Magnetohydrodynamic simulation of dynamical behavior of a field-reversed
configuration during magnetic mirror reflection
T. Kanki
a)
Japan Coast Guard Academy, 5-1 Wakaba, Kure, Hiroshima 737-8512, Japan
S. Okada and S. Goto
Plasma Physics Laboratory, Graduate School of Engineering, Osaka University, 2-1 Yamada-oka, Suita,
Osaka 565-0871, Japan
͑Received 22 November 2002; accepted 19 June 2003͒
A two-dimensional magnetohydrodynamic ͑MHD͒ simulation of the reflection dynamics of a
field-reversed configuration ͑FRC͒ plasma is performed by numerically modeling a confinement
region of the FRC Injection Experiment ͓H. Himura et al., Phys. Plasmas. 2, 191 ͑1995͔͒ machine.
The FRC plasma is reflected by a downstream magnetic mirror field at the end of the confinement
region without severe destruction of the closed magnetic flux surfaces even when injected at
supersonic velocity into the magnetic mirror region, showing the robustness of the FRC against
external perturbations. By examining the details of FRC motion, it is also predicted for any
translation velocities that the FRC might eventually settle down in the confinement region and
approach a MHD equilibrium condition. Interestingly, it is observed that the formation of a
discontinuous wave front is caused by a shock when the FRC at supersonic velocity is reflected by
the magnetic mirror. © 2003 American Institute of Physics. ͓DOI: 10.1063/1.1600735͔
I. INTRODUCTION
A field-reversed configuration ͑FRC͒
1
is an extremely
high-

, elongated compact toroid which ideally has no tor-
oidal magnetic field. The plasma is confined principally in-
side a separatrix by a poloidal magnetic field. A FRC can be
translated axially since it is not linked by material objects.
Axial translation has offered an attractive and essential in-
gredient in present experiments as well as an engineering
convenience in D–
3
He fueled FRC fusion reactor studies
2
in
which the start-up, heating, and burn chamber section can be
physically separated. The establishment of controlled, stable
FRC translation is important in present FRC studies to im-
prove confinement time and to realize the steady state of the
FRC plasma. Recently, sustainment and additional heating
experiments by neutral beam injection
3
and applications of a
low frequency magnetic pulse
4
and a rotating magnetic field
5
have been performed intensively. As an adjunct to these in-
vestigations, numerous experiments of translation
6–10
have
been carried out.
In the translation experiment using the FRC Injection
Experiment ͑FIX͒ machine
9,10
at Osaka, FRC plasma is pro-
duced by a field-reversed theta-pinch method in a source
region, and is injected into an adjacent confinement region
with magnetic mirror fields at either end. The injected FRC
moves along the magnetic field of the confinement region at
supersonic velocity. Subsequently, the FRC is reflected by
the downstream magnetic mirror ͑first reflection͒. The re-
flected FRC moves back toward the source region and is
reflected by the upstream magnetic mirror ͑second reflec-
tion͒. It eventually settles down the center of the confinement
region without severe confinement degradation. As a result,
FRC translation has been successfully achieved. However,
this demonstration of FRC translation is based on empirical
adjustments of the strength of the confining magnetic field.
Specifically, it is observed in the first reflection from the
downstream mirror that the separatrix radius of the FRC ex-
pands excessively when the confining field is reduced, and
that more energy of the translated FRC is lost in a case where
the translation velocity is larger and the magnetic mirror ra-
tio is smaller. The details concerning how such a reflection
process works remain unclear. Also, in the translation pro-
cess, so far, it is difficult to control FRC motion externally.
In regard to the establishment of controlled, stable FRC
translation, important questions exist concerning FRC reflec-
tion: ͑1͒ Can the closed flux surfaces of the FRC be retained
during the reflection process? ͑2͒ How can the magnetic mir-
ror play a role in the motion of the FRC? ͑3͒ How is the
behavior of the FRC dependent on translation velocity? In
the future we expect to control the motion of the FRC exter-
nally using the basic properties of the behavior during reflec-
tion outlined here.
In order to answer the questions stated above, we inves-
tigate the fundamental physics of the reflection dynamics of
a FRC plasma by means of an axisymmetric numerical simu-
lation. In this paper, we will focus our attention on the dy-
namical behavior of the poloidal flux contours and the
plasma pressure distributions. In addition, we explore the
effects of the magnetic mirror field on FRC plasmas. For this
purpose, we have modified a two-dimensional magnetohy-
drodynamic ͑MHD͒ simulation code.
11,12
In Sec. II, we de-
scribe our simulation model. In Sec. III, simulation results
are presented. On the basis of the results, the effects of trans-
lation velocity are given in Sec. IV. Finally, a summary and
conclusions are described in Sec. V.
a͒
Electronic mail: kanki@jcga.ac.jp
PHYSICS OF PLASMAS VOLUME 10, NUMBER 9 SEPTEMBER 2003
36351070-664X/2003/10(9)/3635/9/$20.00 © 2003 American Institute of Physics