New technique for the solution of the problem of forced oscillations in a Vlasov plasma

The determination of the space behavior of a plasma under an external time oscillating charge distribution is an important problem in fundamental plasma physics. Within the linearized collisionless Vlasov plasma model, the solution presents a great deal of difficulties, specially from a computational point of view. Several techniques (e.g. the methods of Gould, Derfler-Simonen and Buzzi) have been proposed; they all refer to the application of the space Fourier transform and then they have to tackle the hard problem of the inverse transform of 1/var-epsilon(k,iω), where E(k,iω) is the usual plasma dielectric constant. All these techniques turn out to be very complicate. In this paper an alternative procedure is proposed. It is based on an integro-differential equation. The integro-differential equation can be deduced directly from the Vlasov-Poisson model, without application of the Fourier transform. The equation is handled directly by means of numerical techniques employing spatial finite elements leading to a linear algebraic system of equations to be solved by simple iterative techniques. Physically significant results are presented and discussed. Also the possibility to extend the present procedure to more complicate plasma configurations is considered