Numerical calculation based on multipole expansions was used to study the linear instability in a DP machine

Experiments to excite ion acoustic instability in ion beam plasma system have been carried out during the last years. Numerical studies to characterize these phenomena based on the wavelengths and growth rates of the linear instability are in good agreement with the observations. In this paper we report the effect produced by addition of impurities in the system and analyzing this via the solution of the dispersion relation of the electrostatic mode with the impurity term. To solve the resulting equation we use the multipole expansion for the dispersion relation of Martin and Gonsalez to get an expression easier to work numerically. In order to follow the evolution of this region versus the concentration of the impurity as parameter and observing the change of the growth rate of the most unstable mode. In the case of no impurity we compare our results with those obtained by G. Bonhomme et al. (author) 7 refs., 3 figs