Table Of ContentFusion
VOLUME 1
Magnetic Confinement
PART В
EDITED BY
EDWARD TELLER
Lawrence Livermore National Laboratory
University of California
Livermore, California
1981
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Library of Congress Cataloging in Publication Data
Main entry under title:
Fusion.
Includes bibliographies and index.
Contents, v. 1. Magnetic confinement (2 v.)
1. Nuclear fusion. I. Teller, Edward, Date.
QC791.F87 621.48'A 80-69419
ISBN 0-12-685241-3 (v. 1, pt. B) AACR2
PRINTED IN THE UNITED STATES OF AMERICA
81 82 83 84 9 8 7 6 5 4 3 2 1
List of Contributors
Numbers in parentheses indicate the pages on which the authors' contributions begin.
ROBERT W. CONN (193), Center for Plasma Physics and Fusion Engineering,
School of Engineering and Applied Science, University of California,
Los Angeles, California 90024
R. A. DANDL (79), Applied Microwave Plasma Concepts, Inc., Encinitas,
California 92024
JOHN M. DAWSON (453), Department of Physics, University of California,
Los Angeles, California 90024
G. E. GUEST (79), Applied Microwave Plasma Concepts, Inc., Encinitas,
California 92024
W. B. KUNKEL (103), Department of Physics, Lawrence Berkeley Labora-
tory, University of California, Berkeley, California 94720
R. W. MOIR (411), Lawrence Livermore National Laboratory, University of
California, Livermore, California 94550
MIKLOS PORKOLAB (151), Department of Physics and Plasma Fusion Center,
Massachusetts Institute of Technology, Cambridge, Massachusetts
02139
W. E. QUINN (1), Los Alamos National Laboratory, Los Alamos, New
Mexico 87545
F. L. RIBE (39, 59), Department of Nuclear Engineering, University of Wash-
ington, Seattle, Washington 98195
A. R. SHERWOOD (59), Los Alamos National Laboratory, Los Alamos, New
Mexico 87545
R. E. SIEMON (1), Los Alamos National Laboratory, Los Alamos, New
Mexico 87545
ix
Contents of Part A
Introduction
Edward Teller
Tokamak Plasma Stability
M. N. Rosenbluth and P. H. Rutherford
The Tokamak
H. P. Furth
Stellarators
J. L. Shohet
Mirror Theory
T. Ê. Fowler
Experimental Base of Mirror-Confinement Physics
R. F. Post
The Reversed-Field Pinch
D. A. Baker and W. E. Quinn
INDEX
xi
FUSION, VOLUME 1, PART Β
8
Linear Magnetic Fusion Systems
W. E. QUINN AND R. E. SIEMON
Los Alamos National Laboratory
Los Alamos, New Mexico
I. Introduction 2
II. Heating Methods 5
A. Implosion Heating 5
Β. Laser Heating 7
C. Relativistic Electron-Beam (REB) Heating 9
D. Auxiliary Heating 11
III. Equilibrium and Stability 12
A. Rotational Instabilities 12
B. Curvature-Driven Instabilities 14
C. Tearing Modes 14
IV. Transport 15
A. Axial Particle Loss 16
B. Axial Heat Loss 16
C. Radial Particle Diffusion 17
D. Radial Heat Diffusion 18
V. Impurities 18
VI. Scaling Laws for LMF Devices 19
A. Particle End Loss 19
B. Electron Thermal Conduction 22
C. Radial Transport 24
D. Total Plasma Energy 25
VII. End-Stoppering Methods 26
A. Material End Plugs 26
B. Magnetic Field End-Stoppering Techniques 28
C. Reentrant End Plugs 29
VIII. Reactor Considerations 30
A. Linear Theta-Pinch Reactor (LTPR) 31
B. Laser-Heated Solenoid Reactor (LHSR) 31
C. Electron-Beam-Heated Solenoid Reactor (EBHSR) 32
D. Steady-State Solenoidal Fusion (SSF) Systems 32
References 33
/
COPYRIGHT C 1981 BY ACADEMIC PRESS, INC.
