AG 2 - 13590 AIAA - 2002 - 0487 Hall Thruster Far Field Plume Modeling And Comparison to Express Flight Data

Hall thrusters are an attractive form of electric propulsion that are being developed and implemented to replace chemical systems for many on orbit propulsion tasks on communications satellites. One concern in the use of these devices is the possible damage their plumes may cause to the host spacecraft. Computer models of Hall thruster plumes play an important role in integration of these devices onto spacecraft as the space environment is not easily reproduced in ground testing facilities. In this paper, a hybrid particle-fluid model of a Hall thruster plume is applied to model the SPT-100 thrusters used on the Russian Express satellites. The emphasis of the paper is on making assessment of the model through direct comparison with measurements of ion current density and ion energy distributions taken on board Express spacecraft. These data challenge the model in two ways. First, they represent the first set of Hall thruster plume measurements obtained in space, whereas the computer models have been developed based on measurements taken in ground-based facilities. Second, most of the data measurement locations are several meters from the thruster requiring careful consideration of the plume far-field. Introduction Hall thrusters are under development in several countries including the United States, Russia, Japan, and France. These electric propulsion devices typically offer a specific impulse of about 1,600 sec and a thrust of about 80 mN. These characteristics make them ideally suited for spacecraft orbit maintenance tasks such as north-south station keeping. Under typical operating conditions, at a power level of about 1.5 kW, a voltage of 300 V is applied between an external cathode and an annular anode. The electrons emitted from the cathode ionize the xenon propellant efficiently aided by magnetic confinement within an annular acceleration channel (creating an azimuthal Hall current). The ions are accelerated in the imposed electric field to velocities on the order of 17 km/sec. New classes of Hall thrusters are being developed at low power (100 W) for use on micro-spacecraft, and at high power (25 kW) for spacecraft orbit-raising. As with any spacecraft propulsion device (chemical or electric), computer modeling is used to assess any interactions between the plume of the thruster and the host spacecraft. In the case of Hall thrusters. * Associate Professor. Department of Aerospace Engineering. Senior Member AIAA 1 (c)2002 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization. there are three particular spacecraft integration issues: (1) the divergence angle of these devices is relatively large (about 60 deg) leading to the possibility of direct impingement of high energy propellant ions onto spacecraft surfaces that may result in sputtering and degradation of material properties. Material sputtered from spacecraft surfaces in this way may ultimately become deposited on other spacecraft surfaces such as solar cells, causing further problems; (2) back flow impingement of ions caused by formation of a charge exchange plasma; and (3) the high energy ions created inside the thruster cause significant erosion of the walls of the acceleration channel (usually made of metal or a ceramic such as boron nitride) and the erosion products may expand out from the thruster and become deposited on spacecraft surfaces. A number of Hall thruster plume models have been developed and these are reviewed in a recent article by Boyd. These models have been assessed against detailed experimental data taken in the plumes of a variety of Hall thrusters in ground-based vacuum chambers. For a 1.5 kW class Hall thruster, the lowest background pressure that can be obtained in vacuum chambers is about 10~ torr, which corresponds to an orbital altitude of about 185 km. Clearly, this represents a pressure that is orders of magnitude higher than that encountered in the operation of Hall thrusters in geostationary earth orbit (GEO). Another limitation of vacuum chambers concerns their size. Most Hall thruster plume measurements have been taken such that the maximum distance from the thruster that was probed was about 1 m. The primary objective of this article is to assess a state-of-the-art Hall thruster plume model in terms of its predictions for realistic space conditions of the far field of the plume. The assessment is made possible by the recent, in-orbit, plume measurements of SPT-100 Hall thrusters taken on board the Russian Express spacecraft. The outline of the paper is as follows. First, an outline of the Express spacecraft and the plume measurements is provided. Then, a description is given of the hybrid particle-fluid plume model employed in this study. Results consisting of comparisons between measured and computed data for ion current density and ion energy distributions are then presented and discussed. The sensitivity of the model predictions to various physical modeling assumptions and boundary conditions is considered. The paper closes with some conclusions and suggestions for further work. Express Flight Data A complete description of the two Russian Express-A satellites and the flight data collection program are provided by Manzella et al.. The thrusters employed on the spacecraft were SPT-100 models with a nominal thrust level of about 82 mN while operating at a discharge current of 4.5 Amp and a total flow rate (anode plus cathode) of 5.3 mg/sec. In some ways, the use of SPT-100 thrusters for the first recording of in-orbit plume data is most appropriate as this thruster has received the most attention in terms of both laboratory studies'''' and computational analysis.'' A variety of sensors were employed on board the two spacecraft to characterize the effects of firing the Hall thrusters on the spacecraft operation and environment. These include electric field sensors, Faraday probes to measure ion current density, retarding potential analyzers (RPA's) to measure ion current and ion energy, and pressure sensors. In addition, disturbance torques on the