language: en

ICOPS 97 ICOPS 97

Nonlinear Poisson Solve for Boltzmann Electrons

K. L. Cartwright , J. P. Verboncoeur , and C. K.Birdsall
Electronics Research Laboratory University of California,
Berkeley, CA 94720
October 29, 1997

Abstract Kinetic simulation of plasmas in which equilibrium occurs over ion timescales poses a computational challenge due to the disparate timescales of the electron plasma frequency (~ 10 9 ), the ion plasma frequency (~ 10 7 ), ion transit frequency (~ 10 6 ), and the ionization frequency (~ 10 7 ). Hybrid electrostatic PIC algorithms are presented in which the electrons reach thermodynamic equilibrium with the ions each time step. There are two different approximations for the electrons. First, the nonlinear Boltzmann relationship for the electrons can be applied to the bulk of a plasma. Second, there is a truncated Maxwellian which is used in sheaths; this approximation truncates the electron distribution at the wall potential. The error associated with neglecting this second approximation in the sheath is small. The collision cross section, (E), can be a tabulated or fitted function; the method is implemented with He cross sections. These approximations neglect effects faster than ion time-scales, decreasing the computer time used by over an order of magnitude; however, they increase the complexity of the boundary conditions and the simulation is no longer self-consistent. Theoretical ramifications of these approximations are examined, and results are compared with full

[Supported by ONR-AASERT N100014-94-1-1033 Supported by the Air Force Office of Scientific Research-MURI under grant F49620-95-1-0253 Supported by the Air Force Office of Scientific Research-under grant FDF49620-96-1-0154]