Covariant Form of the Ponderomotive Potentials in a Magnetized Plasma

Abstract

With use of the Lie transform technique, a simple and compact but quite general expression is derived for the ponderomotive scalar and vector potentials ${\ensuremath{\phi}}^{\mathrm{av}}$ and ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{A}}}^{\mathrm{av}}$ in the covariant form $({\stackrel{\ensuremath{\rightarrow}}{\mathrm{A}}}^{\mathrm{av}},i{\ensuremath{\phi}}^{\mathrm{av}})={{A}^{\mathrm{av}}}_{\ensuremath{\mu}}=\ensuremath{-}\frac{1}{2}〈{F}_{\ensuremath{\mu}\ensuremath{\nu}}{\ensuremath{\zeta}}_{\ensuremath{\nu}}〉$. The four-vector ${\ensuremath{\zeta}}_{\ensuremath{\nu}}$ is the particle excursion in four-dimensional space due to the rf electric and magnetic fields, ${F}_{\ensuremath{\mu}\ensuremath{\nu}}$ is the high-frequency electromagnetic tensor, and the brackets denote an average over the high-frequency phase $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{x}}\ensuremath{-}\ensuremath{\omega}t$.