . . 57 2.4.5 Tokamak T-10, Successor to T-3 and T-4 . . . . . . . . . . 58 2.4.6 HL-2A, Formerly ASDEX, and HL-2 M . . . . . . . . . . 59 2.4.7 START . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 2.4.8 GLOBUS-M and GLOBUS –M2 . . . . . . . . . . . . . . . . 62 2.4.9 QUEST . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 2.4.10 General Fusion’s Spector and SLiC . . . . . . . . . . . . . . 64 2.5 Design Space Catalogue of Tokamak Operational Scenarios . . . 65 2.5.1 Vacuum Vessel and Component Conditioning . . . . . . 65 2.5.2 Plasma Start-Up and Current Ramp . . . . . . . . . . . . . . 65 2.5.3 MHD Equilibrium and High Beta . . . . . . . . . . . . . . . 66 2.5.4 Particle and Energy Confinement and H-Modes . . . . . 66 2.5.5 Heating, Current Drive and Their Role in Controlling Instabilities and Disruptions . . . . . . . . . . . . . . . . . . . 68 2.5.6 Divertor Radiation and Plasma-Wall Interaction . . . . . 69 2.5.7 Plasma Diagnostics and Machine Control . . . . . . . . . . 70 2.5.8 High Power Tritium Burning and Alpha Particle Heating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 2.5.9 Long Pulse and Steady-State Operation . . . . . . . . . . . 71 2.6 Tokamak Simulation Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 2.6.1 Plasma Simulation and Design Codes . . . . . . . . . . . . 72 2.6.2 Integrated Workflows of Simulation Codes . . . . . . . . 73 2.6.3 Systems Engineering Codes . . . . . . . . . . . . . . . . . . . 74 2.7 Component Design Options . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 2.8 Integration of the Systems Design Space . . . . . . . . . . . . . . . . . 78 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 Part II High-Current Tokamaks 3 Doublet III/DIII-D and 1–2 MA Tokamaks: Robustness and Adaptation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 3.1 Systems Analysis Strategy for Doublet III/DIII-D . . . . . . . . . . . 89 3.1.1 Overall Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 3.1.2 Application of Checklist 1.2 . . . . . . . . . . . . . . . . . . . 89 3.1.3 Doublet III Form and Function Choices . . . . . . . . . . . 90 3.2 Doublet III Experiments and Scenarios . . . . . . . . . . . . . . . . . . . 94 3.2.1 MHD Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . 94
- 16. xii Contents 3.2.2 Plasma Energy Confinement in Different MHD Equilibria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 3.2.3 Doublet III Scenarios . . . . . . . . . . . . . . . . . . . . . . . . 95 3.3 DIII-D Design and Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 3.3.1 Upgrade of Doublet III to DIII-D . . . . . . . . . . . . . . . . 98 3.3.2 DIII-D Scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 3.4 DIII-D Systems Analysis of Emergent Properties and Tradeoffs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 3.4.1 Analysis of Emergent Properties . . . . . . . . . . . . . . . . 104 3.4.2 Systems Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 3.4.3 Fault-Tolerance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 3.4.4 Modularity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 3.4.5 Decoupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 3.4.6 Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 3.4.7 Avoidance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 3.4.8 Resource Demands . . . . . . . . . . . . . . . . . . . . . . . . . . 106 3.4.9 Robustness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 3.4.10 Fragility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 3.4.11 Performance and Metrics . . . . . . . . . . . . . . . . . . . . . 107 3.5 Asdex-Upgrade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 3.5.1 Asdex-Upgrade Design . . . . . . . . . . . . . . . . . . . . . . . 107 3.5.2 Asdex-Upgrade Scenarios . . . . . . . . . . . . . . . . . . . . . 109 3.5.3 Robustness and Performance Analysis . . . . . . . . . . . . 110 3.6 Alcator C and C-Mod . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 3.6.1 Alcator and Alcator C-Mod Design . . . . . . . . . . . . . . 111 3.6.2 Alcator C and C-Mod Scenarios . . . . . . . . . . . . . . . . 112 3.6.3 Robustness and Performance Analysis . . . . . . . . . . . . 115 3.7 FTU . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 3.7.1 FTU Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 3.7.2 FTU Scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 3.7.3 Robustness and Performance Analysis . . . . . . . . . . . . 117 3.8 Spherical Tokamaks MAST, MAST-Upgrade and STEP . . . . . . 117 3.8.1 MAST Design and Results . . . . . . . . . . . . . . . . . . . . 117 3.8.2 Energy Confinement in MAST . . . . . . . . . . . . . . . . . 118 3.8.3 Robustness and Performance Analysis . . . . . . . . . . . . 119 3.8.4 MAST Upgrade First Results . . . . . . . . . . . . . . . . . . 119 3.8.5 STEP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 3.9 Spherical Tokamaks NSTX and NSTX-U . . . . . . . . . . . . . . . . . 119 3.10 Low Aspect Ratio with High Vertical Elongation ST-40 . . . . . . 120 3.11 Discussion of the Robustness and Performance of 1–2 MA Tokamaks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
- 17. Contents xiii 4 TCV: A Case Study in Systems Forward Engineering of a MA Tokamak . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 4.1 Systems Forward Engineering Strategy for TCV . . . . . . . . . . . . 125 4.1.1 Case Study Strategy . . . . . . . . . . . . . . . . . . . . . . . . . 125 4.1.2 TCV Capabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 4.2 Systems Approaches to the Design of TCV . . . . . . . . . . . . . . . . 128 4.2.1 Suitability of TCV as a Case Study in Systems Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 4.2.2 Systems Forward Engineering – Getting Started . . . . . 128 4.2.3 Predecessor Tokamak TCA Design . . . . . . . . . . . . . . 129 4.2.4 TCA Technical Choices . . . . . . . . . . . . . . . . . . . . . . 129 4.2.5 TCV First Goals and Design Options . . . . . . . . . . . . . 130 4.3 Review and Prioritize Goals and Evaluate Variants for TCV . . . 132 4.3.1 Systems Review Process in Early Stages and Prioritizing Goals . . . . . . . . . . . . . . . . . . . . . . . . 132 4.3.2 Scenarios for TCV from the Tokamak Design Space and Revised Priorities . . . . . . . . . . . . . . . . . . . 132 4.3.3 The Intermediate Design Research Areas for TCV . . . 133 4.3.4 Tokamak Systems Basic Parameters for Further Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 4.3.5 TCV Systems Architecture . . . . . . . . . . . . . . . . . . . . 134 4.3.6 Scoping the Systems for Creating High Current and Highly Elongated Plasmas . . . . . . . . . . . . . . . . . 136 4.3.7 Power supply Requirements for Shaping and Controlling Plasma . . . . . . . . . . . . . . . . . . . . . . . . . . 138 4.3.8 Phase I Proposal and Euratom Review . . . . . . . . . . . . 140 4.3.9 Phase II Proposal to Euratom . . . . . . . . . . . . . . . . . . 141 4.4 TCV Top Level Robustness Properties and Tradeoffs . . . . . . . . 142 4.4.1 Robustness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 4.4.2 Fragility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 4.5 TCV Final Design for Construction . . . . . . . . . . . . . . . . . . . . . 144 4.5.1 Phase II Committee Review and Approval . . . . . . . . . 144 4.5.2 Systems Level Considerations for Final Design and Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 4.5.3 TCV System Level Final Design for Construction . . . 145 4.5.4 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 4.6 TCV Subsystem-Elements Descriptions and Robustness Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 4.6.1 Toroidal Field Coils, Power Supplies and Systems Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 4.6.2 Poloidal Field Coils, Power supplies and Systems Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 4.6.3 Flywheel Motor Generator and Systems Analysis . . . . 151
- 18. 4 xiv Contents 4.6.4 Vacuum Vessel and Vacuum Equipment Systems Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 4.6.5 Management of Procurement, Construction and Initial Testing . . . . . . . . . . . . . . . . . . . . . . . . . . 152 4.6.6 Auxiliary Heating Upgrades for TCV . . . . . . . . . . . . 153 4.6.7 Machine and Plasma Control and Data Acquisition . . . 153 4.7 TCV Scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 4.7.1 High Elongation Plasmas and Ohmic H-Modes . . . . . 15 4.7.2 Fully Digital Plasma Control . . . . . . . . . . . . . . . . . . . 154 4.7.3 Fully Non-inductive Steady-State Plasmas with Electron Cyclotron Current Drive . . . . . . . . . . . . 155 4.7.4 Limits of Operating Space for High Plasma Elongation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 4.7.5 High Power Electron Cyclotron Heating and Bootstrap Current Drive . . . . . . . . . . . . . . . . . . . 155 4.7.6 Electron Internal Transport Barriers with EC Current Drive . . . . . . . . . . . . . . . . . . . . . . . 156 4.7.7 H-mode Regimes with Ohmic Heating in H, D and He . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 4.7.8 Neutral Beam Current Drive and Heating . . . . . . . . . . 156 4.7.9 Multi-machine ITER Scenario to Maximize Edge Pedestal Height . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 4.7.10 Exhaust Control and Detachment in Snowflake and Super-X Divertors . . . . . . . . . . . . . . . . . . . . . . . 157 4.7.11 Vessel Wall Conditioning with ECRH . . . . . . . . . . . . 157 4.7.12 Real Time Plasma Control Systems . . . . . . . . . . . . . . 158 4.7.13 Disruption Avoidance by Real-Time Locked Mode Prevention with ECCD . . . . . . . . . . . . . . . . . . . . . . . 158 4.7.14 Elimination of Disruption Runaway Electron Current with Current Ramp Down . . . . . . . . . . . . . . . . . . . . . 158 4.7.15 High-βN Fully Noninductive Scenarios with Combined EC and NBI . . . . . . . . . . . . . . . . . . . . . . . 158 4.7.16 Reduced Heat Flux with Grassy ELM’s at High Triangularity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 4.7.17 High-Shared-Flux Doublet Configuration with Separate Lobe ECRH . . . . . . . . . . . . . . . . . . . . 159 4.7.18 Removable Gas Baffles Separating Main and Divertor Chambers . . . . . . . . . . . . . . . . . . . . . . . 159 4.8 Lessons Learned About Systems Forward Engineering . . . . . . . 160 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 5 JET – World’s Largest Tokamak and its d-t Fusion Experiments Plus TFTR’s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 5.1 Systems Analysis Strategy for JET . . . . . . . . . . . . . . . . . . . . . . 163 5.2 JET Goals, Machine Parameters and Systems Integration . . . . . . 164
- 19. Contents xv 5.2.1 JET Design and Systems Architecting of Highest Level Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 5.2.2 Elements of Next Level Systems, Form Relationships and Design Choices . . . . . . . . . . . . . . . . . . . . . . . . . 166 5.3 Operational and Experimental Evidence of Success in Machine Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 5.3.1 Initial JET Operation Pre-1989 . . . . . . . . . . . . . . . . . 168 5.3.2 High Performance Plasmas in Preparation for Tritium Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 5.3.3 Analysis of Emergent Properties of Systems and Robustness Against Faults . . . . . . . . . . . . . . . . . . . . 171 5.4 Neutron and Fast Particle Diagnostics . . . . . . . . . . . . . . . . . . . . 173 5.4.1 JET Plasma Diagnostics and the Role of Fusion Product Diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . 173 5.4.2 Fusion Products and Diagnostics . . . . . . . . . . . . . . . . 173 5.4.3 Measurements with Neutron and Fast Particle Diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 5.4.4 Robustness Analysis of Neutron and Fast Particle Diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 5.5 Preliminary Tritium Experiments (PTE) . . . . . . . . . . . . . . . . . . 179 5.5.1 Systems Design of Preliminary Tritium Experiments (PTE) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 5.5.2 Preliminary Deuterium-Tritium Fusion Experiments (PTE) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 5.6 Full Power Deuterium-Tritium Experiments (DTE1) . . . . . . . . . 184 5.6.1 JET Optimization in Preparation for DTE1 . . . . . . . . . 184 5.6.2 Machine Upgrades . . . . . . . . . . . . . . . . . . . . . . . . . . 184 5.6.3 Experimental Preparation for Q = 1 Energy Breakeven Experiments at High Power . . . . . . . . . . . 185 5.6.4 Systems Approaches to Planning Full Power Deuterium-Tritium Fusion Experiments . . . . . . . . . . . 186 5.6.5 Deuterium-Tritium High Power Nuclear Fusion Operational Scenarios and Results in JET . . . . . . . . . . 193 5.7 Post-DTE1 Operation in JET – Preparation for DTE2 . . . . . . . . 197 5.7.1 Planning for DTE2 Experiments in JET . . . . . . . . . . . 198 5.7.2 Extrapolated Baseline Scenario . . . . . . . . . . . . . . . . . 199 5.7.3 Extrapolated Hybrid Scenario at High Normalized Beta . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 5.7.4 Completed Preparations for d-t Experiments . . . . . . . . 199 5.7.5 Successful DTE2 Operation . . . . . . . . . . . . . . . . . . . 200 5.8 Fusion Power Experiments in TFTR . . . . . . . . . . . . . . . . . . . . . 200 5.8.1 Tokamak Fusion Test Reactor (TFTR) Design . . . . . . 200 5.8.2 TFTR Experimental Results . . . . . . . . . . . . . . . . . . . 201 5.8.3 Robustness and Fragility Analysis . . . . . . . . . . . . . . . 201 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
- 20. 2 xvi Contents 6 Superconducting and Long-Pulse Tokamaks for Prototyping Reactor Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 6.1 Systems Analysis Strategy for Prototyping Reactor Subsystems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 6.1.1 Goals and Systems Architecture Choices for Superconducting and Steady-State Tokamaks . . . . . . . 208 6.1.2 Key Elements and Constraints of Steady-State Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210 6.2 Design Space for Superconducting and Long-Pulse Tokamaks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210 6.2.1 Goals for Using the Design Space . . . . . . . . . . . . . . . 210 6.2.2 Technical Aspects of Superconducting Magnets . . . . . 211 6.2.3 Systems Architecture of Choices and Trade-Offs . . . . 21 6.3 HT-7 (Formerly T-7) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 6.3.1 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 6.3.2 Scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 6.3.3 Robustness, Fragility and Relevance to Steady-State Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 6.4 TRIAM-1M . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 6.4.1 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 6.4.2 Scenario: 5 h Fully Non-inductive Steady-State Operation with LHCD . . . . . . . . . . . . . . . . . . . . . . . 217 6.4.3 Robustness, Fragility and Relevance to Steady-State Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218 6.5 T-15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218 6.5.1 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218 6.5.2 Scenario: Ohmic Heating in T-15 and Test of Superconducting Windings . . . . . . . . . . . . . . . . . . . . 218 6.5.3 Robustness, Fragility and Relevance to Steady-State Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218 6.6 Tore-Supra, Later WEST, a Case Study of Prototyping a Superconducting Tokamak Reactor . . . . . . . . . . . . . . . . . . . . . 219 6.6.1 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 6.6.2 Scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 6.6.3 Robustness, Fragility and Relevance to Steady-State Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 6.7 WEST (Tungsten {Symbol “W”} Environment in Steady-State Tokamak) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 6.7.1 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 6.7.2 Scenario: Plasma and Impurity Confinement in a Long Pulse, High Power, Tungsten Divertor Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 6.7.3 Robustness, Fragility and Relevance to Steady-State Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224