ALL RIGHTS OF REPRODUCTION IN ANY FORM RESERVED
ISBN 0-12-685241-3
2 W. E. QUINN AND R. E. SIEMON
I. Introduction
Linear magnetic fusion (LMF) is a classification for systems having in
common a linear, cylindrical geometry of plasma, blanket, and confinement
system with transverse confinement primarily by a quasistatic magnetic
field and open-ended field lines. Because of their relative simplicity, LMF
system., provide an attractive approach to the development of fusion
reactor systems. The basic advantages of LMF systems include MHD
stability, high plasma beta, modest impurity problem, and simple fueling.
In the case of the theta pinch, effective heating to fusion temperatures has
been demonstrated. In addition, there are several heating methods available,
and the reactor would have the potential of simple engineering and main-
tenance for a modular system composed of identical, straight, cylindrical
elements of modest size.
The most serious problem of all LMF systems is the open field line
geometry and the consequent length required to sustain the plasma for
reactor burn times. Particle loss through open ends and classical heat loss by
electron thermal conduction along the field present fundamental limitations
on the particle and energy confinement times, implying reactor systems
with lengths of tens of kilometers. 1 Such systems are found to produce an
unacceptably large power and are unattractive unless their length is reduced
by at least one order of magnitude. The length requirement is the single
major disadvantage of LMF reactor systems and provides a strong impetus
to find an appropriate end-stoppering arrangement. Several methods have
been proposed, and in some cases demonstrated, for reducing system length
by means of end stoppering. These include material end plugs, multiple
mirrors, cusps, plasma injection, rf stoppering, electrostatic trapping, field
reversal, and "reentrant" end plugs (elongated racetrack). (The "reentrant"
end-plugged system consists of two long linear systems connected at the
ends by semicircular sections to form a very elongated racetrack.) Both the
field-reversal and reentrant systems have closed magnetic field lines to
prevent both particle losses and heat loss by electron thermal conduction.
The reactor embodiment for a system with closed field lines is hoped to be
superior, but the physics of the more complicated configurations of magnetic
field are not well enough understood to allow an evaluation at the pre-
sent time.
In LMF systems, the plasma is confined radially by an axial magnetic
field. It is well established that plasma equilibrium exists in the straight field
line configuration. Theory predicts the LMF plasma to have neutral stability
in the absence of field curvature and plasma rotation. Finite Larmor radius
(FLR) effects provide stabilization of m > 2 perturbations2-5 in the presence
8. LINEAR MAGNETIC FUSION SYSTEMS 3
of curvature or rotation that may result from field errors, boundary con-
ditions, or from end-stoppering techniques. Unstable m = 1 motions are
expected if field lines have unfavorable curvature or if the whole plasma
column achieves a rotation which exceeds certain bounds. Experiments have
demonstrated stable plasma confinement prior to propagation of end effects
to the central plasma region. An m = 1 wobble instability, which saturates
at low amplitude, is observed after an Alfvén transit time from the ends. The
rotation which drives the instability is most likely associated with shorting
of the radial electric fields and the boundary conditions at the ends.
All LMF experimental results to date appear to be consistent with classical
transport of particles and energy, in both the radial and axial directions,
although the time scale imposed by axial losses limits the accuracy of radial
loss measurements. Classical radial losses provide very favorable scaling to
reactor parameters. When heating is performed in a theta pinch, i.e., by
rapidly strengthening the magnetic field lines and thereby imploding the
plasma which they carry, electron energy loss appears almost immediately
as a result of thermal conduction parallel to the field lines. Subsequently the
major energy loss becomes convective as a result of the end loss of particles.
The theta pinch is an electrodeless discharge created by shock-implosion
heating followed by adiabatic compression in an axial magnetic field
generated by an azimuthal or theta current flowing in a solenoidal coil as
illustrated in Fig. 1. It is to be distinguished from the Ζ pinch in which the
magnetic field is perpendicular to that of a theta pinch.
