Instability studies of a spherical electrostatic confinement

The spherical inertial electrostatic confinement concept offers an alternative fusion plasma confinement scheme, where charged particles are accelerated and confined electrostatically with a series of biased spherical concentric electrodes. It is very attractive for a power plant due to its mechanical simplicity and high power-to-mass ratio. However, its beam-plasma interactions are not clearly understood. In order to evaluate the concept, a perturbative ($\delta f$) particle simulation technique\footnote{S. E. Parker and W. W. Lee, {\em Phys. Fluids B} {\bf 5}, 77 (1993).} for a kinetic analysis is applied to simulate completely the dynamic evolution of perturbed Vlasov-Poisson equations. This model is used to study the behavior of two-stream-like instabilities related to the trapped spherically converging ions. Results show that steady-state solutions of the self-consistent Vlasov-Poisson equation in which angular momentum of positively charged particle becomes lower correspond to the formation of a deep potential well. Also, it is shown that the growth rates are a decreasing function of angular momentum spread and an increasing function of longitudinal velocity spread.