Derivation of a generalized Boltzmann type kinetic equation
Abstract
A quasiclassical approximation for the amplitude of particle scattering in a medium is analyzed, which depends on the total momentum of the colliding particles, and which statistically and correctly describes diffraction effects during forward scattering. With the aid of this approximation the KadanovBeim (1964) equations can be considerably simplified, and a generalized kinetic equation is obtained for the distribution function with generalized selfconsistent field, which is determined from the amplitude of forward scattering in the medium. Corresponding transport equations have a general form, although the hydrodynamic quantities appearing in them take into account correlations in the medium. An eikonal Tapproximation enables representing them in the form of the sum of a term corresponding to an ideal gas and a term for the correlation correction. A procedure is developed for solving the resulting equation, which yields nonlocal solutions taking into account delay.
 Publication:

Leningradskii Universitet Vestnik Matematika Mekhanika Astronomiia
 Pub Date:
 July 1976
 Bibcode:
 1976VeLen.......66D
 Keywords:

 Boltzmann Transport Equation;
 Kinetic Equations;
 Particle Collisions;
 Real Gases;
 Self Consistent Fields;
 Eikonal Equation;
 Gas Density;
 Operators (Mathematics);
 Scattering Amplitude;
 Fluid Mechanics and Heat Transfer