Covariant form of the ponderomotive potentials in a magnetized plasma

With use of the Lie transform technique, a simple and compact but quite general expression is derived for the ponderomotive scalar and vector potentials phi-bar and A in the covariant form (A,iphi-bar)=A-bar/sub μ/=-1/2. The four-vector zeta/sub ν/ is the particle excursion in four-dimensional space due to the rf electric and magnetic fields, F/sub munu/ is the high-frequency electromagnetic tensor, and the brackets denote an average over the high-frequency phase kxx-ωt