- 21. Contents xvii 6.8 SST-1 (Steady-State Superconducting Tokamak) . . . . . . . . . . . . 224 6.8.1 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 6.8.2 Scenario: LHCD . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 6.8.3 Robustness, Fragility and Relevance to Steady-State Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 6.9 EAST (Experimental Advanced Superconducting Tokamak) . . . 225 6.9.1 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 6.9.2 Scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 6.9.3 Robustness, Fragility and Relevance to Steady-State Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228 6.10 KSTAR (Korea Superconducting Tokamak Advanced Research) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228 6.10.1 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228 6.10.2 Scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 6.10.3 Robustness, Fragility and Relevance to Steady-State Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230 6.11 JT-60-U (Japan Tokamak 60 m3 Plasma: Upgraded JT-60) . . . . 230 6.11.1 JT-60-U Design and Relevance to JT-60SA . . . . . . . . 230 6.11.2 Scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230 6.11.3 Robustness, Fragility and Relevance to Steady-State Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232 6.12 JT-60SA (JT-60 Super Advanced) . . . . . . . . . . . . . . . . . . . . . . 232 6.12.1 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 6.12.2 Commissioning Until Superconducting Coil Connector Fault . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234 6.12.3 Robustness, Fragility and Relevance to Steady-State Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234 6.13 Summary Evaluation of Robustness and Fragility in Prototyping Fusion Reactor Subsystems . . . . . . . . . . . . . . . . 235 6.13.1 Plasma Start-Up and Current Drive . . . . . . . . . . . . . . 235 6.13.2 Resistance to Disruptions . . . . . . . . . . . . . . . . . . . . . 235 6.13.3 True Steady-State Operation . . . . . . . . . . . . . . . . . . . 235 6.13.4 Long Term Gas Inventory . . . . . . . . . . . . . . . . . . . . . 235 6.13.5 ITER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236 Part III Prototype Tokamak Fusion Reactors 7 ITER: A Fusion Proto-Reactor and its Large Scale Systems Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241 7.1 Systems Analysis Strategy for the ITER Tokamak . . . . . . . . . . . 241 7.1.1 Overall Systems Analysis Strategy . . . . . . . . . . . . . . . 241 7.1.2 ITER Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241 7.1.3 ITER Top Level Parameters and Scoping Comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242
- 22. xviii Contents 7.1.4 Systems Engineering Approaches Used in ITER Design and Construction . . . . . . . . . . . . . . . . . 244 7.2 Review of Top Level Systems Architecture and Innovations . . . 246 7.2.1 Overall Systems Architecture . . . . . . . . . . . . . . . . . . 246 7.2.2 Innovation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247 7.3 Plasma with Heating and Current Drive . . . . . . . . . . . . . . . . . . 248 7.3.1 Design Choices . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248 7.3.2 Robustness, Fragilities and Opportunities . . . . . . . . . . 251 7.4 Detailed Subsystem Design and Emergent Properties . . . . . . . . . 252 7.4.1 Instability Coils . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252 7.4.2 In-Vessel Diagnostics . . . . . . . . . . . . . . . . . . . . . . . . 254 7.4.3 Plasma Facing Components and Neutron Shield . . . . . 254 7.4.4 Test Tritium Breeding Modules (TBM) . . . . . . . . . . . 255 7.4.5 Divertor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256 7.4.6 Vacuum Vessel and Disruption Mitigation . . . . . . . . . 258 7.4.7 Superconducting Magnetic Coils . . . . . . . . . . . . . . . . 259 7.4.8 Auxiliary Heating and Current Drive . . . . . . . . . . . . . 260 7.4.9 Diagnostics and Control for Plasma and Neutrons . . . . 261 7.4.10 Balance of Plant Including Power Systems, Cooling, Refrigeration and Tritium Processing . . . . . . . . . . . . . 264 7.5 Systems Aspects of Construction and Operation . . . . . . . . . . . . 264 7.5.1 Systems Aspects of Machine Assembly and Commissioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264 7.5.2 Systems Integration of Construction and Operation . . . 265 7.5.3 Preparation for Assembly and Commissioning . . . . . . 265 7.5.4 Robustness and Fragilities of the Construction Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266 7.5.5 Research Plans to Fulfil Goals . . . . . . . . . . . . . . . . . . 266 7.5.6 Robustness and Fragilities of Physics Research Programme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267 7.6 Conclusions and Lessons for Future Machines . . . . . . . . . . . . . 267 7.6.1 Conclusions on Systems Approaches . . . . . . . . . . . . . 267 7.6.2 Lessons for Future Machines . . . . . . . . . . . . . . . . . . . 267 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268 8 Demonstration Tokamak Fusion Reactors and Their Systems Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 8.1 Systems Strategy for Demonstration Tokamak Reactors . . . . . . . 273 8.1.1 Identify Goals and Essential Elements of a Fusion Reactor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274 8.1.2 Paths to an “ITER-based” Reactor . . . . . . . . . . . . . . . 275 8.1.3 Key Choices for Neutronics and Reactor Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276 8.1.4 Use Systems Codes to Develop Design Analysis Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279
- 23. Contents xix 8.2 The EU DEMO and Planning Major Steps for Designing a Fusion Reactor – Case Study . . . . . . . . . . . . . . . . . . . . . . . . . 282 8.2.1 Use of Systems Approaches in the Staged Design Approach in Europe . . . . . . . . . . . . . . . . . . . . . . . . . 282 8.2.2 Application of Systems Codes . . . . . . . . . . . . . . . . . . 284 8.2.3 Systems Design Point Studies, Sensitivities and Trade-Offs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288 8.2.4 Systems Integration and Key Design Issues . . . . . . . . 289 8.2.5 Fusion Blanket and Shield Thickness for DEMO . . . . 289 8.2.6 Systems Management Structures . . . . . . . . . . . . . . . . 292 8.2.7 Robustness and Fragilities . . . . . . . . . . . . . . . . . . . . . 292 8.3 Japan Demo and Fusion Reactor Designs and Their Variations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293 8.3.1 Current Japan DEMO Design . . . . . . . . . . . . . . . . . . 293 8.3.2 Robustness of Japan DEMO Current Design . . . . . . . 295 8.3.3 Japan DEMO Designs and Options in Systems Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295 8.3.4 Summary of Previous Design Variants . . . . . . . . . . . . 297 8.4 China Fusion Engineering Test Reactor (CFETR) . . . . . . . . . . . 297 8.4.1 Two Phase Design . . . . . . . . . . . . . . . . . . . . . . . . . . 297 8.4.2 Tritium Fuel Cycle Studies for CFETR . . . . . . . . . . . 297 8.4.3 Toroidal Field Coils . . . . . . . . . . . . . . . . . . . . . . . . . 298 8.5 Korea K-DEMO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298 8.5.1 A High Field Reactor . . . . . . . . . . . . . . . . . . . . . . . . 298 8.5.2 Fragility – Cyclotron/Synchrotron Radiation . . . . . . . 299 8.6 USA DEMO and Fusion Reactors . . . . . . . . . . . . . . . . . . . . . . 299 8.6.1 A High Elongation Fusion Reactor . . . . . . . . . . . . . . 299 8.6.2 Water or Liquid Nitrogen Cooled Toroidal Field Coil Reactors . . . . . . . . . . . . . . . . . . . . . . . . . . 300 8.6.3 Advanced Tokamak Reactors . . . . . . . . . . . . . . . . . . 300 8.7 Large Scale DEMOs – Robustness and Fragilities . . . . . . . . . . . 301 8.7.1 Common Features of Large Scale DEMOs . . . . . . . . . 301 8.7.2 Robustness Summary for Large DEMO Machines . . . 302 8.8 Very High Magnetic Field Reactors . . . . . . . . . . . . . . . . . . . . . 303 8.8.1 SPARC (Soonest/Smallest Private-Funded Affordable Robust Compact) . . . . . . . . . . . . . . . . . . . 303 8.8.2 ARC (Affordable Robust Compact) . . . . . . . . . . . . . . 305 8.8.3 Innovations Required for Very High Field Reactor . . . 307 8.8.4 Fragilities of Very High Field Tokamaks . . . . . . . . . . 308 8.9 Compact Spherical Tokamak Fusion Reactors . . . . . . . . . . . . . . 310 8.9.1 ST-135 and STEP (Spherical Tokamak for Energy Production) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310 8.9.2 USA Sustained High-Power Density (SHPD) Tokamak Facility . . . . . . . . . . . . . . . . . . . . . . . . . . . 312
- 24. xx Contents 8.9.3 Robustness of Spherical Tokamak Reactors . . . . . . . . 312 8.9.4 Fragilities of Spherical Tokamak Reactors . . . . . . . . . 313 8.9.5 A Pulsed Reactor Concept Using Coaxial Helicity Injection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313 8.10 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315 Part IV Helical, Linear and Inertial Fusion Reactor Concepts 9 Helical Fusion Reactor Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . 321 9.1 Introduction to the Stellarator and Heliotron Families . . . . . . . . 321 9.1.1 Systems Analysis Strategy . . . . . . . . . . . . . . . . . . . . 321 9.1.2 Magnetic and Coil Configuration . . . . . . . . . . . . . . . . 322 9.1.3 Early History of Stellarator Development . . . . . . . . . . 323 9.1.4 Required Properties of Stellarator Fields . . . . . . . . . . 324 9.1.5 Main Stellarator Configurations and Design Space Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324 9.1.6 MHD Equilibrium and Stability . . . . . . . . . . . . . . . . . 325 9.1.7 Particle and Energy Transport . . . . . . . . . . . . . . . . . . 325 9.1.8 Symmetry and Stellarator Design Space Optimization Criteria . . . . . . . . . . . . . . . . . . . . . . . . 327 9.1.9 Coil Errors and Tolerances . . . . . . . . . . . . . . . . . . . . 328 9.2 Wendelstein7-AS (W7-AS) . . . . . . . . . . . . . . . . . . . . . . . . . . . 329 9.2.1 W7-AS Systems Architecture and Technical Choices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329 9.2.2 W7-AS Stellarator Field Optimization . . . . . . . . . . . . 331 9.2.3 W7-AS Operational Scenarios . . . . . . . . . . . . . . . . . . 332 9.2.4 W7-AS Goals Achieved, Robustness and Fragilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334 9.3 Wendelstein 7-X: A Case Study in Systems Forward Engineering of a Superconducting Helias . . . . . . . . . . . . . . . . . 334 9.3.1 Systems Analysis Strategy for the Superconducting W7-X Helias as a Case Study . . . . . . . . . . . . . . . . . . 334 9.3.2 Systems Approaches to the Design and First Goals of W7-X . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335 9.3.3 Review and Prioritize Goals and Evaluate Variants for W7X . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337 9.3.4 W7-X Revised Proposal, Robustness and Tradeoffs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339 9.3.5 W7-X Final Design for Construction . . . . . . . . . . . . . 340 9.3.6 Procurement, Construction, and Initial Testing of W7-X . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 340 9.3.7 W7-X Operational Scenarios . . . . . . . . . . . . . . . . . . . 341 9.3.8 W7-X Metrics and Performance . . . . . . . . . . . . . . . . 343
- 25. Contents xxi 9.4 Heliotron-E . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343 9.4.1 Heliotron-E Systems Architecture and Technical Choices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343 9.4.2 Heliotron-E Operational Scenarios . . . . . . . . . . . . . . . 344 9.5 Heliotron-J, a Helical Axis Configuration . . . . . . . . . . . . . . . . . 344 9.5.1 Heliotron-J Systems Architecture and Technical Choices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344 9.5.2 Heliotron-J Operational Scenarios . . . . . . . . . . . . . . . 345 9.6 Superconducting Large Helical Device (LHD) . . . . . . . . . . . . . 345 9.6.1 LHD Goals, Systems Architecture and Technical Choices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346 9.6.2 LHD Operation Scenarios . . . . . . . . . . . . . . . . . . . . . 348 9.6.3 LHD Robustness and Fragilities . . . . . . . . . . . . . . . . 349 9.7 Alternative Helical Configuration Systems Architecture and Operational Scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . . 350 9.7.1 TJ-II Heliac . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 350 9.7.2 Model Validation in Stellarators . . . . . . . . . . . . . . . . 352 9.7.3 Uragan-2 M and Uragan 3-M Torsatrons . . . . . . . . . . 352 9.7.4 H-1NF Heliac . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352 9.7.5 HSX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353 9.7.6 WEGA/HIDRA . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353 9.7.7 Scyllac . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353 9.7.8 CTH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354 9.7.9 NCSX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354 9.7.10 Stellarator Robustness and Fragilities of Alternative Architectures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355 9.7.11 Comparison of Stellarators and Tokamaks . . . . . . . . . 355 9.8 Helias Fusion Reactor Concept HELIAS 5-B . . . . . . . . . . . . . . 356 9.8.1 Basic Design Considerations . . . . . . . . . . . . . . . . . . . 356 9.8.2 Updated Reactor Design . . . . . . . . . . . . . . . . . . . . . . 358 9.8.3 A Systems Approach to Optimization . . . . . . . . . . . . 359 9.8.4 Detailed Breeding Blanket Design . . . . . . . . . . . . . . . 359 9.8.5 Balance of Plant . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360 9.8.6 Robustness and Fragilities . . . . . . . . . . . . . . . . . . . . . 360 9.9 Heliotron Fusion Reactor Concept FFHR-d1 . . . . . . . . . . . . . . . 360 9.9.1 Basic Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360 9.9.2 A Systems Approach to Reactor Design and Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361 9.9.3 Use of Joints and High Temperature Superconductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362 9.9.4 Helical Divertor . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362 9.9.5 A Liquid salt Breeding Blanket . . . . . . . . . . . . . . . . . 363 9.9.6 Robustness and Fragilities . . . . . . . . . . . . . . . . . . . . . 363 9.9.7 A Helical Volumetric Neutron Source FFHR-b2 . . . . . 364 9.10 Prospects for Stellarators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364
- 26. xxii Contents 10 Linear Magnetic Traps, Field Reversal and Taylor-State Configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371 10.1 Linear Mirror Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371 10.1.1 Basic Magnetic Mirror Machine . . . . . . . . . . . . . . . . 371 10.1.2 Minimum-B Magnetic Wells . . . . . . . . . . . . . . . . . . . 372 10.1.3 Direct Conversion and Reactor Systems Analysis . . . . 373 10.1.4 Tandem Mirror TMX and TMX-Upgrade . . . . . . . . . . 374 10.1.5 Tandem Mirror PHAEDRUS-B . . . . . . . . . . . . . . . . . 375 10.1.6 Tandem Mirror GAMMA 10 . . . . . . . . . . . . . . . . . . . 375 10.1.7 Tandem Mirror KMAX . . . . . . . . . . . . . . . . . . . . . . . 376 10.2 Mirror Fusion Test Facility (MFTF) and MFTF-B – A Case Study of Systems Forward Engineering . . . . . . . . . . . . . . . . . . 377 10.2.1 Systems Forward Engineering and Architecture in MFTF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377 10.2.2 First Design Improvement of MFTF, One Year Later . . . . . . . . . . . . . . . . . . . . . . . . . . . . 378 10.2.3 Systems Review Process in Early Stages . . . . . . . . . . 379 10.2.4 Alteration of MFTF to Tandem Mirror MFTF-B . . . . . 379 10.2.5 Revised Goals of MFTF-B . . . . . . . . . . . . . . . . . . . . 383 10.2.6 Final Construction Status Report and Project Cancellation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383 10.2.7 Robustness, fragilities and Implications of Cancellation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383 10.3 Gas Traps, Multiple Mirrors, Cusps and Field Reversal . . . . . . . 384 10.3.1 Gas Dynamic Trap (GDT) . . . . . . . . . . . . . . . . . . . . . 384 10.3.2 Multiple Mirror GOL-3 and GOL-NB . . . . . . . . . . . . 385 10.3.3 Cusps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 386 10.3.4 Tri Alpha Energy C-2U and C-2W Field Reversed Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 386 10.4 Linear Fusion Reactors and Systems Design Space . . . . . . . . . . 387 10.4.1 Physics of the Systems Architecture Design Space . . . 387 10.4.2 Design-Space Building-Blocks for Systems Architecture of Linear Machines . . . . . . . . . . . . . . . . 388 10.4.3 Linear Fusion Reactors . . . . . . . . . . . . . . . . . . . . . . . 390 10.4.4 Synthesis of Linear Mirror Design Space . . . . . . . . . . 391 10.5 Toroidal Versions of Linear Mirror Concepts . . . . . . . . . . . . . . 392 10.5.1 ELMO Bumpy Torus (EBT) . . . . . . . . . . . . . . . . . . . 392 10.5.2 Nagoya Bumpy Torus (NBT-1 M) . . . . . . . . . . . . . . . 392 10.5.3 Auto-injection Mirror . . . . . . . . . . . . . . . . . . . . . . . . 392 10.6 Taylor State q < 1 Torus: Spheromak and Reversed Field Pinch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393 10.6.1 Spheromak, Reversed Field Pinch and Taylor State . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393 10.6.2 SSPX Spheromak . . . . . . . . . . . . . . . . . . . . . . . . . . . 394
