Transverse beam temperature effects on mixed Two-Stream/Filamentation unstable modes

We investigate transverse beam temperature effects on the coupling between Two-Stream and Filamentation instabilities for an electron beam passing through a hot plasma with return current. By denoting θ k , the angle between the wave vector and the beam, transverse beam temperature effects are important for θ k larger than a critical angle θ c which can be determined exactly, the resulting effects being a damping of the instabilities. On the other hand, effects are small for θ k < θ c . In particular, the absolute maximum growth rate is found for a wave vector in this region and is therefore not damped by transverse beam temperature.