The two stream instability in the ‘resonance’ model

In this note the problem of stability of two hot collisionless streams of charged particles is considered. The masses, charges, densities, and temperatures are arbitrary and the distribution functions are modelled by one ‘resonance’ function for each stream. The problem of stability is resolved by Nyquist diagrams, and, for the case of equal plasma frequencies, also by solving the dispersion relation in ω. A comparison with two Maxwellians on the one hand, and a two step function model on the other, is given. Step functions appear to be too crude for this problem.