- 27. Contents xxiii 10.6.3 Reversed Field Experiment RFX-Mod and RFX-Mod2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395 10.6.4 MST and Reactor Studies . . . . . . . . . . . . . . . . . . . . . 395 10.6.5 Review and Prospects for RFP . . . . . . . . . . . . . . . . . 396 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397 11 Inertial Fusion and Magnetic Fast Pulsed Systems . . . . . . . . . . . . . 401 11.1 Systems Analysis Strategy for Laser Inertial Confinement . . . . . 401 11.1.1 Introduction to Inertial Confinement . . . . . . . . . . . . . 401 11.1.2 Progress in Inertial Fusion Driver Concepts . . . . . . . . 402 11.1.3 Challenges for Inertial Fusion Reactor Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404 11.1.4 Systems Analysis Strategy . . . . . . . . . . . . . . . . . . . . 404 11.2 Case Study of Architecture and Forward Engineering of NIF . . . 405 11.2.1 NIF Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405 11.2.2 NIF Systems Approach . . . . . . . . . . . . . . . . . . . . . . . 405 11.2.3 NIF Beamline Systems Architecture and Design Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407 11.2.4 Highly Modular and Robust Construction . . . . . . . . . 409 11.2.5 Operation and Control Systems . . . . . . . . . . . . . . . . . 409 11.2.6 NIF Physics Results . . . . . . . . . . . . . . . . . . . . . . . . . 409 11.2.7 Computer Simulations of Inertial Confinement Laser and Target Interactions . . . . . . . . . . . . . . . . . . . . . . . 411 11.2.8 Near Breakeven Production of 1.3 MJ of Fusion Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . 411 11.2.9 Laser Inertial Fusion Energy (LIFE) Reactor . . . . . . . 412 11.2.10 Overall Fusion Efficiency . . . . . . . . . . . . . . . . . . . . . 412 11.2.11 Laser Mega-Joule (LMJ) and ShenGuang III (SG-III) Large Scale Indirect Drive Lasers . . . . . . . . . . . . . . . 413 11.3 Direct Drive, Fast and Shock Heating and Alternate Laser Technologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413 11.3.1 PETAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413 11.3.2 Direct Drive Laser Fusion with OMEGA . . . . . . . . . . 414 11.3.3 Gekko and LFEX Lasers for Fast Ignition Realization EXperiment (FIREX) . . . . . . . . . . . . . . . . . . . . . . . . 416 11.3.4 The UK Central Laser Facility (CLF) and DiPOLE . . . 418 11.3.5 Petawatt and Exawatt Lasers . . . . . . . . . . . . . . . . . . . 418 11.3.6 Non-thermal p-11 B Fusion from Picosecond Lasers . . . 419 11.4 Design Space and Systems Approaches for Laser Fusion . . . . . . 419 11.4.1 Design Space for a Laser Inertial Confinement Fusion Reactor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419 11.4.2 HiPER Laser Inertial Confinement Fusion Reactor Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423 11.4.3 Detailed Systems Modelling of HiPER . . . . . . . . . . . 425 11.4.4 The Future for Laser Fusion Reactors . . . . . . . . . . . . 426
- 28. xxiv Contents 11.5 Magnetic Fast Pulsed Systems . . . . . . . . . . . . . . . . . . . . . . . . . 427 11.5.1 Dense Plasma Focus . . . . . . . . . . . . . . . . . . . . . . . . . 427 11.5.2 Plasma-Jet-Driven Magneto-Inertial Fusion (PJMIF) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 427 11.5.3 MagLIF Z-pinch Experiments . . . . . . . . . . . . . . . . . . 427 11.5.4 Z-pinch Fusion Reactor . . . . . . . . . . . . . . . . . . . . . . . 429 11.6 Prospects and Systems Robustness of Inertial Fusion Reactors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 429 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 430 Part V Synthesis and Conclusions 12 Synthesis and Conclusions on the Applications of Systems Approaches to Fusion Reactors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435 12.1 Methods Developed and Lessons Learned . . . . . . . . . . . . . . . . . 435 12.2 Overall Systems Analysis Strategy for Comparing Concepts by Systems Architecture . . . . . . . . . . . . . . . . . . . . . . 438 12.2.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 438 12.2.2 Systems Strategy for Comparing Different Fusion Reactor Concepts . . . . . . . . . . . . . . . . . . . . . 439 12.3 Progress in Existing and Planned Machines . . . . . . . . . . . . . . . 439 12.3.1 Systems Level Performance Metrics: Lawson Criterion and Triple Product . . . . . . . . . . . . . 439 12.3.2 The Cost Metric of Fusion Experiments and Reactors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 440 12.3.3 Metrics, Scaling Laws, Systems and Predictive Codes, Innovation and Breakthroughs . . . . . . . . . . . . 442 12.3.4 The Central Role of ITER . . . . . . . . . . . . . . . . . . . . . 443 12.4 Pathways Towards an Operating Fusion Reactor . . . . . . . . . . . . 444 12.4.1 Pathways Towards a Working Fusion Reactor for Each Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . 444 12.4.2 Robustness and Fragilities of Different Concepts . . . . 445 12.4.3 Tokamak Reactors . . . . . . . . . . . . . . . . . . . . . . . . . . 445 12.4.4 Stellarator, Helias and Heliotron . . . . . . . . . . . . . . . . 447 12.4.5 Mirrors, Linear Traps and Field Reversal . . . . . . . . . . 447 12.4.6 Inertial Fusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 449 12.5 Overall Conclusions: Optimization of Fusion Reactors by Systems Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 450 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 450 Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 459
- 29. About the Author Fredrick B. Marcus graduated from MIT in 1969 with high honours for a BS in physics. He won a USA NSF graduate fellowship to attend the University of Oxford in the UK and obtained a DPhil in plasma physics, working at the United Kingdom Atomic Energy Authority (UKAEA) Culham Laboratory. An Oxford postdoc was carried out on the Culham superconducting levitron. At Oak Ridge National Labo- ratory (ORNL), he worked on the design of the EPR tokamak fusion reactor. At General Atomic (GA), he was a physics group leader and principal scientist on Doublet III. At the Swiss École Polytechnique Fédérale de Lausanne (EPFL), he was co-responsible for the physics and engineering design and initial construction of the TCV tokamak. At the European Commission’s fusion project Joint European Torus (JET) at Culham, he was a member of the neutron diagnostics group and was scientific secretary for designing the high-power deuterium-tritium fusion (DTE1) programme. The EURATOM-employed team on JET was then dissolved, and he finished his career as a project officer and expert scientist at the European Commis- sion in Brussels, directing systems biology and bioinformatics projects and publish- ing two related monographs with Springer. His hybrid interests in systems approaches and the recent progress in fusion research led to this book. xxv
- 30. Part I Introductory Systems and Plasma Fundamentals
- 31. Chapter 1 Introduction to Systems Approaches to Nuclear Fusion Abstract Current experiments and supporting theory have developed much of the knowledge needed to design a nuclear fusion reactor. Since reactors are highly complex and interactive, their optimized and successful design relies on the appli- cation of systems approaches and numerical models. This chapter presents basic physics and engineering concepts needed for understanding reactor components. It explains the detailed logical structures of systems approaches, including engineering to examine relationships between elements, architecture to develop the layouts and links between form and function, and emergent properties to evaluate operation. Systems approaches are developed with fusion-specific examples and are summa- rized by checklists. Successive chapters apply this analysis, starting with existing experiments and finally reaching the complexity needed for fusion reactors. 1.1 Fusion Physics and Systems Approaches 1.1.1 Fusion Reactors and Systems 1.1.1.1 Introduction One of the world’s greatest challenges and opportunities is to build reactors that harness the nuclear fusion process which powers the sun, to provide a clean and inexhaustible energy source. The sun uses its own immense size and gravity to compress, confine and heat its hot plasma of ions and electrons to temperatures of millions of degrees. It can fuse protons together by overcoming electrostatic repul- sion and burn for billions of years. Here on earth, there are two main methods of achieving controlled fusion by burning the more reactive hydrogen isotopes of deuterium (d) and tritium (t). One method uses strong magnetic fields to confine the hot ionized plasma away from surrounding vacuum vessel walls to produce nearly steady-state confinement. The other method is to use an ultra-high-power rapidly-pulsed energy source, usually lasers, to compress and heat a hydrogen pellet or plasma to very high density and temperature. Inertial confinement must last long enough for the fuel to burn before the pellet is blown apart. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 F. B. Marcus, Systems Approaches to Nuclear Fusion Reactors, Springer Series in Plasma Science and Technology, https://doi.org/10.1007/978-3-031-17711-8_1 3
- 32. 4 1 Introduction to Systems Approaches to Nuclear Fusion Controlled nuclear fusion research has been advancing steadily over decades. As physics and technical capabilities have increased, so have the complexities of the machines used to produce the plasmas. The results of these experiments have become so impressive that near energy-breakeven fusion conditions (where fusion output equals heating input) have been obtained in both magnetic and inertial confinement experiments. However, the next generations of machines beyond these, leading to a fusion reactor, will become yet more complex and more internally coupled, so that systems approaches will be required to design, construct and operate them. The word system stands for connectivity between elements, often dynamic in nature. Logical structures and sets of procedures have been developed to deal with this complexity. It is the goal of this monograph to describe systems approaches and apply them to machines of increasing complexity, including potential fusion reactors. 1.1.1.2 Experiencing Fusion Research An introduction to fusion research should not neglect to mention the excitement of actually participating in experiments. I was fortunate enough to participate in the high power fusion experiments on the world’s largest operating magnetic confine- ment machine, the Joint European Torus (JET). On 9 November 1991, high energy tritium was injected into a deuterium plasma, resulting in the world’s first controlled release of fusion energy and a power production of 1.7 megawatts [1]. The exper- iments were led by Paul Rebut, the director and inspiration for these experiments. Almost exactly 6 years later, we carried out maximum fusion power experiments. I had been scientific secretary to Alan Gibson for planning the experimental cam- paign. The need to limit vacuum vessel radioactivity meant we were allowed only two attempts at the highest fusion power. The control room was packed with operators, diagnostic physicists, directors, TV reporters and cameramen. The plasma discharge in JET was ready to be started, the klaxon sounded, the machine countdown began. The computers controlled the pre-programmed sequences. Suddenly, the plasma viewing camera inside JET, which was sensitive to fusion-produced neutrons, showed a white haze characteristic of a giant neutron flux. The measurement of the total neutron power was 16 megawatts [2], ten times greater than in our first experiments. The fusion power was nearly equal to the plasma loss power. In February 2022, JET operation was extended to 5 s of fusion power production of over 11 megawatts [3] in nearly steady-state conditions. The highest amount of controlled fusion energy of 59 megajoules was produced, paving the way for successful operation of ITER, a proto-reactor designed to follow on from JET.
- 33. 1.1 Fusion Physics and Systems Approaches 5 1.1.1.3 Types of Systems Approaches The approaches used are systems engineering [4], systems architecture [5] and systems emergent properties [6, 7]. These procedures are best described using relevant examples from fusion research. Therefore, a brief introduction is provided of essential plasma physics and engineering concepts for fusion machines. A system comprises parts or elements that have relationships with each other. In this context, systems thinking [4] is a way of understanding these relationships and connections. Systems engineering [4] involves developing the relationships between elements and the problem solving process. Forward engineering is applied to designing a new machine. Reverse engineering is the process of studying an existing machine. Systems architecture [5] describes the physical layout and relationships between form and function of elements to optimize machine design and its imple- mentation. Systems modelling [6] uses mathematics or computations of the interac- tions of the components of the system. Systems complexity [7] leads to systems emergent properties, particularly performance and metrics, robustness and fragility, which can be optimized or used for mitigation. The analysis of systems involves choices of the correct levels of detail and simplification. In an ideal world with infinite resources, the dictum of Max Planck might be achieved: “The goal is nothing other than the coherence and completeness of the system not only in respect of all details, but also in respect of all physicists of all places, all times, all peoples, and all cultures [8].” This monograph demonstrates that by breaking down a system into component parts which are analysed at an appropriate level, successful machine designs can be efficiently produced without needing infinite resources. 1.1.2 Detailed Monograph Organization The overall strategy of this monograph is to start by developing the formalisms and then analysing many of the relevant tokamak (toroidal magnetic chamber) experi- ments using both systems reverse and forward engineering with the aim of demon- strating ever increasing levels of complexity. Next, systems approaches are shown to be essential for the proto-reactor ITER [9, 10] and the European Union (EU) funded consortium (EUROfusion)-sponsored demonstration fusion reactor (DEMO) [11– 14] using systems codes [15, 16]. An EU DEMO case study examines how the designers used a methodology which is consistent with that developed in this book and the best principles of systems engineering. The monograph then goes on to explore stellarator, linear, reversed field and inertial confinement devices and their possibilities for fusion reactors. A synthesis and comparison of various concepts is developed.
