Spherical-harmonics decomposition of the Boltzmann equation for charged-particle swarms in the presence of both electric and magnetic fields

Journal Article · Fri Jan 01 04:00:00 EST 1993 · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States)

DOI:https://doi.org/10.1103/PhysRevE.47.327· OSTI ID:6306574

Ness, K F ^[1]

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1. Physikalisches Institut der Universitaet Heidelberg, Philosophenweg 12, D-6900 Heidelberg (Germany)

The Boltzmann equation for reacting charged-particle swarms in neutral gases in the presence of both electric and magnetic fields is decomposed into a hierarchy of kinetic equations by expanding the velocity dependence of the phase-space distribution function in terms of spherical harmonics. No limit is set on the number of spherical harmonics and no approximation is made concerning the mass of the charged particles related to that of the neutrals species. The space-time dependence is treated by making the hydrodynamic assumption which is taken to second order in density gradients. Spherical tensors are used throughout. The resulting heirarchy of equations has universal validity and is amenable to a range of numerical solutions. The structure of these equations is discussed and the inadequacies of a Legendre-polynomial expansion are pointed out. The special configurations of the magnetic field parallel and perpendicular to the electric field are discussed in detail.

• OSTI ID: 6306574
• Journal Information: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States), Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States) Vol. 47:1; ISSN 1063-651X; ISSN PLEEE8
• Country of Publication: United States
• Language: English

Related Subjects

661300* -- Other Aspects of Physical Science-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOLTZMANN EQUATION
CALCULATION METHODS
CHARGED-PARTICLE TRANSPORT
DIFFERENTIAL EQUATIONS
ELECTRIC FIELDS
EQUATIONS
FLUIDS
GASES
KINETIC EQUATIONS
MAGNETIC FIELDS
MATHEMATICAL SPACE
PARTIAL DIFFERENTIAL EQUATIONS
PHASE SPACE
RADIATION TRANSPORT
SPACE
SPHERICAL HARMONICS METHOD