Results6-8 with material end plugs indicate that the free-streaming particle
loss can be reduced significantly, leaving only the problem of energy loss
by electron thermal conduction. Plasma confinement has also been demon-
strated in linear systems at low beta using multiple magnetic mirrors. 9 The
FIG. 1. Simplified schematic view of the
theta pinch: (a) Implosion heating dynamic
phase characterized by irreversible shock
heating, (b) Adiabatic compression of the
shock-heated plasma followed by quiescent
phase and plasma confinement.
4 W. E. QUINN AND R. E. SIEMON
study of end-stoppering techniques at high density (~ 10 16 cm"3) and high
beta (~0.5 to 0.9) is in its infancy: no end-stoppering techniques have been
tested at conditions at which they are expected to be the most effective;
some have not been tested at all; and no experiment has used a combination
of techniques. Somewhat related concepts are being worked on in the
magnetic mirror program (cf. Chap. 6), but at lower plasma densities where
ambipolar sheaths are effective in reducing the effects of electron thermal
conduction.
Plasma heating in LMF consists of a staged process beginning with rapid
heating by a primary heater, which is followed by adiabatic compression.
Three primary heaters have been studied: implosion heating by rapidly
increasing the axial magnetic field, laser heating, and, to a lesser extent,
relativistic electron-beam heating. Shock-implosion heating is a proven
technique for achieving kilovolt ion temperatures and has been applied in
many theta-pinch experiments. This technique heats the ions directly. Ex-
periments have demonstrated effective coupling of laser and electron beams
to plasma energy in plasma columns of mederate temperature (~ 100 eV).
Laser heating occurs by inverse bremsstrahlung absorption and works best
for higher-density plasmas (~10 17 cm"3). The energy-coupling process of
e beams is anomalously high and appears to be effective for plasma densities
in the 1016-cm~3 range. On the basis of classical collision processes, rela-
tivistic electron beams (REB) should pass through a plasma without losing
much energy, but anomalous effects arise through the coupling of the two-
stream instability between the REB and the electrons in the plasma, resulting
in a collective deposition of energy in the plasma. Both lasers and e beams
heat the plasma electrons rather than the ions. Auxiliary heating processes
may also be used to augment the primary heater and reduce its engineering
requirements.
The excessive length required for an LMF reactor to sustain the plasma
density and energy against end loss for times required to achieve net energy
breakeven presents a singular disadvantage that has limited LMF systems
as a serious contender for a fusion power reactor. A solution to the axial
confinement problem is crucial for the development of a viable reactor
concept. Reactor technology requirements for LMF systems are likely to
include high-field magnets, efficient energy transfer, and storage systems,
and a large first-wall loading.10 The linear geometry is simple, and the
magnets can be constructed in modular elements. Refueling can readily be
performed during the interval between pulses, in the absence of a plasma.
The linear theta-pinch device, which has been extensively studied, is
typical of LMF systems. A review of the linear theta-pinch concept has been
given by Freidberg et al.11 A summary of LMF topics discussed at an LMF
8. LINEAR MAGNETIC FUSION SYSTEMS 5
Workshop in 1977 gives a review of LMF physics and technology. 12 An
overview of end-stoppering techniques for open magnetic containment
systems has been given by Hinrichs. 13
II. Heating Methods
LMF systems employ at least two plasma heating techniques, a primary
heater which produces a plasma of 1-2 keV, followed by adiabatic com-
pression and possibly an auxiliary heater which increases the temperature
to ignition. The primary heater usually delivers its energy on a microsecond
time scale and requires expensive, high-quality energy storage, efficient
transfer, and rapid conversion of electrical energy to plasma energy. The
adiabatic compression or secondary heating usually occurs on a much
slower time scale, typically in the millisecond range. The secondary heater
generally requires considerably more energy than the primary heating, but
the slower pulse time allows cheaper energy storage, such as fast-discharging
homopolar generators. Additional auxiliary heating can be used to relax the
engineering requirements of the primary heater.
