A kinetic approach to the Ponderomotive Force

[1] It has been suggested that Magnetic Holes ( MHs) are caused by perpendicular proton energization due to the Ponderomotive Force ( PF) associated with phase steepened Alfven waves. Here we include particle finite Larmor radius ( FLR) effects and the effects of ion gyroharmonics in the PF expression. The general expression for the PF is derived by using the hot plasma dielectric tensor from kinetic theory. The fully kinetic expression has a multiple resonance character which is not revealed in the fluid picture. It will be shown that by including such effects, the expression for the PF will be significantly altered, both at the low frequency and high frequency limit. Also, an explicit analytic expression for the PF keeping only the first order FLR terms is given for conceptual purposes for the readers.