spacecraft imparted by the Hall thruster plumes were recorded. (c)2002 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization. From all of the above, the present study focuses on the RPA data for ion current density and ion energy distributions. This is in part due to the overlap with ground-based measurements of these properties, the relatively good apparent fidelity of these data, and the lack of post-flight reduction of much of the other data. The locations where RPA data was measured are plotted in Fig. 1 with respect to an origin in the thruster exit plane on the thruster centerline. The variation in location is due to the firing of eight different thrusters and the fact that some of the sensors could be moved. Note that some of the sensors were as much as 8.8 m away from the thruster which is well in to the far-field region of the plume. Hall Thruster Plume Model To understand the type of numerical approach required to accurately model Hall thruster plumes, it is informative to consider some of the basic physical characteristics of the flow exiting from the thruster. In Table 1, typical values of some of the pertinent properties are listed at the thruster exit for the SPT-100. For these plasma densities, the Debye length is very small, on the order of 10~ m which indicates that the plume is charge neutral for a relatively large distance away from the thruster. At the same time, the collision mean free paths are very large, on the order of 1 m. These fundamental physical properties of the plume suggest that a kinetic approach is necessary that simulates both plasma and collision effects. In this study, a hybrid particle-fluid model is employed. The Particle In Cell method (PIC) is employed to model the plasma dynamics, and the direct simulation Monte Carlo method (DSMC) is used to simulate the collision dynamics. In the following, these models are briefly outlined. Plasma Dynamics The first efforts to use a combination of the PIC and DSMC methods to model the plumes of Hall thrusters were made by Oh et al. and this approach has formed the basis for subsequent work.' In general, the PIC method accelerates charged particles through applied and self-generated electric fields in a self-consistent manner. In Ref. 7, based on the plasma jet physical properties, the ions are modeled as particles and the electrons as a fluid. The plasma potential is obtained by assuming quasi-neutrality, which allows the ion density to represent the electron density. By further assuming that the electrons are isothermal, collisionless, and un-magnetized, and that their pressure obeys the ideal gas law, p = nfcT, the Boltzmann relation is obtained: where n is the electron number density, * indicates a reference state, 0 is the plasma potential, k is Boltzmann's constant, T is the constant electron temperature, and e is the electron charge. The potential is differentiated spatially to obtain the electric fields. There are several limitations of this approach. Firstly, experimental evidence' indicates that there is variation of the electron temperature in Hall thruster plumes. The variation occurs mainly in the near-field (c)2002 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s) Sponsoring Organization. of the plume. At the thruster exit the electron temperature can be as high as 10 eV and in the far field typical values are 1 to 2 eV. This creates a difficulty in the choice of T to be used in Eq. (1). A further difficulty with application of the Boltzmann relation to Hall thruster plumes is the possible effects of the magnetic field. The combination of permanent and electro-magnets employed in Hall thrusters are designed to provide optimum device performance. However, some of the magnetic field may leak out into the plume of the thruster. The amount of this leakage will depend strongly on the Hall thruster type and configuration. Despite these limitations, the simple Boltzmann relation is widely used and has produced remarkably good agreement with a number of different plume properties measured in vacuum chambers, see Ref. 1 for examples. This approach therefore forms the baseline model for the present study. An alternative approach sometimes employed in plasmadynamics is to assume that the electrons behave adiabatically in which the pressure, density, and temperature are related by: where 7 is the ratio of specific heats, and * again indicates a reference state. Thus, changes in the electron temperature are related to changes in the electron density. Substitution of Eq. (2) into the electron momentum equation, assuming collisionless, un-magnetized electrons gives: (3) e 7. Results obtained with this adiabatic approach are compared to the baseline solutions obtained with the Boltzmann relation. Collision Dynamics The DSMC method uses particles to simulate collision effects in rarefied gas flows by collecting groups of particles into cells which have sizes of the order of a mean free path. Pairs of these particles are then selected at random and a collision probability is evaluated for each pair that is proportional to the product of the pair's relative velocity and collision cross section. The probability is compared with a random number to determine if that collision occurs. If so, some form of collision dynamics is performed to alter the properties of the colliding particles. There are two basic classes of collisions that are important in Hall thruster plumes: (1) elastic (momentum exchange); and (2) charge exchange. At first glance, based on the low number densities at the thruster exit, it appears that collisions are unimportant in Hall thruster plumes. However, it will be found in the discussion of results, that these collisions have a profound effect on the Hall thruster plume structure even though the mean free path for all collisions is large. Two different approaches to modeling the ion atom collision processes are followed. In the first, simple scattering laws are combined with analytical models and experimental measurements for the cross sections. In the second approach, the scattering is determined by detailed calculations. (c)2002 