Development of implicit kinetic simulation methods, and their application to ion beam propagation in current and future neutralized drift compression experiments

Ion beams can be accelerated and focused to hit a target thus releasing high density power to achieve nuclear fusion. They can also be used to study phase transition from the solid to the Warm Dense Matter state. The Neutralized Drift Compression Experiment (NDCX) at the Lawrence Berkeley National Laboratory is being used to investigate the possibility of developing drivers for the heavy ion fusion reactors, and for Warm Dense Matter experiments. Because ion beams are positively charged, repulsive forces act on the beam ions. These electrostatic forces defocus the beam, increasing the beam size and degrading the applied compression and focus. Electrons are introduced via a preformed plasma to eliminate the electrostatic forces that defo- cus the beam in the NDCX. The spread of the background plasma electrons inside the beam, and the adjustment of their velocity to the beam propagation velocity is called neutralization process. Because collisions occur on time scales much larger than the time scales for the neutralization process, the plasma can be considered collision-less. Thus, the neutralization process is dominated by plasma-wave interactions instead of collisions, and the kinetic approach is required to model this phenomenon. In this dissertation, the neutralization process in the NDCX configuration is stud- ied. The collision-less kinetic equations of plasma are solved numerically using two implicit Particle-in-Cell methods. The implicit nature of the time-differenced gov- erning equations leads to unconditional numerical stability. The primary numerical scheme is based on an implicit moment Particle-in-Cell approach. It has been devel- oped for the electromagnetic case and implemented in a 3D, parallel code to study the neutralization process. In addition, a fully implicit Particle-in-Cell method to solve the particle and field equations has been also developed and implemented for a simple one dimensional, electrostatic configuration. The goal of the fully implicit scheme was to demonstrate that a fully implicit scheme can indeed converge as it has been a challenge. It has been demonstrated that fully implicit schemes (at least 1D, electrostatic configuration) can in fact converge. The schemes developed and implemented are used extensively to study the neutralization dynamics. The aim of this study is to analyze the dynamics that governs the neutralization process in the NDCX configuration. It has been found that the neutralization is a transient phenomenon, typically occurring on time scales of tens of plasma periods. During this transient, the ion beam undergoes through large electron oscillations. The oscillations are damped by a sheath. This sheath regulates the electron flux into and out of the beam, and because it opposes the electron oscillations, it also oscillates. The forward moving and oscillating sheath persists after the transient, and forms an oscillating shock at the front of the ion beam. The shock is in the form of a moving and oscillating discontinuity in the electric field, the charge density, and the electron average velocity. It has been found that the background plasma and beam densities influence the neutralization process, changing the properties of the sheath at the beam-plasma interface. The damping of the oscillations is important when the background plasma and beam densities are close in value, while it is weaker when the background plasma density is higher than the beam density. Moreover, the magnetic field does not have a significant effect on the ion beam neutralization process in the current and future NDCX configurations, and the simulations can be carried out in the electrostatic limit, achieving the same results as those obtained using electromagnetic simulations. A comparison of the implicit Particle-in-Cell methods with the explicitly time differenced Particle-in-Cell method shows that the implicit moment and the fully im- plicit Particle-in-Cell methods are on average 4 to 40 times computationally more expensive if the same simulation time step is used. Because the ion beam neutral- ization process in the NDCX occurs on the plasma period time scales and on the Debye length spatial scales, these scales need to be resolved to correctly describe the neutralization phenomenon. Because of these constraints on the time step and the grid spacing, the implicit Particle-in-Cell methods are here used on space and time scales where the explicit Particle-in-Cell method is numerically stable, hence denying the advantage that implicit methods have over explicit schemes. However, it is clear that implicit schemes are more efficient for problems that allow large time steps