Conservation laws and exact solutions of the Boltzmann equation
The distribution function f which satisfies the time-dependent Boltzmann equation (BE) for a Lorentz model with perfectly elastic random scatterers is proved nonnegative, and is computed exactly when backscattering dominates. Joule heating and Ohm's law are recovered, although f has no steady-state limit, contrary to the relaxation-time approximation. (The conventional approximation to the time-independent BE also yields OHm's law but not the Joule heating and, worse, it unphysically predicts f < O.) The exact solution is compared with various effective-temperature approximations, and is shown to remain very nearly unchanged over a wide range of times even in the presence of a small amount of inelastic scattering.
- Research Organization:
- Utah Univ., Salt Lake City, UT (USA). Dept. of Physics
- OSTI ID:
- 5977112
- Journal Information:
- Mod. Phys. Letters B; (United States), Journal Name: Mod. Phys. Letters B; (United States) Vol. 3:3; ISSN MPLBE
- Country of Publication:
- United States
- Language:
- English
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71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BACKSCATTERING
BOLTZMANN EQUATION
COMPUTER CALCULATIONS
CONSERVATION LAWS
DIFFERENTIAL EQUATIONS
DISTRIBUTION FUNCTIONS
ELASTIC SCATTERING
ELECTRIC HEATING
EQUATIONS
FUNCTIONS
HEATING
INELASTIC SCATTERING
JOULE HEATING
LIE GROUPS
LORENTZ GROUPS
LORENTZ TRANSFORMATIONS
PARTIAL DIFFERENTIAL EQUATIONS
PLASMA HEATING
POINCARE GROUPS
RESISTANCE HEATING
SCATTERING
SYMMETRY GROUPS
TIME DEPENDENCE
TRANSFORMATIONS