Algebraic method to analyse the ion-beam plasma instability in quasineutral plasma

Summary form only given, as follows. In this paper we present a method for solving the dispersion relation in the ion-beam plasma system for the quasineutral regime where we perform a transformation of the dispersion relation using a multipolar and very accurate approximation of the Z dispersion function obtaining a polinomial form easier to solve than other methods currently presented in the literature. In order to obtain the dispersion relation in the one dimensional quasineutral ion-beam plasma system, we use in a global sense, quasineutral fluid techniques in order to describe the electrons and the ambipolar field to avoid the use of the Poisson equation. Kinetic treatment and a Maxwellian distribution function are used for ions. Calculations for a single beam-plasma system are carried out and time and space growth rates are obtained (a multi beam-plasma system can also be analysed). This kind of treatment is very relevant to simulate such systems via PIC methods.