- 34. 6 1 Introduction to Systems Approaches to Nuclear Fusion 1.1.2.1 Part I – Introductory Systems and Plasma Fundamentals This Chap. 1 presents a basic overview of plasma and tokamak physics [17–25] followed by the development of systems formalisms applied to experiments, with applications summarized in checklists. Chapter 2 creates the design space for tokamaks and different views of interacting system elements. Medium plasma current experiments are examined to classify machine elements and plasma operational scenarios. 1.1.2.2 Part II – High-Current Tokamaks Chapter 3 examines Doublet III [26] and its upgrade DIII-D [27] with its flexible shaping system to serve as a case study of systems reverse engineering. Other machines reviewed are Asdex-U, Alcator C-Mod, MAST-U and NSTX-U [28–31]. Chapter 4 discusses TCV [32] as a case study for design and operation, chosen for its maximum flexibility plasma shaping system [33]. Chapter 5 studies JET [34] in depth, including forward engineering of the first high power d-t (deuterium–tritium) fusion experiments [2]. Further d-t experiments were conducted under EUROfusion management [35] and obtained a record fusion energy production. Experiments using d-t on TFTR [36] are summarized. Chapter 6 makes a case study of the superconducting and long-pulse Tore Supra and WEST and reviews EAST, KSTAR, SST-1, JT-60U and JT-60SA [37–43]. 1.1.2.3 Part III – Prototype Tokamak Fusion Reactors Chapter 7 analyses the role of research, innovation and prototyping in systems integration of the design and construction of ITER [20] with the aim of achieving sustained fusion power. Chapter 8 considers concepts for tokamak fusion reactors, highlighting the EU DEMO [44] as a case study in the advantages of systems engineering for designing fusion reactors. This is followed by analysis of other fusion reactor concepts and designs, some based on ITER, others exploring compact machines with high mag- netic field and/or low aspect ratio. 1.1.2.4 Part IV – Helical, Linear and Inertial Fusion Reactor Concepts Using the systems formalism already developed for tokamaks, Chap. 9 explores in detail the stellarator, helias, heliotron/torsatron and other concepts, which are con- sidered in terms of robustness and fragilities. A case study is made of the W7-X [45]
- 35. helias. Reactor concepts are considered based on W7-X and on the LHD torsatron/ heliotron [46]. 1.1 Fusion Physics and Systems Approaches 7 Chapter 10 analyses linear magnetic traps and their toroidal versions and makes a forward engineering case study of MFTF-B [47]. Geometries include simple and tandem mirrors, field reversed configurations and reversed field pinches [48]. Poten- tial reactor developments are examined. Chapter 11 investigates inertial fusion concepts such as direct-drive and indirect- drive laser implosion, laser shock and fast ignition and linear z-pinch compression. The laser powered National Ignition Facility (NIF) [49] which has had the very impressive recent result of energy breakeven, is presented as a case study in forward engineering. Reactor concepts are examined including HiPER [50]. 1.1.2.5 Part V – Synthesis and Conclusions Chapter 12 provides a synthesis of the conclusions presented in this monograph relating to the advantages of using systems approaches. Comparisons are made of various concepts. 1.1.3 A Simplified Description of Plasmas The following basic description of plasmas [21, 22, 24] provides background for reading this monograph and clarifies the examples used when discussing systems definitions. Readers who are familiar with plasmas and tokamaks can jump to Sect. 1.2. • Plasma: A plasma is an electrically conducting collection of ions and electrons (ionized atoms) that provide charge (quasi-) neutrality. The ions in fusion reactors are mostly deuterium and tritium. • Density and temperature: A plasma is locally characterized by density per cubic metre (m3 ) for electrons and hydrogen isotope ions as ne and ni, impurity ions with charge Z as nz. A collection of ions and electrons interact and collide with each other via the Coulomb force, establishing a Maxwellian distribution of energies characterized by a temperature T, where 1 keV (kilo electron volt) is equivalent to 11.6 million degrees Kelvin, since they are related by the Boltzmann constant. A Maxwellian velocity distribution is proportional to E times exp(-E/T), where the particle energy is E = mv2 /2. Electron and ion temperatures are defined as Te and Ti. A singly charged particle has an energy of 1 keV when accelerated through a potential of 1 kV (kilovolt). The most probable particle energy in kV equals the temperature in keV in a Maxwellian distribution. Fast electrons or ions created or injected externally or by resonant electromagnetic fields, will deposit energy and heat via Coulomb collisions.
- 36. 8 1 Introduction to Systems Approaches to Nuclear Fusion • Current and ohmic heating: The electrons flowing in a plasma and creating a current encounter a resistivity η = 2.8 × 10-8 / T1.5 e,keV ohm-meters. In a plasma with radially varying electron temperature, plasma current will redistribute until there is constant applied voltage everywhere. At constant applied voltage, the resistivity drops as the plasma heats above 1 keV, so it is difficult to reach fusion conditions with ohmic heating alone. • Plasma creation and start-up: The plasma is usually created by accelerating electrons with electric fields or microwaves in a mostly hydrogen isotope gas. These electrons create a cascade which results in full ionization. During ioniza- tion, other processes are important, such as plasma resistivity, atomic and molec- ular physics, charge exchange, ionization, and radiation from electron bremsstrahlung (slowing-down radiation). • Plasma frequency and waves: Approximate charge neutrality of the plasma is maintained by electric fields that appear when separation begins to occur. These fields cause oscillations at the electron plasma frequency (in radians/sec) ω2 pe = ne q2 e= me ε0 ð Þ, where the quantities are electron density (ne), charge (qe) and mass (me) plus the permittivity of space (ε0) in SI units. At 1020 m-3 , the plasma frequency (fpe = 2πωpe) is 90 GHz (gigahertz). Plasmas can oscillate and carry waves. Microwaves propagating through a plasma are cut-off below this frequency. When ions are better confined than electrons, a confining electrostatic potential in kV is created of the order of a few Te/e. • Magnetic field: When a plasma is immersed in a magnetic field (B), each ion and electron has velocity components parallel and perpendicular to the magnetic field. Ions and electrons rotate perpendicularly to the magnetic field in Tesla (T) at a cyclotron circular frequency of Ωce, ci = qi, e B / me, i . At a field of 1 T, the electron cyclotron frequency fce is 28 GHz. The perpendicular radius (ρ) of the orbit of the particle with velocity (v) around the field line is given by ρe,i = vei perp / Ωce,ci . For a 15 keV (kiloelectrron volt) ion in a field of 1 T, ρi is 0.025 m. • Instabilities: An instability can result when a plasma can move from a higher to a lower energy state. Instabilities can be macroscopic at the plasma fluid level description, or microscopic at the particle velocity distribution level, and can propagate and grow via waves in the plasma. Sources of instability can be gradients in density and temperature, the plasma, its current and high energy particles. Instabilities can result in plasma motion that destroys plasma magnetic confinement or leads to enhanced energy losses either inside or at the plasma edge. Much of fusion research is devoted to creating machine configurations that suppress instabilities. • Nuclear fusion: Fusion reactions occur when fast ions collide with enough energy to tunnel through the repelling Coulomb barrier. The most energetically favourable fusion reaction is d + t → n (14.1 MeV) + He4 (3.5 MeV). The reaction rate per unit volume is given by the product of the cross section (σ) and ion relative velocity (v) averaged over the velocity distribution as hσvi. The peak value for deuterium and tritium is 0.9x10-21 m3 s-1 at about 60 keV temperature,
- 37. h i 1.1 Fusion Physics and Systems Approaches 9 but is nearly half of the maximum at 20 keV. The reaction rate per unit volume is ndnt σv . The He4 (α-particle) ion deposits heat in the plasma. • Radioactivity: Fusion product alpha particles and neutrons deposit their energy in structures surrounding the plasma and generate energy as heat, which could be processed into electricity. The neutrons also induce radioactivity into the struc- ture, and can be used to breed tritium. Tritium itself is radioactive. • Fusion gain Q: An important metric is Q, the energy gain of a plasma, defined by the total fusion power (or energy) produced by the plasma, divided by the heating power (or energy) applied to it. Therefore, Q = 1 is referred to as the breakeven condition. The ignition condition Q = infinity(1) occurs when no external heating is required, i.e. when contained alpha particles heat the plasma and maintain a fusion burn. 1.1.4 Tokamak Magnetic Field Coils and Geometry In this chapter, examples of systems concepts are applied to the nuclear fusion concept called the tokamak, an acronym for (toroidal chamber magnetized). In early 1969, Lev Artsimovich was in charge of the T-3 tokamak, which had reported record results [51]. He presented four lectures at the Massachusetts Institute of Technology (MIT) in April 1969 (which I attended). MIT soon proposed its own high magnetic field version of a tokamak based on Bitter magnet technology [52]. Many other tokamaks were constructed around this period [53]. Tokamaks are currently the most investigated fusion concept, shown schematically in Fig. 1.1. The main elements of a tokamak are: • Vacuum chamber: The torus-shaped vacuum chamber is surrounded by poloidally wrapped coils which produce a toroidal magnetic field pointed along the axis of the inside of the vacuum vessel, so that plasma particles flow along the directions of the field inside the torus and are contained. • Toroidal magnetic field and its gradient: The toroidal field is stronger than the poloidal field and provides particle confinement. However, because of the toroi- dal geometry, the toroidal magnetic field is stronger nearer the inner part of the torus than the outer part, decreasing with the major radius (R) as 1/R. This magnetic gradient causes electrons and ions to drift upwards and downwards producing an electric field,. Without confining fields, the particles would escape and hit the walls of the vessel. • Plasma current: In order to stop particles drifting out, an electrical current is induced in the plasma, which creates a magnetic field circling around the plasma current, the so-called poloidal field. The individual plasma particles follow the combined toroidal and poloidal field, and spiral around the plasma. Since parti- cles are then drifting upwards half the time and downwards half the time, the drift is cancelled and the particles are confined.
- 38. Poloidal magnetic field Plasma electric current (secondary transformer circuit) Toroidal magnetic field Toroidal field coils Inner poloidal field coils (primary transformer circuit) Outer poloidal field coils (for plasma positioning and shaping) Resulting helical magnetic field 10 1 Introduction to Systems Approaches to Nuclear Fusion Fig. 1.1 Schematic of a tokamak chamber and magnetic profile. (From [54], Fig. 1) • Poloidal field coils: These are fields that are symmetric around the torus and generated by coils that are wound in the toroidal direction. They can be wired to produce special multipole fields (see below) or they can produce a superposition of these fields by individual coil current control to provide plasma positioning and shaping and confinement. • Transformer: The plasma current itself is generated by transformer action either by a coil with changing current or a coil plus an iron core going through the hole in the vacuum vessel torus. A magnetic flux change in this primary winding creates a one-turn voltage that acts on the plasma to ionize the gas and create a flowing current which ohmically heats the plasma by collision with the acceler- ated electrons. • Vertical field: As the plasma current and pressure from ohmic and external heating increase, the toroidal plasma expands radially outwards. A vertical magnetic field perpendicular to the plasma current, generated by external coils, produces a radially inward force which holds the plasma in place. • Shaping field: Although the simplest plasma shape is a circular torus, it is often desirable to further shape the plasma with additional coils in the toroidal direction to generate shaping poloidal magnetic fields. • Horizontal field: Vertically elongated plasmas can be up-down unstable. A horizontal field can raise or lower the plasma and be used with feedback for positional stability. • Plasma exhaust: At the same time as the plasma is being heated, particles and energy are also escaping in the form of electromagnetic radiation, energetic ions,
- 39. 1.1 Fusion Physics and Systems Approaches 11 electrons and fusion products. Some power is going either to a plasma limiter structure and the walls, or to a magnetic configuration that removes plasma energy (divertor). The plasma escape needs to be controlled to avoid damaging surrounding structures. 1.1.5 Plasma Current and MHD Fluid Equilibrium There are essential physics elements [21] that are central to tokamak design. Current in the ionized plasma flows along the toroidal magnetic field Btor, which creates a poloidal magnetic field Bpol (see Fig. 1.1) that is perpendicular to the plasma current. Closed surfaces of constant poloidal magnetic flux are formed on which there is a force equilibrium between magnetic fields and the plasma pressure. Magnetic field lines lie on a flux surface, so particles following field lines will stay on that surface. The shape of these nested flux surfaces can be calculated by using Magneto-Hydro- Dynamic (MHD) fluid equations developed by Grad and Shafranov [21], which describe the force balance in equilibrium conditions. The so called safety factor (q) is defined as the number of times a magnetic field line goes around toroidally for each time it goes around poloidally on a flux surface, and it is a function of minor radius. q may be non-integral and is calculated in a circular plasma with major radius R and minor radius r by the formula: q = rBtor RBpol ð1:1Þ It is valid in the large aspect ratio A = R/r regime. In a tokamak, the lowest value of q at the plasma edge r = a is kept above 2 and often 3, otherwise resonant instabilities may occur. The current in MA in a plasma with toroidal field Btor and vertical elongation κ is approximately given by: IMA = 5aκBtor R a q ð1:2Þ The number of volt-seconds of magnetic flux required from the primary transformer and ohmic heating coil is given by LIplasma, where L is the plasma self inductance. Additional voltage used to sustain plasma resistance is calculated as resistivity times plasma circumference divided by cross section. As an example, the self inductance of an unshielded current loop of major radius R and cross section a, for uniform current, is given by.
