While it is common knowledge that ion beams are easily neutralized for both current and charge density using a variety of means, the precise process of neutralization remains unknown. With the increasing importance of electric propulsion, and in particular micropropulsion systems, this question is of significant importance. Additionally, it has bearing on thruster design, space instrument calibration, electrodynamic tethers, and ionospheric research. A review of the present state of knowledge on this topic is presented as well as results from ion beam simulations using 2D and 3D Particle-in-Cell (PlC) codes. We investigate both the early "filing" problem of the beam starting to move away from the spacecraft and the steady state problem where the beam encounters a wall at an infinite distance from the spacecraft.

While it is common knowledge that ion beams are easily neutralized using a variety of means, the precise process of neutralization remains unknown. With the increasing popularity of electric propulsion, and in particular micropropulsion systems, this question is of significant importance. Additionally, it has a bearing on thruster design, space instrument calibration, electrodynamic tethers, and ionospheric research. A review of the present state of knowledge on this topic is presented as well as results from ion beam simulations using 2D and 3D Particle-in-Cell codes. The grid generation methodology, adaptation, charged-particle transport, and field solver methodologies of the 3D code are reviewed. The simulations show electrons moving to neutralize the ion beam from background and neutralizer sources. The simulations show the dependence of neutralization on beam energy and the electron/ion velocity ratio. The results are compared favorably with previous computations and experimental observations.

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.

The fact that ion beams readily neutralize given a source of electrons is well known, but the physics behind that process is not. As electric propulsion devices move into the micro and macro regions with colloids, FEEPs, and large arrays of thrusters, the interactions between the neutralizer and the thruster are under examination. Simulations using 2D and 3D Particle-in-Cell (PIC) codes are presented, detailing starting and steady state interactions between an ion beam and an electron beam. It is shown that the starting conditions require detailed current coupling to propagate normally. Steady state simulations show robust behavior regardless of ion or electron currents. Further investigation of steady state reveals no mechanism for imparting ion beam bulk velocity to electrons.

The Neutralized Transport Experiment (NTX) at Lawrence Berkeley National Laboratory has been designed to study the final focus and neutralization of high perveance ion beams for applications in heavy ion fusion (HIF) and high energy density physics (HEDP) experiments. Pre-formed plasmas in the last meter before the target of the scaled experiment provide a source of electrons which neutralize the ion current and prevent the space-charge induced spreading of the beam spot. NTX physics issues are discussed and experimental data is analyzed and compared with 3D particle-in-cell simulations. Along with detailed target images, 4D phase-space data of the NTX at the entrance of the neutralization region has been acquired. This data is used to provide a more accurate beam distribution with which to initialize the simulation. Previous treatments have used various idealized beam distributions which lack the detailed features of the experimental ion beam images. Simulation results are compared with NTX experimental measurements for 250 keV K ion beams with dimensionless perveance of 1-7 x 10−4. In both simulation and experiment, the deduced beam charge neutralization is close to the predicted maximum value.