| 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. The inertia of the accelerated ions compresses the ions and builds up the space charge at the center of the cathode grid. The space charge of the ions attracts electrons which in turn accumulate a space charge. The accumulation of collective space charge creates a series of deep "virtual" electrostatic potential wells which confine and concentrate ions into a small volume where an appreciable number of nuclear fusion reactions could occur. 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 inertial electrostatic confinement concept, it is essential to develop a reliable and flexible instability analysis method for an equilibrium plasma in a potential well. Subsequently stability of this well can be studied. As a part of this study, methods are sought to avoid or suppress any destructive instabilities. Methods to be explored include modification/control of the well profile, control of the electron to ion beam density ratio, control of the angular momentum of the beam, etc. For this purpose, a perturbative (deltaf) particle simulation techniques for a kinetic analysis is applied to simulate completely the dynamic evolution of perturbed Vlasov-Poisson equations and, in addition, to achieve much more accurate simulations of the nonlinear dynamics using less simulation particles compared to conventional particle-in-cell method. 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. |
