A new fast method to solve the dispersion relation in multispecies plasmas

Summary form only given. In this paper a new accurate and fast method for solving the linear dispersion relation for multispecies plasmas is introduced. The method uses a four poles fractional approximation for the Z dispersion function, transforming the dispersion relation into a polynomial form. Time and space growth rates are then calculated. Calculations for a single beam-plasma are carried out being in good agreement with several authors. This method is very effective to simplify the calculation of growth rates in multi-ion plasmas. For multispecies plasmas several new modes of propagation arise. For the two ion beam-plasma system, two slow modes can propagate, both which are unstable. Two maxima in the growth rates corresponding to each of these modes can be excited. The instability of one of the slow modes is fed by the energy of the light ion beam and the other one is fed by heavy beam ions. Each one of these two maxima is increased when the concentration of the corresponding species increases, but even for a small concentration of the light beam, the growth rate of the mode fed by it is the largest one. Because in the single ion beam-plasma system the lighter ion yields the largest growth rate.