Alternative technique to study the evolution of perturbations in a magnetized collisionless plasma

In a recent paper a new technique has been proposed to study the classical problem of Landau damping in a collisionless unmagnetized plasma. This technique, alternative to the classical one, is based on a time integral equation for the amplitude of the plasma density perturbation. The method is particularly useful to calculate the full evolution of a given initial perturbation. In this work the procedure is extended to magnetized Vlasov plasmas. For an electron plasma, the density perturbation n1(r,t), due to an initial phase space perturbation f1(v)exp(ik · r) can be written as n1(t)exp(ik · r), and n1(t) obeys an integral equation of the type: n1(t) = ∫0t K (t - t')n1(t')dt' + A(t) where the functions K(t) and A(t) depend on the plasma parameters and the external magnetic field; moreover, A(t) is functional of the initial perturbation. The above equation can be solved analytically in simple cases or numerically in more general cases. Results for situations of special physical interest will be presented and discussed