The primary plasma heating can be achieved by means of implosion
heating in a theta pinch, or by absorption of energy from an axially directed
laser or electron beam. Secondary heating can be achieved through adiabatic
compression by a slowly rising magnetic field. Auxiliary heating could use
magnetoacoustic heating, ICRH, Alfvén-wave heating, magnetic pumping,
or neutral-beam injection.
A. Implosion Heating
Implosion or shock heating is a proven method for heating plasmas to
thermonuclear conditions. It has the advantage of directly heating the
ions, and multikilovolt ion temperatures have been achieved with plasma
densities in the 10 14-1015 cm-3 range. Implosion heating requires a rapidly
rising magnetic field (τ/4 ~ 0.5/isec,i? ~ lOkG), and therefore high-quality
energy storage. In the theta pinch, the implosion phase is followed by slow
magnetic compression. The implosion circuit is applied to a preionized
plasma. During the initial phase of the implosion, some magnetic field
becomes imbedded in the plasma. As the plasma current sheath becomes a
few ion Larmor radii in thickness, the field diffusion slows. For low filling
pressures (~ 3-10 mTorr), the density profile is approximately Gaussian and
the peak value of beta is high but less than unity. Higher filling pressures
6 W. E. QUINN AND R. E. SIEMON
implode to flat-topped density profiles with beta (ratio of plasma pressure
to external magnetic field pressure) values approaching unity.
The implosion heating phase of the theta pinch has been studied over a
wide range of parameters and is understood both experimentally and
theoretically. An international effort to understand collisionless shocks in
the implosion heating process concentrated on low-density implosion
phenomena.14-2 2 Experiments at higher densities with initial fill pressures
of 5-10 mTorr, characteristic of reactor conditions, produced plasmas with
ion energies of 1.6 keV.23 This temperature from implosion heating, when
combined with a compression phase, represents a reasonable approximation
to the heating requirements in a theta-pinch reactor. The implosion heating
phase of the theta pinch is produced by a rapidly rising axial magnetic field
which induces an azimuthal electric field in the outer plasma region. The
electric field drives an azimuthal current in the cylindrical plasma sheath,
which implodes toward the axis because of the increasing pressure of the
axial magnetic field. Depending on the parameters of the experiment either
a "bounce"24'25 or a "snowplow"26 model is used to describe the non-
adiabatic heating process. The bounce model has been used to describe the
implosion process in collisionless plasmas. In this model, the collisionless
plasma ions are reflected from the rapidly inward moving plasma sheath at
twice the imploding sheath velocity. The fast, radially imploding ions
thermalize through nonadiabatic turbulent processes. The cold electrons are
then heated by collisional equilibration with the ions. For higher-density,
collisional plasmas the "snow plow" model describes the implosion process.
As the plasma sheath is driven inward by the "magnetic piston," it sweeps up
all the charged particles it encounters. The plasma ions are pushed ahead of
the imploding sheath rather than being reflected since turn around is im-
peded by collisions with other particles and by turbulence. The rate of
momentum change of the plasma, balanced against the external magnetic
pressure, then gives the inward velocity of the sheath as a function of time.
In order to describe the broad sheaths, diffuse profiles, and magnetic field
diffusion that are observed in the implosion heating phase, it has been
necessary to invoke nonclassical effects, in particular, anomalous resistivity.
Currently, numerical methods provide the best means of understanding the
implosion heating phase. The hybrid code of Sgro and Nielson 27 uses
kinetic ions and massless, fluid electrons; Ohm's law is supplemented with
suitable anomalous resistivity coefficients. Simulations of experiments have
demonstrated that this code, and others like it, 2 8 -0 3can accurately reproduce
gross experimental features such as magnetic field, density and temperature
profiles as well as more subtle effects such as neutron emissions, Faraday
rotation, and plasma rotation.
The staged theta-pinch experiment has successfully demonstrated the
