Kinetic Theory for a Dilute Gas of Particles with Spin

Abstract

The kinetic theory of particles with spin previously developed for a LORENTzian gas is extended to the case of a pure gas. In part A the transport (BOLTZMANN) equation for the one particle distribution operator is stated and discussed (conservation laws, Η-theorem). A magnetic field acting on the magnetic moment of the particles is incorporated throughout. In part B the pertaining linearized collision operator and certain bracket expressions linked with this operator are considered. Part C deals with the expansion of the distribution operator and of the linearized transport equation with respect to a complete set of composite irreducible tensors built from the components of particle velocity and spin. Thus, the distribution operator is replaced by a set of tensors depending only on time and space-coordinates. The physical meaning of these tensors (expansion coefficients) is invoked. They obey a set of coupled first-order differential equations (transport-relaxation equations) . The reciprocity relations for the relaxation matrices are stated. Finally a detailed discussion of angular momentum conservation is given.