A comparison of Vlasov with drift kinetic and gyrokinetic theories

TL;DR

This paper compares Vlasov, drift kinetic, and gyrokinetic theories in axisymmetric plasma equilibria, highlighting differences in particle distribution behavior near the magnetic axis and implications for plasma physics modeling.

Contribution

It reveals fundamental differences in particle distribution functions predicted by Vlasov versus reduced kinetic theories near the magnetic axis.

Findings

Vlasov theory predicts non-vanishing distribution functions on axis.

Reduced theories can have vanishing or non-vanishing distributions on axis.

Differences affect current construction and plasma physics interpretations.

Abstract

A kinetic consideration of an axisymmetric equilibrium with vanishing electric field near the magnetic axis shows that del f should not vanish on axis within the framework of Vlasov theory while it can either vanish or not in the framework of both a drift kinetic and a gyrokinetic theories (f is either the pertinent particle or the guiding center distribution function). This different behavior, relating to the reduction of phase space which leads to the loss of a Vlasov constant of motion, may result in the construction of different currents in the reduced phase space than the Vlasov ones. This conclusion is indicative of some limitation on the implications of reduced kinetic theories in particular as concerns the physics of energetic particles in the central region of magnetically confined plasmas.