Island Stability in Phase Space

Starting with a conventional bump on tail problem, which is equivalent to finding a solution of the Vlasov/Fokker-Planck equation in the presence of the phase space island, we obtain a primary equilibrium state. The stability of this state is investigated as a function of the effective velocity-space drag and diffusion, as well as the width of these phase space islands. The secondary instabilities have been found in a certain range of plasma parameters and wave numbers. Solving the full Vlasov/Fokker-Planck - Poisson system, we obtain the dispersion function, which provides information about the secondary mode onset and allows an estimate of the secondary mode growth rate for different input plasma parameters.