WAVE-EQUATIONS FOR A RELATIVISTIC MAGNETOPLASMA

The linearized relativistic Vlasov-Maxwell system for a hot inhomogene ous relativistic magnetized electron plasma is studied through particl e orbit theory using the techniques of Fourier transform. An analytica l integral expression in the (k, omega)-space is obtained for the curr ent density for waves propagating across an externally applied uniform static magnetic field (k is the wavenumber and omega is the wave freq uency). After applying inverse Fourier transform, differential equatio ns for the electric field are obtained from the expression for the cur rent density combined with Maxwell's equations. These fully relativist ic equations are correct up to second order in r(c)/L, where r(c) is t he electron gyroradius and L is the gradient length of the plasma inho mogeneity.