Hydrodynamic Model of Hall Thruster Channel Wall Erosion

Overview

The main life-limiting factor for Hall thrusters is the erosion of the channel walls. As Hall thrusters are beginning to be used on more extended missions (10000 hours+), lifetime issues become a priority. Characterizing this erosion experimentally in ground based vacuum chambers is prohibtively long and expensive. Thus there is a need for quick and cheap, yet accurate, simulations and this is the main motivation behind this research.

Modeling the erosion rates along the channel walls incorporates two major parts. First, the ion current to the walls needs to be determined. Then the sputter yields need to be found in order to obtain the erosion rates. Two ion flux models are examined. One is based on scattering collisions while the other focuses more on a hydrodynamic description of the plasma. The sputter yields are obtained from an empirical model based on curve fits to experimental data.

 

Models

Scattering collisions model

Experimental data of the total volumetric erosion rate of the SPT-100 as a function of time is shown below. There is a rapid decrease in the erosion early on, but levels off after about 1000 hours. Explanations have ranged from a two-mechanism process to a logarithmic one. A possible physical underpinning behind a logarithmic decrease in the erosion rate may be explained by scattering collisions as the channel width increases due to erosion.

The scattering collisions model assumes that most of the ion flux to the walls is due to collisions of the ions with the neutral atoms in the channel. The ions are diverted from their trajectory and possibly into the walls.

Hydrodynamic model

The hydrodynamic model uses a fluid description of the plasma to calculate the ion flux to the walls. The ion continuity and momentum equations are solved in an iterative manner. The electron momentum and energy equations are also solved to determine the electron temperature and the components of the electric field. The neutral flow is modeled as one-dimensional with a constant axial velocity.

The near-wall processes are also modeled, as they are important in determining the erosion rates. The boundary conditions are set by those on the edge of the plasma sheath. The Bohm condition is not assumed a priori, but rather, a smooth presheath-sheath matching technique is applied to find the electric field and entrance velocity at the sheath edge. The effects of secondary electron emission are also included. This affects, among other things, the potential drop across the sheath, which in turn influences the ion impact parameters and thus the erosion rate.

Sputtering model

The above ion flux models are coupled with a sputtering model to calculate the erosion rates. Sputter yields are primarily a function of wall material, ion species, angle of incidence, and ion energy. We have used experimental data of xenon ions striking boron nitride samples at various angles and energies [1]. For our purposes, we have applied a curve fit to model the sputter yield for xenon ions on boron nitride.

Results

The results using the scattering model are shown below. Overall, the model shows fairly good comparison with the experimental data [2].

The hydrodynamic model results are shown below. Again the model compares fairly well to the data. However, there are some deficiencies, such as underpredicted erosion in the later stages of thruster life. The erosion at the exit plane (figure on the far right below), however, matches quite well with experimental data [2,3]. Since this is usually the location of greatest erosion, and thus the location under most concern, the results are promising.

Overall, the two models here show fairly good comparison with existing experimental data. The models are also computationally inexpensive, running on the order of minutes, making them attractive for future design and prediction purposes. However, there remains much work to be done in improving the models, making sure they capture all of the necessary physics and are applicable over a variety of thruster types and operating conditions.

References

1. Garnier, Y., Viel, V., Roussel, J.-F., and Bernard, J., "Low-Energy Xenon Ion Sputtering of Ceramics Investigated for Stationary Plasma Thrusters," Journal of Vacuum Science and Technology A, Vol. 17, No. 6, Nov/Dec 1999, pp. 3246-3254.

2. Absalamov, S. K., et al., "Measurement of Plasma Parameters in the Stationary Plasma Thruster (SPT-100) Plume and Its Effect on Spacecraft Components," 28th AIAA/SAE/ASME/ASEE Joint Propulsion Conference and Exhibit, 1992, AIAA-92-3156.

3. Garner, C. E., Brophy, J. R., Polk, J. E., and Pless, L. C., "Cyclic Endurance Test of a SPT-100 Stationary Plasma Thruster," 30th AIAA/SAE/ASME/ASEE Joint Propulsion Conference and Exhibit, 1994, AIAA-94-2856.

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