Investigation of ion beam neutralization processes with 2D and 3D PIC simulations

Abstract

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 (PIC) codes. We investigate both the early “filling” 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.

Introduction

Ion beam neutralization during operation of electric propulsion devices requires both current and charge density matching with an emitted electron beam. We describe the phenomenon as “current coupling” and note that it is easily accomplished in practice, yet the exact process remains unknown. Currently the neutralization process is described through an “effective collision frequency” that binds electrons to the ion beam. As electric propulsion becomes more prevalent in space missions, this question is of significant importance. Proper modeling of current coupling and neutralization will enable development of low-current neutralizers and optimization of neutralizers for micropropulsion devices. Explanation of the effective collision frequency also has bearing on space instrument calibration, electrodynamic tethers, and ionospheric research.

In the early years of electric propulsion research, the ion beam neutralization question was one of the fundamental issues for successful development of this promising technology. A dense ion beam requires space charge neutralization to avoid a potential barrier that can divert or reflect the beam. The vehicle on which the thruster operates needs current-neutrality to avoid excessive charging. In the context of collisionless plasma theory, achieving both current and charge neutrality with the same source of electrons appears to be nearly impossible owing mostly to the large difference in mass between electrons and the ions. For example, define the ion flux, F_i=N_iv_i and the net electron flux, F_e=1/4N_ev_et where N is density, v_i is the ion drift velocity, and v_et is the electron thermal velocity for a simple effusion model. Achieving both equal density and flux requires v_et=4v_i. For example, a 1-keV Xenon beam has v_i=38,000 m/s so a matching electron velocity requires a source temperature of about 0.05 eV; a challenging, but not impossible number. Replacing this simple electron effusion assumption with an injected distribution does not change the misleading picture of a precise balance requirement. A higher temperature, lower density electron source will lead to a positive potential well that does trap electrons, but then the theory must explain by what process the trapped electrons shed energy so as to actually fill the well. Another observation is that when ion beams and neutralizers are operated in conducting vacuum tanks, the currents are closely coupled even though the grounding tank eliminates the charge accumulation that could provide feedback for current balance so it appears that one or more plasma mechanisms must be responsible for current coupling.

Possibly first pointed out by L. Spitzer in 1952 [uncited note in Seitz et al., 1961], electric propulsion plumes needed to be properly mixed with electrons or else severe space-charge effects would result. Before the first space tests, there were serious doubts as to the stability of any neutralization approach to the ion beam created by an electrostatic thruster. The general idea was for neutralization to occur shortly after emission to prevent beam return. However, there was lack of understanding as to how the electrons would stay within the beam if they were injected or if the neutralization process was unstable to small perturbations. Failing to properly neutralize the beam would cause a dramatic reduction in thrust, as a significant portion of the beam would return to the spacecraft. This problem was first addressed by the Ramo-Wooldridge Staff in their review of electrostatic propulsion in 1960 [1]. Their one-dimensional investigation was admittedly unrealistic enough to provide a satisfactory indication as to the stability and practicality of neutralization.

Over the next few years, many theorists who looked at 1- and 2D models predicted growing instabilities that could turn the beam back to the spacecraft. Some findings pointed towards the possibility of neutralization, such as French's [2] finding that oscillations in electron current density aided in neutralization or Mirels [3] in 1961, who found that emitter location and thermal electrons motion would not significantly impact beam neutralization. Others pointed towards potential problems, such as Seitz et al. [4] who noted that, if electrons were left to drift into the exhaust beam from a stationary start outside of it, the center of the beam would still develop a virtual cathode and suffer from thrust reduction. Some of the earliest computational studies were brought to bear on the problem, and Buneman and Kooyers [5], using a one-dimensional PIC code in 1963 were able to provide a neutralized beam when electrons were injected at velocities lower than the directed ion velocity. Fluctuations in the space charge field provided mixing of the beam. Two years later Wadhwa et al. [6] performed a two-dimensional PIC simulation showing that electrons would oscillate within the beam to allow for neutralization, but theorized that oscillations was not the only mechanism at work. One method suggested was that fluctuations in the space-charge field allowed for entropy increase to mix the electrons, but these fluctuations were not found downstream of the neutralizer.

The 1964 Space Electric Rocket Test I (SERT I) found that it was quite easy to neutralize ion beams in space from a simple neutralizer geometry. In a series of tests it was shown that the ion thruster developed thrust at a level indicating complete beam neutralization. After SERT I, proof of concept was achieved and the theoretical discussion of beam neutralization was dropped in favor of engineering new thrusters. Studies after SERT I include evaluations of neutralizer placement [7], [8], optimization of the thrusters, and simulations to analyze spacecraft-plume interactions [9], [10]. A few numerical simulations of neutralization have been performed recently, including Othmer et al. [11], [12], [13] using a relativistic 3D PIC simulation and Tajmar and Wang investigating FEEP neutralizer placement [7]. Neither proposed a solution to the mechanism of current coupling.

Despite decades of research and the implementation of electric propulsion devices, the detailed process by which an ionized beam is neutralized in space is still unknown. Assorted methods to fit data with theory have been found, but the actual process has yet to be studied in sufficient detail to fully understand the subject. Further, new electric micropropulsion devices such as the FEEP or the colloidal thrusters or large arrays of ion and Hall thrusters are still not guaranteed to behave. We might also desire a means to predict and optimize neutralizer operations. Thus, a simulation technique exhibiting beam coupling is needed. Additionally, results from ion beam neutralization modeling will be applicable to ion beams for instrument calibration, electrodynamic tethers, ionospheric research, and fundamental plasma physics.

Our immediate goal is to determine if a standard Particle-In-Cell, PIC, technique is adequate or if additional treatment is needed to understand and capture the current coupling process. We present a series of simulations using a 2D PIC code [14], [15], [16] as well as a 3D PIC/DSMC code [17], [18]. These simulations show the dependence of the beam neutralization on beam energy and neutralization current during the initial “filling” problem and the lack of coupling in the steady-state problem. The simulations presented in this paper serve also as means of validation of the PIC-modules of the 3D PIC/DSMC code under development.