Lagrangian Formulation of a Consistent Relativistic Guiding Center Theory

Abstract

A new relativistic guiding center mechanics is presented that conserves energy (in timeindpendent Fields) and satisfies a Liouville's theorem. The theory reduces to Littlejohn's theory in the non-relativistic limit and agrees to leading orders in ε ≡ rg/L with the relativistic theory by Morozov and Solov'ev (which generally lacks a Liouville's theorem). The new theory is developed from an appropriate Lagrangian and is supplemented by a collisionless relativistic kinetic equation for the guiding centers. Moment equations for guiding center density and energy density are also derived