Simulation of the two-stream convective instability

A ring/disk model is used in numerical experiments to investigate the two-stream convective instability in a cylindrically symmetric system with finite transverse dimensions. The spatial growth rates obtained in the linear region agree well with the predictions of the linear theory. The development of a vortex structure in velocity-phase space is associated with the saturation of the instability. Generation and amplification of harmonics occur abundantly as expected. The two electron streams exchange kinetic energy over a very short distance and become thoroughly mixed and randomized (thermalized). Due to the choice of geometry, no coherent oscillations are established in the transverse plane, and although they increase, the radial and angular kinetic energies remain much less than the axial.