Non-Maxwellian Electron Distribution Functions in Z-Pinch Plasmas
NAVAL RESEARCH LAB WASHINGTON DC
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The heating and cooling a a z-pinch electron distribution is studied using the Fokker Planck equation. Included in the analysis are the usual Fokker Planck term for distant small-angle electron-electron collisions, a semi- empirical term representing inelastic charge-conserving collisions, ohmic heating by the electric field acting on the current, and compressional heating or cooling. Ions are represented as heavy, highly-charged Maxwellian particles, and electron-ion collisions are given in terms of a Coulomb collision frequency. In deriving the Fokker Planck equation, a first-order Cartesian tensor expansion is performed in a local coordinate system which is spatially uniform and moving with the fluid. The first-order vector term in the expansion is assumed to equilibrate much faster than the zero-order scalar term. Under some conditions, the electron distribution function has an analytic self-similar solution. A numerical time-dependent solution is also obtained, through an implicit finite-differencing scheme. Advantages of a time-dependent model are noted. The behavior of the electron distribution function and conductivity are demonstrated for different parameters. Production of runaway electrons with perpendicular electric and magnetic fields is discussed. Keywords Z pinch dynamics Kinetic theory Conductivity Non equilibrium distributions Runaway electrons.
- Plasma Physics and Magnetohydrodynamics