- 40. 12 1 Introduction to Systems Approaches to Nuclear Fusion Lcircular = μ0 R In 8R r - 2 ð1:3Þ For an aspect ratio of 3, L becomes 1.5 microhenries times R. Hence to produce a plasma current of 1 MA at R = 0.8 m requires about 1.2 volt-seconds for the magnetic energy of an unshielded plasma, and less if nearby shaping coils reduce the effective inductance. The resistive losses in forming the plasma need to be added into the volt-second flux requirement from the ohmic heating transformer coil. 1.1.6 Plasma Pressure and Confinement Time Plasma stability requirements limit the ratio beta (β) of the plasma pressure (nT) integrated over particle species and space to the magnetic field pressure, β = nT= Btor 2 2μ0 ð1:4Þ The Troyon Limit [21] in a tokamak on β was determined from computation and experiment to be: β % ð Þlimit 2:8 x IMA=aBtor ð1:5Þ The Lawson criteria is the value of plasma density (n) times energy confinement (τ) at which a fusion reactor reaches energy breakeven, and is approximately equal to an nτ product of 1020 m-3 s-1 for deuterium and tritium at 10 or more keV temperature. Combining the above formulas (with MKS units), the Lawson criteria for plasma self-ignition becomes τ Btor2 κ R a q 17 ð1:6Þ Using suggested reactor parameters of Btor = 5 Tesla, elongation κ = 2, Aspect ratio R/a = 3, and q = 2, an energy confinement time of about 2 seconds is required, which is the confinement time estimated for the so-called L-mode confinement in ITER. With divertor plasmas, enhanced confinement modes become possible with even higher confinement times. Wesson [21] notes that for a parabolic radial distribution of deuterium and tritium total ion density with peak density values ni(0), ion temperature Ti(0) and global energy confinement time τE, the triple product for plasma ignition by self-heating from fusion product alpha particles is:
- 41. 1.1 Fusion Physics and Systems Approaches 13 ni 0 ð ÞTi 0 ð ÞτE 5 × 1021 m- 3 keVs ð1:7Þ A group of scientists developed a scaling law of energy confinement time for the ITER project (see Chap. 7), the ITER ELMy H-mode confinement time [55, 56]. It is valid operating in a high confinement mode (H-mode) when the plasma has Edge Localized Mode (ELM) instabilities and is given by: τH98ðy,2Þ = 0:144I0:93 B0:15 n0:41 20 P- 0:69 R1:97 κ0:78 a ε0:58 M0:19 ð1:8Þ Various tokamak designs have taken different approaches to maximizing the figures of merit, either by emphasizing an increase in the toroidal field or an increase in elongation, or a reduction in the aspect ratio as in spherical tokamak design. JET (see Chap. 5) tried to optimize all three of these, with R/a = 2.4, Btor = 3.5 tesla and elongation κ = 1.7. Ignition in JET would have required a confinement time of about 4 seconds, whereas only about 1 second was reached. Even this lower confinement time allowed the approach to Q = 1, where the plasma loss power from auxiliary heating equals the plasma loss power. 1.1.7 Individual Particle Effects in Toroidal Systems In fusion reactors with spatially dependent magnetic fields, the mirror effect occurs when a particle follows a magnetic field line. The gyroradius-averaged motion of a particle is constrained by adiabatic invariants, meaning constants of motion where external fields change slowly. During a time much shorter than the time to signifi- cantly collide with other particles, the total particle energy E is constant, and the magnetic moment involving the energy perpendicular to the field M = Eperp/B is an adiabatic constant of the motion. As the particle moves into a higher magnetic field, the perpendicular energy increases and conservation means the parallel energy and velocity decreases. If the field variation is large enough, the parallel energy becomes zero, and the particle is reflected (mirrored) back in the opposite direction. The mirror ratio is defined as the ratio between the maximum and minimum magnetic field along this trajectory. In linear mirror machines, fast particles bounce back and forth between two intense magnetic fields. In toroidal tokamaks and stellarators, particles are trapped between the inside and outside of the spatially varying toroidal field. Since particles drift vertically in opposite directions on one bounce and on the return bounce, the shape of their orbits is that of a banana, hence the term banana orbits, which can have a significant effect on plasma transport. These orbits and the rate of collision with other particles determine the rate of transport labelled as neoclassical in a torus, which is enhanced compared to classical losses of non-trapped particles. Banana orbits can contribute to a current referred to as bootstrap, which is generated by plasma pressure radial gradients.
- 42. 14 1 Introduction to Systems Approaches to Nuclear Fusion 1.1.8 Auxiliary Heating and Current Drive Auxiliary heating methods can be chosen to preferentially heat ions or electrons, and also to impart momentum and drive spin and plasma current. When one species is heated, it can transfer energy to the other species by Coulomb interactions, which are stronger at high density and weaker at high electron temperature. • Neutral beam injection (NBI): An external source is used to inject ions into a high voltage static electric field which accelerates them to high energy. They are then neutralized by charge exchange with a cold gas and travel into the vacuum vessel, where they are then ionized by the plasma, then trapped by the magnetic field. These injected ions slow down and heat the plasma. They can contribute to fusion via beam-plasma and beam-beam collisions. • Electron cyclotron resonance heating (ECRH): A microwave source such as a high power gyrotron injects microwaves into the plasma where they are resonant with the electron cyclotron frequency at its first or higher harmonics. These waves can heat the electrons and also induce current drive. • Lower hybrid current drive (LHCD): Lower hybrid current drive is produced by injecting microwaves via waveguides at a frequency intermediate between the electron and ion cyclotron frequencies. It has proved to be relatively efficient for current drive by interaction with electrons. • Ion cyclotron resonance heating (ICRH): Antennas inside the vacuum vessel are used to launch radio frequency waves resonant with the cyclotron frequency of ions. ICRH is most efficient when heating minority helium or impurity species of a few percent which in turn heat the main plasma. • Alfven Wave Heating (AWH): Alfven waves are created at low radio frequency by antennas inside the vacuum vessel. Heating seems to be accompanied by continuous plasma density rise. • Alpha particle heating (APH): When d-t fusion occurs, the alpha particles are trapped by the magnetic field, if strong enough. The plasma is heated as the alphas slow down, with heat transfer typically to electrons. 1.1.9 Elements of a Tokamak Fusion Reactor Tokamak reactor designs were initiated during the 1970’s, including the Experimen- tal Power Reactor (EPR) [57], based upon previous general reactor considerations [58]. This design was superseded, but it highlighted several features illustrating the complexity of a fusion reactor compared to existing tokamaks without neutron production. In a reactor, plasma self-heating and ignition require confinement of charged alpha particles from d-t fusion, while neutrons escape the plasma into the surrounding structure. A plasma current of at least 1 MA is required for some alpha confinement and 2.5 MA is a minimum for confining most alpha particles. Shielding was essential to protect components against sustained 14 MeV neutrons. A breeding
- 43. blanket with lithium-6 and lithium-7 was needed to breed tritium fuel from their reactions with neutrons. 1.1 Fusion Physics and Systems Approaches 15 Fig. 1.2 The ARIES-AT fusion power core. (From [62], Fig. 1) The EPR parameters were derived from systems scoping studies [59]. The nuclear blanket and shield were sufficiently thick so as to protect the superconducting coils. The result was a tokamak with minor radius of 2.25 m, major radius of 6.75 m, magnetic field on axis of 4.8 T and plasma current of 7.2 MA. The poloidal magnetics system [60] was designed both to reduce the total volt-second energy requirements and to reduce the field time-variation at the toroidal field coils. Reactor studies in the USA continued as a community effort that produced the ARIES series, starting with ARIES-I, ARIES-II and ARIES-III [61]. A design shown in Fig. 1.2 is for the ARIES-AT Advanced Tokamak fusion reactor [62]. This particular 1000-MWe ARIES-AT design had a major radius of 5.2 m, minor radius of 1.3 m, toroidal β of 9.2% (βN = 5.4) and on-axis toroidal field 5.6 T. The plasma current was 13 MA and the current-drive power was 35 MW. These concepts evolved and demonstration reactors are being designed [63].
- 44. 16 1 Introduction to Systems Approaches to Nuclear Fusion 1.2 Systems Engineering and Architecture Principles 1.2.1 Elements, Relationships and Systems Thinking Let us begin by looking at the essentials of systems engineering [4] and how they apply to fusion experiments and reactors. The word system stands for connectivity and in this context refers to a fusion experiment or reactor installation. Systems consist of elements, which have properties and functions, and can themselves be seen as systems, with their own subsystems. Such an element could be an ionized plasma with properties such as density and temperature, and functions such as producing fusion products such as neutrons and alpha particles. Another element might be the poloidal field shaping coils in a tokamak. Elements are linked to each other through relations. For example, poloidal field shaping coils influence the plasma shape, but a moving or disrupting plasma can induce currents in the shaping coils. Relations can be in one direction or in both directions and can be complex, involving several types of interactions. Elements and relations form a construct which demonstrates an order, forming the structure of a system. Examples of structural types include hierarchical, network and structures with feedback. Subsystems are found by taking a system and determining its constitutive ele- ments at a lower level and then connecting them by means of relations. Two plasma subsystems might be the electron temperature radial profile (determining plasma resistivity), and the plasma current radial profile. Their steady-state relationship is determined by Ohm’s law, where the voltage (V) is the product of current (I) and resistance (R) as V=IR when there is a constant voltage across the plasma. Systems have emergent properties [7] of robustness and fragility, for example in the context of dynamic systems biology [64]. These properties and metrics allow the designer to evaluate the stability and probable success of systems. These elements and their relations are discussed in detail in Chap. 2 in the context of the design space available for nuclear fusion experiments and reactors. 1.2.2 Hierarchy A system divided into multiple levels results in a systems hierarchy. Under the system, there is a level of subsystems of order 1 and below are subsystems of order 2, etc., and the lowest level is the element level, with relations acting as connectors. A typical hierarchy might involve the following descending levels: tokamak; power supplies; poloidal coil power supplies and transformer; coil #5 power supply; solid state thyristor rectifiers. The lowest element would require a controlling systems relationship with the power supplies. The elements can be seen as black boxes, so only the function (the purpose) or desired inputs and outputs (results) are of significance. For a thyristor, we do not
- 45. need to know the detailed semiconductor physics, only that a control signal will open a gate and produce a voltage and current in a power supply and coil. 1.2 Systems Engineering and Architecture Principles 17 A white box, for example a plasma in a tokamak, is when the exact connection between output and input is of great significance, such as whether heating a fusion plasma produces enough fusion self-heating for near-ignition and enough neutrons to breed tritium and to heat coolant to power an electrical generator. A grey box is roughly or partially structured. As system design is developed, there is a transition from black to grey to white boxes. 1.2.3 Aspects Every system consisting of elements and relations can be described from different viewpoints, called aspects. For example, in its interaction with other parts of a fusion reactor, a plasma can be regarded from various aspects; a source of neutrons for tritium breeding and electricity generation; energy flow; a component in a plasma- coil electromagnetic system; a danger to the vacuum vessel in case of disruption. Different views of a system are possible, depending on the level of complexity required to study a problem. These different views include a simple system, mas- sively interconnected complicated system, dynamic complicated system, complex system. One of the goals of systems engineering is to look for the simplest view and structure that allows analysis. The choice of level of complexity is central to whether useful insights can be found. Another possibility is the input/output view, where the relation between input and output is governed by a transfer function, for example a function that related the neutron production from a plasma to the heating power applied. 1.2.4 Models An essential principle of systems thinking involves systems models and model- based illustrations. Models are abstractions of reality, hence they reveal only partial aspects, and thus the question of relevance depends on choosing the correct level of complexity. Simple graphic and tabular models can demonstrate relationships and promote problem awareness, and provide the basis for development of quantitative models. Aids for illustrating relations or structures include graphs and matrices. In the graphs, elements are shown as rectangles which are connected by directional or multi-directional arrows representing relationships. In a matrix, the elements are listed in rows and columns, and the intersections can be text or quantitative numbers representing the strength of the relation. The two row-column and column-row intersections on opposite sides of the diagonal can represent relations in two directions. In the simplified Table 1.1 concerning a tokamak, a sample function matrix in the electromagnetic view is shown.
- 46. Plasma Vacuum vessel Poloidal coils Plasma Vacuum Vessel Poloidal Coils 18 1 Introduction to Systems Approaches to Nuclear Fusion Table 1.1 Sample function matrix for tokamak poloidal field system- electromagnetic view Functional relations Plasma Plasma is internally self connected by inductance, diffusion, instability. Vacuum vessel stabilizes instabilities in plasma. Poloidal coils induce plasma current and shapes and stabilize plasma. Vacuum vessel Plasma current changes and disruptions induce currents in vessel. Vacuum vessel currents redis- tribute within the shape and thickness. Poloidal coils create currents in vacuum vessel which resis- tively decay. Poloidal coils Plasma disruption induces currents in coils. Vacuum vessel currents induced by disruption will decay and induce currents in poloidal coils. Poloidal coils can induce currents in each other. Table 1.2 Sample form matrix for tokamak poloidal field system – Shape View Form relations Plasma X Vacuum vessel toroidally sur- rounds plasma. Poloidal coils are outside vacuum vessel, but near to plasma. Vacuum vessel X Poloidal coils are outside vacuum vessel and inside toroidal field coils. Poloidal coils X Matrix numerical algorithms could optimize the relationships, for example by using mutual inductances between coils and plasma. All elements have both form (what it is) and function (what it does). The architecture also has the goal of determining the functional and spatial relationship of each element, see Table 1.2. An example of the use of function and form studies might be to compare two fusion systems, such as tokamak and laser-driven inertial confinement reactors. In the relationship connecting external heating systems with the fusion plasma, both would have a large number of interactions concerning the effect of heating system on the plasma. Inversely, there is an influence of the plasma on a radio frequency heating system due to neutrons hitting the antenna. A laser system would have fewer inverse interactions, since most of the laser can be relatively well isolated from the neutron source. Thus a matrix reflecting the neutron damage aspect of a fusion system would favour a laser system. The structure-oriented view of a system under different aspects allows observation of the system through different filters. Using system hierarchical thinking, it is possible to analyse a problem, such as the design of a new machine, by a simple model involving a scoping study incorporating the basic elements of a system. For a tokamak, the elements include: toroidal field, plasma current, aspect ratio, elongation, divertor configuration, and auxiliary heating type and power. Then other levels with subsystems can be added until the appro- priate level of detail and analysis is achieved.
