Kinetic theory of a nonequilibrium
plasma: Evaluation of the vectorized collisional Boltzmann
equation
-
Ann W. Morgenthaler
and
Peter L. Hagelstein
-
Department of Electrical Engineering and Computer Science,
Massachusetts Institute of Technology, 38-280, 77
Massachusetts Avenue, Cambridge, Massachusetts 02139
(Received 22 June 1992;
accepted 15 January 1993)
Cartesian
velocity moments of the Boltzmann equation are evaluated using
modal solutions to the spherical harmonic oscillator
as a basis set. The nonlinear collision matrix
describing the interaction between any two modes is
evaluated analytically for the Landau collision operator, and
matrix elements describing collisions between identical
particles are calculated for some pairs of
azimuthally symmetric modes. First-order linear transport
coefficients calculated directly from collision
matrix elements are shown to agree
exactly with previously published results; coefficients of
thermal conductivity and viscosity are computed much
more accurately by trivially extending this
calculation. Relaxation times for self-collisions in a
two-dimensional linearized plasma are also computed,
indicating that the plasma equilibrates in roughly
one to ten times the Spitzer self-collision time. The results
obtained in this paper are useful for both analytic and
numerical simulations of nonequilibrium plasmas and an
explicit six-moment model for a one-component
azimuthally symmetric plasma is given. Physics of Fluids B:
Plasma Physics is copyrighted by The American Institute of
Physics.
|
