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VOLUME 6, NUMBER 5
Plasma simulation studies using multilevel physics models*
W. Parka, a) E. V. Belova, G. Y. Fu, and X. Z. Tang
Princeton University Plasma Physics Laboratory, Princeton, New Jersey
H. R. Strauss
New York University, New York, New York
L. E. Sugiyama
Massachusetts Institute of Technology, Cambridge, Massachusetts
(Received 17 November 1998; accepted 14 January 1999)
The question of how to proceed toward ever more realistic plasma simulation studies using ever
increasing computing power is addressed. The answer presented here is the M3D (Multilevel 3D)
project, which has developed a code package with a hierarchy of physics levels that resolve
increasingly complete subsets of phase-spaces and are thus increasingly more realistic. The rationale
for the multilevel physics models is given. Each physics level is described and examples of its
application are given. The existing physics levels are fluid models (3D configuration space), namely
magnetohydrodynamic (MHD) and two-fluids; and hybrid models, namely
gyrokinetic-energetic-particle/MHD (5D energetic particle phase-space), gyrokinetic-particle-ion/
fluid-electron (5D ion phase-space), and full-kinetic-particle-ion/fluid-electron level (6D ion
phase-space). Resolving electron phase-space (5D or 6D) remains a future project.
Phase-space-fluid models are not used in favor of 8f particle models. A practical and accurate
nonlinear fluid closure for noncollisional plasmas seems not likely in the near future. 1999
American Institute of Physics. [S1070-664X(99)93005-7]
For the study of magnetized plasmas, as for other scien-
tific research areas, three complementary tools are available:
experiment, analytic theory, and numerical simulation. In re-
cent years, as computers become ever more powerful, the
importance of numerical simulation is widely being recog-
nized and promoted. However, how to proceed toward ever
more realistic simulation studies as computing power in-
creases is an important question to be answered. In this pa-
per, we present our answer to this question in the context of
magnetic confinement fusion research.
Simulation of plasmas presents many difficulties. It is a
numerically stiff problem, since plasma behavior contains
wide ranges of length and time scales, e.g., the resistive time
scales of present day large fusion experiments are on the
order of seconds, while the ion and electron cyclotron peri-
ods are on the order of nanoseconds and picoseconds, respec-
tively. It is also strongly anisotropic, e.g., heat conduction
along magnetic field lines is more than 1010 times larger than
that across field lines. Moreover, velocity space effects, such
as wave-particle resonances, are often important due to in-
These and other difficulties preclude the possibility of
simulations including all the relevant physics, at least for the
near future. Approximate models are therefore used, and
more and more realistic studies should be performed as com-
putational capabilities and the understanding of plasmas in-
*Paper K6I1.6 Bull. Am. Phys. Soc. 43, 1810 (1998).
')Electronic mail: email@example.com
crease. Most current 3D (three dimensional) simulations are
global simulations using the MHD (magnetohydrodynamic)
model, which assumes collisional plasmas, or turbulence
simulations using the electrostatic approximation where per-
turbed magnetic fields are neglected.
To determine the best strategy for more realistic simula-
tions, we note that the key factor that determines the degree
of realism and also the corresponding computational require-
ments is the phase-space resolved in the simulation. Thus,
multilevel physics codes which resolve increasingly larger
phase-spaces and are thus increasingly more realistic, can be
built, and higher levels can be added as computing capabili-
ties increase. Each existing physics level is also useful, be-
cause lower levels with less phase-space resolved are com-
putationally more efficient, and more importantly, because
higher level results with more complex physics must be com-
pared to lower level results for the delineation of physics and
to ascertain the basic validity of the higher level results.
Thus, in the M3D (Multilevel 3D) Project,' we have
built a code package which solves a hierarchy of physics
levels with increasing realism. The existing physics levels
which have been used in applications are fluid models (3D
configuration space), namely MHD2 and two-fluids;3 and hy-
brid models, namely gyrokinetic-energetic-particle/MHD4'
(5D energetic particle phase-space), gyrokinetic-particle-
ion/fluid-electron6 (5D ion phase-space), and full-kinetic-
particle-ion/fluid-electron level (6D ion phase-space). At the
present, electrons are described by fluid models only, be-
cause resolving electron phase-space (5D or 6D) at the level
of the electron inertial length (skin depth) is not yet feasible
@ 1999 American Institute of Physics
PHYSICS OF PLASMAS
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Park, W.; Belova, E.V. & Fu, G.Y. Plasma simulation studies using multilevel physics models, report, January 19, 2000; Princeton, New Jersey. (digital.library.unt.edu/ark:/67531/metadc704449/m1/1/: accessed September 24, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.