- 47. 1.3 Systems Engineering Process Model 19 Many models for analysing nuclear fusion plasmas and the surrounding machin- ery have been developed and will be discussed in Chap. 2. There are also dedicated systems engineering and architecture languages such as SysML described in OMG Systems Modelling Language [65] and Object Process Methodology (OPM) [66]. Examples of plasma models include the tokamak simulation code (TCS) [67] and the analysis code TRANSP [68]. 1.2.5 Agility An agile system should be capable of being variable and modified, which can be an important concern in a rapidly changing environment. Agile fusion experiments have been able to incorporate new features which greatly improve their performance. Examples include the addition of auxiliary heating of the plasma, or the installation of divertor coils that improve plasma performance and impurity and gas control. Some machines are designed to be highly flexible from the beginning; others have enough flexibility to allow important upgrades. Plasma physics concepts and new technologies are being developed that could result in machine upgrades allowing significant improvements to the performance of ITER. 1.3 Systems Engineering Process Model Systems engineering [4] involves systems thinking about the relationship between elements and the problem solving process shown in Fig. 1.3. There are four basic systems principles [4] for solving a problem: • Proceed from the general to the detailed. • Think in variants: consider alternative solutions to each problem. • Use a phased approach in developing ideas. • Develop a problem solving cycle as a general work logic. The first stage of a project is the planning of the general objectives of the project and of the general means to carry out the objectives. For a nuclear fusion experiment, it is necessary to look at all of the previous knowledge and experience of related experiments, and then assess what needs to be done to achieve the project objectives. Important inputs are the capabilities of the group planning the experiment and the amount of financing available to carry it out. Proceeding from the general to the detailed involves using the hierarchical method already discussed. It starts with a simple model using black boxes, and evolves to a detailed treatment of more complex white boxes. General objectives and a general solution framework need to be established. Concepts at higher levels serve as guidance for the detailed design. In the context of nuclear fusion experiments, the basic goals need to be decided, the approximate budget applied as a constraint and
- 48. the overall machine parameters initially decided. Then basic choices need to be made such as superconducting or resistive coils, with or without divertor, auxiliary heating, etc. 20 1 Introduction to Systems Approaches to Nuclear Fusion Fig. 1.3 Systems Engineering (SE) concepts. (From [4], Fig. 1) Variant creation involves studying several solutions to the same problem. For example, if the goal is creating a high current tokamak, variants might involve high or low toroidal field, plasma aspect ratio, degree of elongation, type of divertor. Extreme variants could be scoped for feasibility. During the detailed design of the optimum choice, small variations can be explored for optimization. Variants can involve different paradigms, even an entirely different fusion concept. Dividing the development of a project into phases that proceed from one to the next in a logical and timely fashion coincides with moving from the general to the specific. The number of phases and approaches depend on the complexity of the project. Phase I might involve a general specification of machine design suitable for preliminary external evaluation for funding, and Phase II might involve a more detailed design suitable for actual application for funding approval. Phase III might be the production of highly specific details needed for manufacturing. The problem-solving cycle requires a chain of logic for each problem, which involves setting objectives and goals, searching for a solution, and selecting the most appropriate approach. This can include prototyping, where a low cost test of a component or concept may be made to determine its feasibility.
- 49. 1.3 Systems Engineering Process Model 21 1.3.1 Problem Solving Process, Systems Architecture and Design The systems engineering process model is implemented using the tools of systems architecture and concept development. Systems architecture [5] goes beyond struc- ture and involves the allocation of function to the elements of a structure. Systems design involves systems architecture and concept development. Systems architecture is defined as: • the allocation of function to elements; • the arrangement of these elements in a structure; • the definition of interfaces between these elements and the system environment; and • creation of a defined value. An example for a tokamak involves the architecture of the plasma, vacuum vessel, toroidal field coils, and poloidal field shaping coils. Two different architectures could involve having the poloidal shaping coils either inside or outside the toroidal field coils. In the two cases, the functions assigned to each element would differ. The plasma function would be to demonstrate the value of a complex shape while giving the shaping coils the function of producing that configuration, made easier if inside the toroidal field coils. The vacuum vessel would have the obvious function of producing a vacuum for the plasma, but its conducting walls would also have the function of stabilizing the plasma by image currents induced by plasma motion. Each subsystem has its own architecture, but is part of the overall tokamak system. The definition of interfaces between the systems involves different aspects, includ- ing mechanical structure, cooling, electromagnetics, etc. The definition of good architecture [5] is adapted here for fusion reactors: • The experiment’s architecture should be able to make multiple and significant contributions towards a fusion reactor. • It should fulfil the project objectives and goals. • It ensures compliance with regulations, especially health and safety. • It can be operated and serviced efficiently and is sustainable. • It is scalable and adaptable with minimal effort. • Further machines and experiments can be developed from it. • It is elegant. 1.3.2 Concept Development Concept design and development involves producing a selected architectural design in a more concrete and detailed fashion. The process includes searching for objec- tives and possible solutions, then making a selection of the best approach.
- 50. 22 1 Introduction to Systems Approaches to Nuclear Fusion A design space of existing experiments provides a basis for fixing goals and for deciding on the best options for a systems architecture to take forward. A design space is developed for tokamaks in Chap. 2, where lessons learned from existing tokamaks are summarized both for construction choices and for demonstrated operational scenarios obtained in particular systems architectures. The tokamak design space is relevant to other fusion concepts, which have their own design spaces developed in the relevant chapters. A key element of concept design is working with models. These models advance from general concepts to specific designs, with numerical constructs to verify and quantify the concepts. Plasma physics involves developing a mathematical frame- work and numerical solutions for plasma behaviour and its interaction with external systems, including the best theoretical descriptions. Fusion reactor design addition- ally requires very extensive neutronics and other calculations relevant to a fusion product environment. Three additional principles of good design are: • minimizing constraints by preferring solutions that allow the most room for further developments; • minimizing interfaces so that each subsystem can have the maximum robustness; • using modular structures so that components could be used in other situations. In this context, a tokamak design would include the option of reusing the toroidal field coils and power supplies and motor generator in a machine upgrade or replacement. 1.3.3 Constraints Any design is subject to constraints, and choices between variants can be made by applying metrics. Primary among the constraints are logical constraints, which have the character that they involve choices that cannot or should not be done, or that obviously will not work as conceived. There are also constraints of reasonableness, where you probably would not want to exercise a certain option. Externally imposed constraints include a maximum budget for spending on the project, time and manpower limitations, and the level of complexity that can be handled. 1.3.4 Metrics and Risk Metrics allow the quantification of aspects of the design and are an excellent way of choosing between design variants and allowing the evaluation of the success of a system once built and operating. Metrics can include projected performance of the various systems, cost, time to completion, technological difficulty, amount of new
- 51. innovation required, risk and performance. The metrics of actual performance are an emergent property of the entire system (see below). 1.4 Systems Emergent Properties, Robustness and Dynamics 23 Risks can be evaluated at the individual element level or at the project level. A risk on a component might depend on whether or not the component will fail during the lifetime of a project, and is related to the difficulty of repair or maintenance. Risk can also involve failure of the entire project. The risk associated with each element of a system can be quantified, and the overall risk to the system calculated as the product of the individual risks. A typical quantification of a multi-element system in an important final product would be risk level probabilities: high (0.90); medium (0.95), low (0.98), very low (0.99). The project management can then decide what level of risk is acceptable. There will often be trade-offs between total risk and total cost, for example with machining tolerances. 1.4 Systems Emergent Properties, Robustness and Dynamics 1.4.1 Emergent Properties of Systems Emergent properties of systems such as robustness are revealed by analysis, com- putational modelling and experience. Once the interactions are known, they can be integrated into a dynamic simulation. During the design of a fusion machine, the operation phase can be simulated and optimized. During the operations, analysis and simulation can be incorporated for real time control. Emergent properties of systems need to be considered during these optimizations. In a dynamic system, robustness refers to the ability to tolerate perturbations. Robustness includes the ability of a system to resist change without damaging the main system functions. Perturbations can be small at an anticipated level, or large enough to represent a danger to the system. Disruptions in tokamaks are a prime example. Robustness therefore has two dimensions, which are resistance and avoidance. As in the analysis of biological organisms [64], the properties for developing a robust system [7, Chap. 17] in fusion reactors must be optimized, including: • systems control • fault-tolerance • modularity • decoupling
- 52. 24 1 Introduction to Systems Approaches to Nuclear Fusion 1.4.2 Mechanisms for Robustness Systems control involves negative or positive feedback on the desired control variable, which can make a system stable around the desired equilibrium. For example, if a motion is detected in the plasma by a magnetic field sensor, a vertical magnetic field can be strengthened to reduce the displacement to zero via negative feedback. There can also be switches to drive systems from one stable state to another, for example to transform a molecular gas into a plasma. Fault tolerant mechanisms or control systems increase resistance to component failure and external changes, often by having alternate components or methods that maintain system function. If control of a plasma is lost, there need to be mechanisms to minimize the danger to surrounding systems. Fault tolerance can also involve redundancy or diversity. Redundancy occurs when a similar system can take over from another. Diversity involves having several different ways of accomplishing the same goals. When a plasma is in contact with a limiter, there can be other limiters at different locations that protect the vacuum vessel. Modularity provides isolation of a perturbation from the rest of the system. It is perhaps best achieved when each individual subsystem has internal protections and controls designed to maintain it in a state, with interconnections between the sub- systems that are monitored and controlled. If the plasma makes a rapid motion, it should not damage the external magnetic field coils. Decoupling isolates low-level noise and fluctuations from functional structures. Surrounding a plasma with a conducting metal surface will produce image currents in the metal that counteract plasma motion and help to maintain its stability. 1.4.3 Robustness Trade-Offs Robust systems resist fluctuations that attempt to move the system away from its desired state. Robustness involves tradeoffs: • robustness itself • fragility • resource demands • performance Avoidance of fragilities may be achieved by designing a system such that certain fluctuations simply cannot occur. A plasma is subject to instabilities. It is possible to create magnetic geometries where plasma fluctuations are suppressed.
- 53. 1.4 Systems Emergent Properties, Robustness and Dynamics 25 1.4.4 Fragilities A fragility is any event that can damage or destroy a system, ranging from small perturbations during operation to a systematic failure mode. Fragilities can occur even in a system that is designed to be robust against many perturbations [69]. Not all perturbations can be anticipated. For example, a plasma experiment would be highly robust against many plasma instabilities, but could be destroyed by a crack in a vacuum window. Several superconducting magnets in the Large Hadron Collider at CERN were destroyed not by a quench, but by a helium valve not designed for high pressure. A certain level of performance is expected in systems. The goal of a new plasma experiment may be to push performance to new records. Components would be tested to their limits. Obviously, if operations were conducted short of the design limits, then system fragility would be reduced. Hence the size of safety margins affects performance and robustness. 1.4.5 Resource Demands Resource demands can range from the quantity and complexity of components to funding for the project. Quantification of resource demands includes metrics such as expense per element, the cost of systems integration and of the total system itself. Consumption of resources is also important during an experiment such as volt seconds from a transformer or power from a motor-generator. 1.4.6 Performance Performance is an emergent property of a system and is perhaps the most important metric for evaluating original project goals. It can include quantification of the progress made towards a higher level goal. Metrics of success in a tokamak can include maximum toroidal magnetic field and plasma current. Other metrics are the triple product of plasma density, temperature and energy confinement time achieved, as a measure of progress towards building a fusion reactor.
- 54. 26 1 Introduction to Systems Approaches to Nuclear Fusion 1.5 Examples of Systems Engineering, Architecture, and Emergent Properties 1.5.1 Building a House House building is given in [4] as an example of systems engineering. A study was presented to set goals and to develop variants and choose among them. Systems and subsystems were then identified so as to provide assessments and choice of variants so as to proceed to building. The goals altered strongly during the study and illustrated some important lessons: • Objectives direct the solution search and enable decision making. • Thinking in variants is essential and decisions channel the next stages. • Incremental implementation clarifies goals, since a project focus can change. • Working in phases helps and exit possibilities are necessary. • Use of a problem solving cycle (PSC) is essential, where systems logic is applied to each project phase of increasing content. 1.5.2 Landing on the Moon and Returning The design of the lunar mission spacecraft of 1969 was analysed [5] in terms of developing systems architecture. Even very complicated systems can be deconstructed into simpler systems and subsystems, until a level of detail is reached that allows development of variants and optimization and decisions. The goal was to get astronauts to the moon and back, but the choice of means was wide open. The mission plan was divided into nine major decisions, and variants were determined for each, including earth orbit rendezvous, launch type, lunar orbit, etc. To decide among variants, the designers used constraints and metrics including performance, costs, developmental and operational risk. The analysis led to a series of successful missions. Even when one mission experienced major faults, the astronauts returned alive. 1.5.3 Guiding an Airplane in Flight An airplane provides an example of emergent properties [7] such as robustness, and how systems work together to achieve optimum performance. The airplane course is maintained by a pilot and an automatic flight controller which uses control surfaces and negative feedback. Fault tolerance is provided by the pilot, several redundant control surfaces and backup automatic flight controllers. Modularity comes from the steady thrust of multiple and redundant jet engines. Decoupling is achieved by the
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- 56. He thought better of this, however, and continued to creep forward carefully and silently. If he hits you again, he said, speaking to Hal but muttering the words to himself, it can't be helped; but we'll repay those blows with interest. Hal, standing erect before his captors, did not flinch as Lieutenant Steinz drew back his arm for another blow. But his eyes flashed dangerously. You'll be sorry for this, my friends, he said quietly. Threats, eh? sneered the German. You're in no position to threaten, pig. Perhaps not, admitted Hal, but just the same I am warning you. There was something so menacing in the lad's voice, that for a moment the German hesitated; but for a moment only, then he drew back his arm and struck. Once more Hal staggered under the blow, but he did not flinch. The German raised his arm and would have struck again but for a sudden interruption. When Chester saw the German strike Hal a second time, it was more than his blood could stand. He forgot, for the moment, his mission, that his first duty was to pass beyond the German camp. He threw caution to the winds. With a wild cry he leaped to his feet and dashed forward, a revolver levelled in each hand. Startled, the Germans turned to face their new foe. One look at Chester's angry features and they recoiled involuntarily.
- 57. At the same moment Chester fired—both weapons at once. Two of the enemy toppled over in their tracks. Now Hal had a quick mind. At Chester's first cry he knew what was up and he grew instantly alert, ready to take advantage of the first opportunity that presented itself. The opportunity was not long coming. Lieutenant Steinz, turning to get a view of Chester, for a moment left Hal unguarded. In that instant Hal sprang. Both hands he locked about the German's throat, and squeezed with all his strength. In vain the Teuton squirmed, struck and kicked. Suddenly Hal released his right hand and drove it into the man's face. At the same moment his left hand shot out and seized the German's revolver. Then he stepped quickly back, levelled the weapon and fired. Come on, Chester! he shouted. Chester needed no urging. In a few quick strides he was at Hal's side. Let's get out of here, he cried. It's getting too warm. Together the lads dashed toward the trench. A cry of alarm went up from the Germans behind. Shoot them! cried a voice that Hal recognized as that of the German colonel. Zig-zag, Chester! cried Hal, and suited the action to the word. Chester followed his chum's example and the first volley from behind failed to find a mark. By this time the lads were at the edge of the trench. Up and over with you, quick! cried Chester.
- 58. Hal leaped to the top of the trench and toppled to the ground beyond even as half a score of bullets sang across the spot where his head had been a moment before. Chester also sprang for the top of the trench. But he had leaped too soon, and instead of reaching the top he fell short, and dropped down inside the trench again. Germans were almost upon him when he regained his feet. Chester realized that a second leap was out of the question at the minute, so guns in hand he turned and faced his foes. Crack! Crack! Crack! Crack! His automatics spoke angrily and all four bullets found human targets. Hal, meanwhile, safely over the trench, looked around for Chester. When he failed to see him he realized on the instant what had happened. What shall I do? he asked himself. Duty says to hurry to a place of safety, but friendship says help Chester. He wasted little time in thought. He scrambled back to the top of the earthen embankment and took in the sight about him. There Chester stood at bay, his automatics held in steady hands. Hal drew his own weapons. Jump up here quick, Chester! he called. I'll cover you. Don't bother about me, Chester called back. Get away from here. Remember you must get through. I'll hold 'em off. Don't be a fool, shouted Hal, discharging his revolver at a big German who was about to shoot Chester down with his rifle. Come up here.