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s) Sponsoring Organization. Simple Model Elastic collisions involve only exchange of momentum between the participating particles. For the systems of interest here, this may involve atom-atom or atom-ion collisions. For atom-atom collisions, the Variable Hard Sphere (VHS) collision model is employed. For xenon, the collision cross section is: 9 19 v 10~ 2 m (4) where g is the relative velocity, and u;=0.12 is related to the viscosity temperature exponent. For atom-ion elastic interactions, the following cross section of Dalgarno et al. is employed: agL(*e,*e+) = m3 (5) 9 The model of Ref. 13 predicts that the elastic cross section for interaction between an atom and a doubly charged ion is twice that for an atom and a singly charged ion. It should be noted that the model of Ref. 13 employs a polarization potential and therefore is only valid for low energy (a few eV) collisions. In all elastic interactions, the collision dynamics is modeled using isotropic scattering together with conservation of linear momentum and energy to determine the post-collision velocities of the colliding particles. Charge exchange concerns the transfer of one or more electrons between an atom and an ion. This is a long-range interaction that involves a relatively large cross section in comparison to an elastic interaction. This is an important mechanism in Hall thruster plumes because at the thruster exit plane, the atoms and ions have velocities that differ by almost two orders of magnitude (see Table 1). While the ions have been accelerated electrostatically, the atoms remain at thermal speeds. Thus, charge exchange leads to a slow ion and a fast atom. The slow ion is much more responsive to the electric fields set up in the plume and are easily pulled behind the thruster into the back flow region. Thus, the so-called charge exchange plasma is formed near the thruster exit. It is because we need to model the charge exchange behavior accurately that we go to the trouble of using the DSMC technique. For singly charged ions, the following cross section measured by Miller et al. is used: <TCEX ( X e , Xe) = (-23.301ogi0(<?) + 142.21) x 0.8423 x l(Tm (6) Also reported in Ref. 14 are charge exchange cross sections for the interaction where a doubly charged ion transfers two electrons from an atom. These cross sections are a factor of two lower than the values for the singly charged ions. In all charge exchange interactions, the collision dynamics assumes that there is no transfer of momentum accompanying the transfer of the electron(s). This assumption is based on the premise that these interactions are at long range. Detailed Model In this approach, the VHS model for Xe-Xe collisions is again employed along with isotropic scattering. The charge exchange collisions employ the same measured cross sections, but scattering is modeled using 5 (c)2002 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization. data computed by Dressier and reported in Ref. 15. The differential cross sections computed by Dressier are shown in Fig. 2 as a function of scattering angle. These results indicate (as expected) that the majority of charge exchange interactions involve very low angle scattering. However, the calculations do not distinguish between charge exchange and momentum exchange and so the same scattering data is employed for atom-ion momentum exchange interactions. The cross section employed for these elastic collisions is the same as that for charge exchange that is again based on the experimental measurements of Ref. 14. Boundary Conditions For PIC-DSMC computations of Hall thruster plumes, boundary conditions must be specified at several locations: (1) at the thruster exit; (2) along the outer edges of the computational domain; and (3) along any solid surfaces in the computational domain. Several macroscopic properties of the plasma exiting the Hall thruster acceleration channel are required for PIC-DSMC computations. Specifically, the plasma potential, the electron temperature, and for each of the particle species we require the number density, velocity, and temperature. In the real device, these properties will vary spatially across the annular face of the thruster exit plane, but also in many operating modes of the thruster these quantities vary in time. In general, the approach to determining these properties is a mixture of analysis and estimation. By assuming ion and neutral temperatures (typically 4 eV and 1,000 K, respectively) and using measured properties such as thrust, mass flow rate, and current, it is possible to determine the species number densities and velocities. This approach gives uniform profiles of all properties across the exit plane. Generally, a small half-angle is imposed at the thruster exit plane to provide a variation in the velocity vector. An alternative approach considered here uses output from a twodimensional PIC-MCC (Monte Carlo Collision) model of the acceleration channel as input to a PIC-DSMC plume computation. Both field and particle boundary conditions are required at the outer edges of the computational domain. The usual field conditions employed simply set the electric fields normal to the boundary edges equal to zero. For plume expansion into vacuum, the particle boundary condition is to remove from the computation any particle crossing the domain edge. In all configurations, the solid exterior walls of the thruster must be included in the computation. In the present study, the potential of the walls is set to zero. Any ions colliding with the thruster walls are neutralized. Both atoms and neutralized ions are scattered back into the flow field from the surface of the thruster wall assuming diffuse reflection. Results The Hall thruster plume model described above is assessed by making direct comparison with ion current and ion energy distributions measured on-board the Express spacecraft. The baseline simulation is performed as follows: (1) at the thruster exit, the densities and temperatures are assumed to be radially uniform, the velocities are based on a divergence angle of 15 deg., an ion temperature of 4 eY is assumed,