On the relativistic Vlasov equation in guiding-centre coordinates

There is a considerable literature on the wave-particle interactions where the response of electrons is described by nonlinear Vlasov equation expressed in guiding-center coordinates in hot and magnetized plasmas (Liu and Tripathi 1986). However, with the advent of high-power sources of radiation, such as, high-power lasers and radio-frequency (rf) generators the relativistic effects are seen to play an important role (Shukla et al 1986). In this note, the fully relativistic Vlasov equation is described in terms of guiding-center coordinates, where the finite Larmor radius effects become important and expressions for the linear response of electrons corresponding to large-amplitude electrostatic and electromagnetic incident waves (pumps) in a hot magnetized plasma are obtained. (author)