- 59. Chester paid no further heed to his chum. Hal gritted his teeth, dropped one revolver in his pocket, and reaching down grasped Chester by the shoulder. Come on, he called. Chester shook off his chum's hand. Let me alone. he shouted angrily. I'll get a few of these boches before they down me. His revolvers spoke as he talked, and two Germans dropped. Meanwhile bullets were striking on all sides of the two lads, and it seemed a miracle that they were not touched. Hal considered the situation in a flash. There's one chance, he said. Deliberately he sheathed his other revolver, thus leaving himself unarmed in the face of his foes. Then, bracing himself as best he could on the embankment, he reached down and seized Chester by both shoulders. Putting forth all his strength, Hal heaved mightily, and drew his chum to the top of the embankment with him. There he released him and drew his revolvers again. Came a cry of rage from inside the trench as the Germans saw their prey about to escape. Two men dropped on their knees and sighted their rifles carefully. But before they could fire Hal had accounted for one and Chester for the other. Again a howl of rage went up from the German trench. Kill them! Kill them! screamed the German colonel. What a lot of dunderheads! Can't you shoot?
- 60. He seized a revolver from a young officer close by and dashed forward himself. Hal, in the act of tumbling from the embankment, smiled slightly and faced the colonel, unmindful of all other dangers. So you're the man responsible for those blows a moment ago, eh? he muttered. Well, you'll never do it again. Take that! He sighted carefully and fired. The German colonel staggered in his onward rush, reeled crazily, threw up his arms, casting his revolver a dozen paces away, then fell to the ground. So much for you, Hal muttered. You won't bully another American, I'll bet on that. Come on, said Chester, who had stuck close to his chum all the time. It's too warm here. Let's move. Right. Suits me, said Hal quietly. Down we go, then, said Chester. He rolled rather than leaped to the ground on the outside of the trench. Hal did likewise. Both lads were slightly bruised by this method of descent, but they were not injured seriously. They scrambled to their feet. Now, let's see you run! shouted Hal to Chester. They ran. CHAPTER XIV THE CLOSING OF THE NET
- 61. Bullets flew thick and fast after the two lads as they clashed for the shelter of the American lines beyond. Fortunately, however, none touched them. The Germans, it appeared, were so bewildered by the suddenness of Chester's appearance, single-handed attack and the flight of the two chums that followed, that they forgot all about their searchlights, which would have made it possible for them to have picked off fugitives at will; or else they had no searchlights in that section of the field. Zig-zagging from right to left, the lads ran at top speed. For a time bullets whistled unpleasantly close, but soon they became few and far between. Hal slowed down. Chester followed his example. Whew! said Chester. Pretty close, but we're safe enough now, I guess. By George! I hope so, declared Hal. But there is just one job that I would have liked to complete before getting away from there. What's that? demanded Chester. I would like to have let a little lead into that big German lieutenant who battered me up with his fist. Don't blame you, said Chester. I'd like a shot at him myself. Well, said Hal, I left my mark on his throat, and that's some satisfaction. Also, I disposed of the colonel who was responsible, and there's more satisfaction there, too. I saw you, replied Chester. It was a neat shot. Well, said Hal, we've done something that a couple of other couriers sent out by General Rhodes failed to accomplish—we have
- 62. passed through the German lines. The general's plans will not go wrong if we can help it. Right, agreed Chester. And I figure that the sooner we report to General Lejeune the better. Correct as usual. But I don't know that I care to try and repeat the feat of getting through. Besides, we have General Rhodes' permission to stay here until after the big battle if we like. And I vote that we stay, said Chester. Think I'll cast my own ballot that way, declared Hal. We'll stick, unless something turns up to change our minds. Now for the American lines, then, said Chester. They hurried on through the darkness and directly the dim outline of the American trenches loomed up ahead. Here we are, said Hal. Now to get over. As they would have climbed up, however, the figure of a soldier appeared above them. He saw them instantly and levelling his rifle cried: Halt! Who goes there? Friends, said Hal briefly. Advance, friends, and be recognized, said the sentinel. Hal and Chester obeyed and the sentinel scanned them closely. You look all right, he growled at last, but I'm not sure of you. Do you think we'd be coming in here if we didn't belong? demanded Chester. I don't know about that; but I can't see any good reason why you should be prowling around out in No Man's Land if you are not bent on mischief.
- 63. Don't be absurd, man, said Hal. We come from General Rhodes with a message for General Lejeune. A likely story, said the sentry. How'd you get through the Germans? Walking and running, said Chester. But are you going to keep us standing here all night? I tell you we bear an important message from General Rhodes. What'd you both come for? the sentry wanted to know. That, said Chester, thoroughly exasperated, is none of your business, my man! Will you call the sergeant of the guard, or shall I? Oh, I'll call him, said the sentry, but I'll tell you right now I don't think it will do you any good. Kindly step up here, will you? Hal and Chester did so. Then, for the first time, the sentry saw that they were officers in the American army. He looked flabbergasted. I—I—I beg pardon, gentlemen, he said. I didn't know you were officers. Why didn't you tell me? You didn't give us a chance, said Hal shortly. Kindly summon the sergeant of the guard. The sentry argued no longer. He raised his voice in a shout that brought the sergeant of the guard on the dead run. What's the matter with you, you bonehead? demanded the sergeant as he came lumbering forward. Want to arouse the whole camp? It's all right, sergeant, said Hal. He only did as ordered. We have come from General Rhodes with an important message for General Lejeune. Will you direct us to his quarters?
- 64. The sergeant saluted stiffly. Follow me, sirs, he said briefly. Five minutes walk brought the three to the headquarters of the commander of the Second American division. There the lads were accosted by a member of the general's staff, Colonel O'Shea. We desire to see the general at once on a very urgent matter, said Hal. Colonel O'Shea scowled. The general left orders that he was not to be disturbed unless upon a very important matter, he replied. But this is urgent, said Chester. We are instructed by General Rhodes to deliver the message at once. But how am I to know the matter is so urgent? asked the colonel. Because I say so, sir, said Hal quietly. I am not in the habit of lying, nor of having my word doubted. Oh, is that so, said the colonel, though somewhat taken aback. Well, I'm not sure the general will care to be disturbed. You may deliver your message, and then I shall consider whether your business is of such importance as to justify waking the general. We were not instructed to deliver our message to you, sir, said Hal simply. I have to request again that we be given immediate audience of General Lejeune. The colonel hesitated. Apparently he was on the point of refusing to arouse the general, but he thought better of it, shrugged his shoulders and turned away. One moment, he said brusquely.
- 65. He returned a moment later, however, followed by a second figure, attired in a suit of pajamas and rubbing sleepy eyes. General Lejeune? asked Hal. Yes, was the sharp reply. What is it? We bear a message from General Rhodes, sir, said Hal. Well, let's have it, let's have it, exclaimed the general. I've got to get back to bed and get some sleep. First, sir, said Hal, I must explain that we came through the German lines where two or three other couriers lost their lives. General Rhodes wishes you to understand, sir, that the success of the campaign depends upon your acting in accordance with his message. I have no doubt of it, said General Lejeune. I have been unable, since the German wedge was driven between our forces, to get into communication with General Rhodes or other divisional commanders. I am isolated here, but at the same time I consider my position impregnable, so I am standing pat. Hal and Chester bowed in understanding of the general's explanation, and the commander of the Second division added: Come, sirs, what is the message you bring? General Rhodes' message, sir, said Hal, is that he requests you to attack the enemy before Sedan in full force on the evening of November 6, the attack to begin precisely at 6 o'clock. Very well, said General Lejeune, and just what is at the bottom of this plan—what is to be gained by it? That I do not know, sir, said Hal. General Rhodes simply asked us to carry that message. He said that the success of the campaign against Sedan depended upon you doing your part.
- 66. Well, I'll do it, never fear, said General Lejeune. I've got one of the best fighting units in France, and there's not a man in it who's not dead anxious to get another chance at the Huns. You may take back word to General Rhodes for me, that I shall act in accordance with his wishes. If it is all the same to you, sir, said Chester with a slight smile, we're not going back—not, at least, until the battle of Sedan is over. How's that? How's that? asked the general in some surprise. Why, sir, said Chester, General Rhodes gave us permission to stay with you if we deemed it imprudent to try and pierce the enemy's lines again. And you think it would be imprudent? asked General Lejeune with a slight smile. In view of the trouble we had getting here, yes, sir, replied Chester. Very well, then, said the general, you may remain with us. Colonel O'Shea, will you find quarters for these gentlemen? By the way, I did not catch your names. Crawford, sir, said Chester. Paine, sir, said Hal. Very well, General Lejeune continued, Colonel O'Shea, will you please see that Major Paine and Major Crawford are provided with suitable quarters? And will you both report to me at 8 o'clock in the morning, gentlemen? I may have need of you. The Second division is an hospitable unit, but you'll find that guests are required to work as well as home folks. We shall be more than glad to do our parts, sir, said Hal.
- 67. Very well. Now you have kept me out of bed long enough. I'll leave you both to the good graces of Colonel O'Shea, and if he doesn't find suitable quarters for you, you let me know and I'll have him court-martialed. With this, and a smile on his face, the good-natured commander took his leave. By George! said Hal, as the lads followed Colonel O'Shea from the general's quarters, he's the most lively commander I ever did see. Full of 'pep' eh? said Chester with a laugh. Yes, Hal agreed, and I'll bet he's full of the same old 'pep' when it comes down to business. And Hal was right. CHAPTER XV THE CAPTURE OF SEDAN The American advance against Sedan was in full blast. All night the fighting had raged. Promptly at 6 o'clock on the evening of November 6 General Lejeune had hurled the Second division forward in accordance with the plans outlined by General Rhodes of the Forty-second. Apparently the Germans had anticipated the attack, for they were braced to receive it when the first Yankee troops began to move. The enemy stood firm—and was continuing to stand firm almost twelve hours after the assault was launched.
- 68. There was a slight chill in the early November air as it grew light. The air was filled with shrieking shells and shrapnel. Rifle and machine-gun fire rose even above the noise of the field and siege guns. Shrill whistles punctuated intervals of seeming silence as American officers gave orders to their men. In the midst of battle, whistles are depended upon mainly for signals—also there are signals given with the hands. The confusion is usually too great to permit verbal orders being understood. At the same time that General Lejeune attacked the enemy, General Rhodes, to the south, also had advanced. But the enemy was holding stubbornly in that section of the field also, and at 6 o'clock on the morning of November 7 the American forces had made only slight progress. However, they were still hammering hard at the German lines. With a gallantry not exceeded in the annals of the war, the Second division kept at its task. When one enemy machine-gun nest was captured, they found themselves targets for others, whose gunners, discovered, had withheld their fire until the moment when it would be the most effective. Another grand assault was ordered by General Lejeune. The Germans made a determined resistance. They put in fresh troops and subjected the American lines to a terrific artillery bombardment of high explosives and gas shells. Directly in the path of the advancing Americans was a large wood. Although the wood was not yet cleared of the enemy, the American line here was farther advanced. Many prisoners had been taken. A third attack resulted in the capture of still more prisoners and many machine-guns. In the meantime the Ninth infantry, on the
- 69. right of that part of the field where Hal and Chester found themselves, had advanced its position to the northern edge of the Bois de la Jardin and was digging in to beat off a possible counter- attack. In fact, the entire Third brigade, assisted by a battalion of the Second engineers, was strengthening its lines as well as possible under heavy enemy machine-gun and artillery fire. The defensive part played by this brigade was very difficult. Its losses were heavy as a result of enemy shell fire and gas bombardments, to which the Third brigade could not at the moment reply. Its duty now was to hold its lines. Its present action was confined to a rifle and machine-gun duel with the enemy. To the south, the First brigade also was hotly engaged. It had advanced in the face of a terrible artillery and machine-gun fire until at hand grips with the foe. Then ensued one of the fiercest struggles of the war. As in other encounters, the Germans proved no match for the Yankees at hand-to-hand fighting. They resisted desperately, but gradually were driven back. The Americans, with wild cheers, pursued them closely. General Lejeune's center, composed of the Second brigade, with an additional battalion or two of artillery, also was meeting with greater success than the Third brigade, which, for the moment, had been checked. The advance was pushed with desperate energy, and the Germans could not hold their ground in the face of the withering American fire. The German center faltered, then broke. Taking advantage of this success, General Lejeune pushed Brigadier General Abernathy's Second division into the breach.
- 70. Immediately, also, he ordered the First brigade forward in an effort to break through to the south, while orders were rushed to the hard- pressed Third brigade to make a final effort. The task of the Third brigade was easier now. Bereft of its supports, the German center was obliged to yield ground to the Third brigade or risk being cut off and surrounded. The Germans gave ground slowly. To the south, the First brigade also began to drive the foe more swiftly. It appeared for a moment that the Germans would suffer a rout. Under the direction of their officers, however, they braced perhaps half a mile farther back, and again showed a determined front. Trenches dug by the Americans were abandoned now as the Yankees poured forth in pursuit of the enemy. Not a man in the whole Second division who was not sure that the trenches would never be needed for defensive purposes. No one knew better the morale of the American troops than did the men themselves. Nevertheless, the advance slowed down in the face of the resistance being offered by the enemy. For a time it appeared that the fighting had reached a deadlock. The deciding touch to the battle was furnished by General Rhodes. Sweeping up from the south, the Fifth, Sixth and Seventh brigades of the Forty-second division bore off a trifle to the east and then turned north again, thus catching the enemy on the left flank. This maneuver, apparently, had not been anticipated by the enemy's general staff, for it took the Germans by surprise. True, they received warning in time to wheel machine-guns into position and to
- 71. place big guns to rake the Americans as they dashed forward. But the warning had not been received in time to permit the general staff to alter its plan of defense, and for this reason proved the blow that broke the backbone of the enemy's resistance. The enemy, closely pressed by General Lejeune, had no time to make changes in his defensive plan necessitated by General Rhodes' sudden attack. Reinforcements could not be sent to check General Rhodes without weakening the front opposed to General Lejeune. General Schindler, after a hasty conference with his staff, ordered a retreat to the lines just before Sedan. The Germans fell back rapidly. Neither General Rhodes nor General Lejeune was content to rest with this advantage, but each decided to push on. During all this time, the enemy had been successful in keeping a wedge between the Second and Forty-second American divisions. General Schindler realized that if he hoped to extricate his men from the trap sprung by the Americans he must prevent a juncture of the Second and Forty-second at all hazards. Now, however, as the attack seemed on the verge of success, General Lejeune decided that the German wedge separating him from General Rhodes must be pierced. Accordingly, without permitting the advance to slacken elsewhere, he threw the First brigade against it. For perhaps fifteen minutes the fighting was fast and furious. In vain the Germans tried to stem the tide in khaki that rushed forward against them. General Schindler further weakened his center to rush reinforcements in order to retain the wedge intact.
