Analysis of the evolution of perturbations in a magnetized collisionless plasma with an integral-equation technique

Summary A technique recently proposed to study the classical problem of the evolution of small perturbations in a collisionless unmagnetized plasma is extended to a magnetized plasma. A time-convolutive integral equation for the plasma density is obtained from the Vlasov equation for a homogeneous plasma in a uniform, stationary magnetic field. The equation can be solved by means of simple numerical algorithms and, in some cases, analytical solutions can be obtained. The procedure proves to be analytically simpler than the classical one and is more convenient from a numerical point of view. Techniques of solution are presented and analytical and numerical results for electrostatic perturbations are discussed.