CGL Invariants and the Moments of the Boltzmann–Vlasov Equation

Abstract

The transport laws of the noncollisional systems must be obtained from the Boltzmann–Vlasov equation. The most simple cases are the CGL invariants along the magnetic field. The essential problem is to determine the criteria necessary to close the moments system. The lower order in the gyration radius expansion gives the perpendicular contribution to the heat flux. After expansion with the supersonic conditions, the parallel contribution is obtained, and also the second term of the expansions in which the first term is the "invariant." The numerical value of the heat flux can be considered in good agreement with the solar wind parameters, and the corrections to the invariants are found to agree with previous results (kinetical and 20-moments Grad approximation).