- 72. But it was no use. The Americans were not to be denied. They fought with the courage and desperation of lions. Little heed did they pay to the hail of machine-gun bullets that swept them as they advanced. Artillery and explosive shells failed to stop them. Rifle fire was no more effective. Suddenly from the German lines sallied a regiment of cavalry. The American infantry braced to receive the charge. At the same time Hal found himself before Colonel Taylor of the First brigade with dispatches from General Lejeune. He had just delivered them as the German cavalry sallied forth. Great Scott! What a chance to take! the lad muttered under his breath. The Germans must be licked. This move can be for no other purpose than to give infantry time to withdraw. The American infantry stood firm as the German cavalry hurled itself upon them. Not an inch of ground did they give. Horses and men fell in heaps. Other chargers reeled back, throwing their riders beneath their hoofs. At the same time the Yankee infantry poured in a hail of rifle fire. The Germans retired a pace, reformed and charged again. The result was the same. Not an inch did the Americans give, and the execution in the enemy's ranks was fearful to behold. I guess that will stop that, Hal told himself. He was right. When the enemy's cavalry withdrew a second time it did not reform for a third charge. Instead, it fell back upon its infantry and artillery supports, apparently fearing that the American infantry would pursue and annihilate it. I thought so, said Hal.
- 73. In the meantime, the German retirement in other parts of the field had become more rapid. The lines before Sedan were abandoned gradually and at last there was nothing to keep the Americans from entering the city save the cannonading of the German artillery from far to the rear of the town. But although the bulk of the German army had retired safely to the east of Sedan, fortune had not been so kind to the two brigades which had formed the wedge between the Second and Forty-second American divisions. When General Lejeune's men had pushed back the cavalry attack, General Rhodes, to the south, had gained an inkling of what was going on. Accordingly he had ordered an attack upon the hard- pressed foes. Caught thus between two fires, the Germans tried first to hold their ground, and, finding this could not be done, to retreat orderly. But they had delayed too long. Three regiments of the First brigade of General Lejeune's division had been hurried forward to cut off a movement, and the Germans, when they found flight blocked, became disheartened. In spite of the fact that they outnumbered the little force between them and the bulk of their army, thousands of men threw down their arms and surrendered. This forced the others to follow suit or be annihilated. Less than two hours later, with German shells still falling among them, American troops entered Sedan. And the French population, virtual prisoners for many months, received them with wild acclaim. It was a joyous day for the citizens, indeed.
- 74. CHAPTER XVI AN UNEXPECTED HONOR Sedan at last! This settles the war. It was Chester who spoke. Right you are, replied Hal. The poor old kaiser's goose is cooked. Even the most sanguine German can no longer hope for victory. I think the kaiser gave up hope a long while ago, said Chester. He—Hello, what's up now, I wonder? He broke off suddenly and pointed to a horseman who came galloping into the town from the east, gesticulating excitedly as he rode along. Words that he shouted as he dashed forward seemed to create great excitement among the villagers, who, all day, had been parading the streets in celebration of the American occupation of the city. Don't know, said Hal. We'll try and get close enough to hear what he says. As the man drew close, the lads saw that he was a German cavalryman. It appeared strange to both boys that he was thus permitted to ride free, as the feelings of the villagers were very strong against the Germans. But it soon became apparent that the message he brought secured him immunity. What's that he said? asked Chester, with hand to his ear. I didn't catch it, said Hal. Here, get in front of him. We'll stop his wild ride.
- 75. Chester needed no urging. The lads stepped directly in front of the galloping horse. Hal produced his revolvers. The rider checked his steed. Hal approached him. Dismount, said the lad in German. The rider did so. Now, said Hal, what's all the excitement? You seem to have something on your mind. What is it? Haven't you heard the news? demanded the rider. I wouldn't be asking you if I had, said Hal. What is it? The kaiser has abdicated! Hal and Chester started back in pure amazement. What! they exclaimed in a single voice. So I am informed, declared the German. It is true that my information has not been substantiated, but I know enough of conditions in Germany to credit the report. Well, you come with me, said Hal. We'll take this matter to General Lejeune. The German accompanied them without objection. General Lejeune received the report with skepticism. Nothing to it, in my opinion, he said. It is true that conditions in Germany are fast approaching a crisis, but I believe this report is premature. However, I have no doubt that something like that will happen within the next thirty days. But what are you doing in our lines, man? This last to the German soldier. Well, I'm tired of fighting, was the soldier's reply. I want to live to go home again some day. I've a family in Hamburg that will need me. I am content to remain a prisoner until the war is over.
- 76. And so you shall, said General Lejeune. Whether your report is true or not, it has given me an interesting moment. Colonel O'Shea, will you turn this man over to the corporal of the guard? The prisoner was led away. General Lejeune turned to Hal and Chester. I am sorry to lose your services, gentlemen, he said, but I have just been in communication with General Rhodes, and he wishes you to report to him at once. The lads saluted the commander of the Second division and left his quarters. Half an hour later they reported to General Rhodes as he rode into Sedan to establish his own quarters, as the Second division was soon to advance again. General Rhodes greeted the lads warmly. I am certainly glad that you both came through safely, he said, after returning their salutes, and I must say that I didn't expect it. You have been in luck. Now I have another important matter in hand. We shall be glad to offer our services, sir, said Hal. General Rhodes smiled. I've no doubt of it, he replied. However, this mission is not likely to be so dangerous. Don't worry, though, he added, as the faces of the lads fell, I believe I may safely promise you some interesting moments. We're glad of that, sir, declared Chester. I wonder, said General Rhodes, whether you have heard of the reported upheaval in Germany? Yes, sir, said Hal. Only a few moments ago we captured a man who declared the kaiser had abdicated.
- 77. That, said General Rhodes, is probably untrue; however, I know that the kaiser has considered abdicating. In fact, his abdication is being urged by his military leaders—his erstwhile friends, Hindenburg and Ludendorff. Can that be possible, sir? asked Hal. Yes, we have authentic information to that effect. I understand, too, Germany is preparing to ask Marshal Foch for an armistice preliminary to signing a declaration of peace. By Jove, sir! exclaimed Chester, carried away in spite of himself. General Rhodes smiled again. It is good news, he said quietly. Of course, I am not absolutely positive of that, but in view of recent German reverses I do not see how the enemy can do aught else. Well, sir, said Chester, we'll impose terms on them that will make their hair curl. For a third time General Rhodes smiled. We won't be too severe, he said. Remember, we are not German. That's true, too, sir, said Chester. But all the same, it should be done, if you ask me. Perhaps, said General Rhodes. Now, I suppose you are wondering why I called you here? Yes, sir, returned Hal. Well, said General Rhodes, I have been summoned to report to the commander-in-chief and I want a couple of officers to go with me who can be useful as well as ornamental. Both lads flushed.
- 78. I know that you drive an automobile exceedingly well, Major Paine, the general continued, and for that reason I am selecting you as my chauffeur on this trip. But I am afraid I shall not be so useful, sir, said Chester. Well, said the general, I am taking you along because I thought you'd like to go. And so I would, sir, answered Chester. It may be, General Rhodes continued, that before our return we shall be present at a very momentous gathering. You mean, sir— asked Hal. General Rhodes nodded. Exactly, he replied. I mean that the commander-in-chief is summoning me for some purpose other than because he wants to see me. It would seem that matters have reached a point where something is likely to break at any minute. By George! I hope so, sir, declared Chester. I shall expect you to be ready in an hour, said General Rhodes ending the interview suddenly. I shall have a car here at that time. Chester and Hal saluted and departed. Now, this is what I call a regular mission, declared Hal, as they hurried to their quarters. It is if it develops, replied Chester. Something tells me it will develop, said Hal. Let's hope so. The lads were back at General Rhodes' headquarters well within the time allowed them. A large army automobile stood without. Guess this is our steed, said Hal. He was right.
- 79. General Rhodes appeared a few moments later and took his seat. He motioned Chester to a place beside him. Hal took the wheel. Where to, sir? he asked of the general. Rheims, was the reply. The commander-in-chief is there now. You know the road, of course? Yes, sir. Then you will take us there as speedily as possible. The machine shot forward with a lurch. Now if there was one thing Hal did better than anything else it was to drive an automobile. He was a fast though careful driver and his hands and nerves both were like steel when he clutched a wheel. He had been over the road before, and his excellent memory served him in good stead now. It was after 3 o'clock on the afternoon of November 7 when the automobile flashed into the outskirts of Rheims. Hal stopped the car long enough to inquire the way to General Pershing's headquarters, then moved forward again. You are a good driver, Major, said General Rhodes, as he alighted and motioned both boys to follow him. Thank you, sir, returned Hal. I've had experience enough, sir, I should be, at all events. General Rhodes vouchsafed no reply, as he mounted the short flight of steps to General Pershing's offices, with Hal and Chester at his heels. Apparently his arrival was expected, for an orderly saluted and told him that he was to proceed to the commander-in-chief immediately.
- 80. You gentlemen stay here until I send for you, or return, he instructed the two lads. Hal and Chester stood stiffly at attention as he walked away. We're in luck, if you ask me, said Chester after their commander had gone. It would seem so, Hal agreed. If anything happens, I'd like to be in at the finish. So would I. We've been in the war from the first. It would be no more than right for us to see the finale. Maybe we will, said Hal. Here's hoping. They sat quietly for some time. Two hours later an orderly approached. Major Paine! Major Crawford! he said, the commander-in- chief desires your presence at once. Kindly follow me. CHAPTER XVII STUBBS AGAIN General Pershing greeted the lads cordially. Glad to see you again, he said. General Rhodes informs me that you have been up to your old tricks and have again been cited for gallantry in action. However, it is no more than I would have expected of you. The lads bowed in response to this praise, but neither spoke. It is fortunate that General Rhodes brought you with him, General Pershing continued. Still, it may not be so fortunate for
- 81. him, for I am about to deprive him of your services. I take it that you will survive the separation, though, and the commander-in- chief smiled. We are always glad to serve in whatever way we may, sir, said Hal. Good! said General Pershing. Then I shall avail myself of your services. Several hours ago I was in communication with Marshal Foch, who is now in Soissons. General Rhodes informs me that he has made you acquainted with the facts that seem to indicate an early cessation of hostilities, so I need not amplify here. Now, Marshal Foch, anticipating that Germany may really sue for peace, has asked my advice in the matter of armistice terms pending a final treaty of peace. These I have written out. As you will readily recognize, they are not to be trusted to careless hands. I have confidence in you, however, gentlemen, so I shall ask you to carry this paper to Marshal Foch. We shall be glad to do it, sir, said Chester. Very well. Then I intrust this paper to you, and I need not warn you to guard it carefully and keep the matter secret. General Pershing extended a document to Hal. The lad took it and put it carefully in his inside coat pocket. It will be safe there, your excellency, he said quietly. Now, said the commander-in-chief, it is my wish that that paper be placed in Marshal Foch's hands at the earliest possible moment. The car in which you drove General Rhodes is at your disposal. We shall make all possible haste, sir, said Chester. Both lads saluted their commander and left the room.
- 82. By Jove! said Hal, as he sprang into the car, there is no use talking, important developments are pending. It begins to look like peace to me. And to me, Chester agreed. Well, the sooner the better. Four years of war is enough to satisfy Mars himself. Soon the car was speeding westward. It was a long drive to Soissons and it was after nightfall when Hal saw the lights of the city in the distance. A few moments later they entered the town. Hal had no difficulty ascertaining where Marshal Foch made his headquarters and he drove there at once. A few words to a guard before the building brought forth a member of Marshal Foch's staff and the lads explained their mission to him briefly. You are expected, said the French officer. Follow me. He led the way into the house and through a long hall. At the far end he tapped on a door. Who's there? came a voice, that Hal at once recognized as belonging to the French commander-in-chief. Colonel Murrat, said the lads' guide. The messengers from General Pershing have arrived. Show them in at once, said Marshal Foch. A moment later Hal and Chester were in the presence of the generalissimo of all the allied forces. They saluted him respectfully. I may be mistaken, said Marshal Foch, eyeing them searchingly, but I'll wager you are Majors Paine and Crawford. Am I right? Yes, your excellency, said Hal. We are honored that you remember us.
- 83. I never forget a face, replied Marshal Foch; and seldom a name. Then you bring me a communication from General Pershing? For answer Hal produced the document given him by the American commander-in-chief earlier in the day. He passed it to Marshal Foch without a word. The French commander took it and laid it carefully on his desk. That will be all for to-night, gentlemen, he said. I shall be pleased if you will avail yourself of our hospitality. Colonel Murrat will find quarters for you. Will you report to me in the morning at 8 o'clock? I may have a reply for your commander-in-chief. The lads saluted again and withdrew. Colonel Murrat showed them to excellent quarters in a house next to the one in which the French commander had his headquarters and left them. Well, said Chester, after he had gone, looks like we are right in among things, doesn't it? It certainly does, Hal agreed. But say, I'm hungry. Let's step out and round up something to eat. Suits me, declared Chester, I'm half starved myself. At a little restaurant only three or four blocks away they were soon comfortably filled. Hal was on the point of suggesting that they turn in for the night when a figure entering the door caught his eye. By all that's wonderful, he exclaimed, here comes Anthony Stubbs. Hal was right. The little war correspondent espied the lads at the same moment and hurried toward them with outstretched hand. I'm awfully glad to see you boys again, he exclaimed. What brings you here, if I may ask?
- 84. Sit down, Mr. Stubbs, said Hal. Have something to eat with us. Thanks: don't mind if I do. But I repeat, what are you doing here? How long have you been in town, Mr. Stubbs? asked Chester, ignoring the little man's question. About fifteen minutes, more or less. But I say, what are you doing here? This is the third time I've asked that question. Then don't ask it again, Mr. Stubbs, replied Chester. Oh, I see, smiled Stubbs. Can't answer, eh? Well, I'll wager another hat with somebody that I can tell you why you're here. You'd lose this time, Mr. Stubbs, said Hal. Oh, no I wouldn't. You're here in connection with the signing of an armistice by Germany and the allies. Chester started to his feet. Sh-h-h! Not so loud, Stubbs, he exclaimed. Stubbs smiled, but he lowered his voice when he spoke again. Well, would I lose the bet? he asked. I can't say a thing, Mr. Stubbs, was Hal's response. Well, I'm bound by no such orders, said Stubbs, so I can. First, however, I want you to understand that whatever I do say is in confidence. Of course, said Hal. Certainly, Mr. Stubbs, agreed Chester. Well, then, said Stubbs, I want to tell you I'm on the trail of the biggest scoop in newspaper history. I'm going to be the first war correspondent to flash the news that the armistice is signed. You mean you think you are, said Chester.
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