Numerical Modeling of Erosion in Hall Effect Thrusters
Abstract
:1. Introduction
- The threshold energy, Eth (i.e., the minimum energy of an incident particle to allow sputtering to start), is used as fitting parameter with respect to experiments;
- The effect of wall temperature on sputtering [12] has never been taken into account;
- The most recent sputtering data regarding the Xe–Borosil couple by Ranjan et al. [13] has never been considered.
2. Erosion Model
2.1. Plasma Simulation: HYPICFLU2
HYPICFLU2 Validation
2.2. Sputtering Modeling
- Method 3: An interpolation using UnivariateSpline, a built-in function in Python, which interpolates data by Ranjan et al. [13] for a given angle (all the energies) and then extrapolates to the point of interest, in particular the energy at which the sputter yield nullifies. In our case, a spline of the fourth degree was considered.
- The effect of temperature at different energies is unknown, and changing the gradient would imply making assumptions on such an effect. Also, Ranjan’s data [13] at room temperature is the only widespread data on which it is possible to rely;
- Maintaining the same gradient for the extrapolation below 100 eV implicates a reduction in the minimum energy at which sputtering first occurs as temperature increases. As temperature increases, the bond strength may decrease, allowing for atoms to be sputtered from the surface at lower energies. This is yet another assumption but, given the uncertain value assigned to it in past models, it seemed a reasonable one.
- The set of sputter yield points at various angles and energy by Ranjan et al. [13] is multiplied by the temperature coefficient (), obtaining a new set of points with higher sputter yield values.
- From the new value of sputter yield at 100 eV, incremented by , a value of the threshold energy for any given angle is extrapolated following the average gradient of the sputter yield value of Ranjan’s data (without the temperature coefficient—Method 1). This leads to a decrease in threshold energy for an increase in temperature coefficient; hence, simulated surface temperature.
- Added to the set of points are the values of sputter yield at 90° of incidence angle, which is 0 for all energies.
3. Results
4. Discussion
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
Symbols | |
Boltzmann constant | |
e | Electron charge |
Ion mass | |
Erosion rate | |
Ions incidence angle | |
Eth | Threshold energy |
E | Ion impacting energy |
v | Ion velocity |
Y | Sputtering yield |
Temperature coefficient | |
t | time |
r | Radial coordinate |
z | Axial coordinate |
n | Particle number density |
Electron temperature | |
Potential | |
Thermalized potential | |
current density vector | |
V | Volume/voltage |
Flux of electrons | |
SEE yield | |
q | Energy flux to the wall |
Discharge current | |
Discharge power | |
Ion discharge velocity | |
Mass flow rate | |
Specific impulse | |
T | Thrust |
Efficiency | |
Subscripts | |
i | Ion |
e | Electron |
n | Neutral |
w | Wall |
Electron-ion | |
Electron-neutral | |
b | Bohm |
Abbreviations | |
GEO | Geostationary Earth orbit |
LEO | Low Earth orbit |
HET(s) | Hall effect thruster(s) |
SPT | Stationary plasma thruster |
PIC | Particle in cell |
HYPICFLU | HYbrid PIC-FLUid |
SEE | Secondary electron emission |
CSR | Charge saturation regime |
CSL | Charge saturation limit |
BN | Boron nitride |
Borosil | |
IFDM | Irregular-grid finite difference method |
CW | Correct weighting |
VW | Volume weighting |
BF | Bohm criterion forcing |
Xe/ | Xenon/ions |
LIF | Laser-induced fluorescence |
TS | Thermal Spike |
Appendix A. Review of Sputtering-Yield Models
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Exp. | Num. | HYPICFLU2 | HYPICFLU | |
---|---|---|---|---|
(A) | 4.5 | 4.5 | 4.12 | 4.65 |
(W) | 1350 | 1350 | 1251 | 1395 |
(km/s) | 15.7 | 17.0 | 16.2 | 19.8 |
(mg/s) | 5.29 | 5.00 | 4.7 | 4.19 |
(s) | 1600 | 1733 | 1652 | 2016 |
T (mN) | 83 | 85 | 76 | 83 |
(%) | 50 | 55 | 50 | 59 |
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Passet, M.; Panelli, M.; Battista, F. Numerical Modeling of Erosion in Hall Effect Thrusters. Particles 2024, 7, 121-143. https://doi.org/10.3390/particles7010007
Passet M, Panelli M, Battista F. Numerical Modeling of Erosion in Hall Effect Thrusters. Particles. 2024; 7(1):121-143. https://doi.org/10.3390/particles7010007
Chicago/Turabian StylePasset, Matteo, Mario Panelli, and Francesco Battista. 2024. "Numerical Modeling of Erosion in Hall Effect Thrusters" Particles 7, no. 1: 121-143. https://doi.org/10.3390/particles7010007