Viz Glow Validation Hybrid Plasma Model for SPT100

Viz. Glow Validation: Hybrid Plasma Model for SPT-100 Hall Thruster 1301, S. Capital of Texas Highway, Suite B-330 Austin, Texas 78746 www. esgeetech. com Contact : info@esgeetech. com Jan 2019

2 Outlines § Introduction § Basics of propulsion § Thruster parameters § SPT-100 or Hall thruster introduction § Overview of Viz. Glow simulation modeling § Modelling of Magnetized plasmas § Governing equation § Simulation of SPT-100 § Benchmarking with Experimental results § Conclusions

3 Introduction §

4 Thruster Metrics

Mass Requirement comparison between chemical and EP thrusters From: Huang, Ph. D thesis U. Mich, 2011 5

7 Introduction-Hall Thruster § Hall thruster are among the most mature electric propulsion devices for satellites missions § Hall thruster use large local electric field in plasma by using a transverse magnetic field to reduce electron conductivity § This electric field can extract positive ion from plasma and accelerate them to high velocity providing thrust § In-space, propulsion is needed to change/provide spacecraft velocity and orientation

8 Overview § A fast, robust, and accurate predictive simulation tool for Hall thruster plasma phenomena has been developed on the Viz. Glow plasma modeling tool framework § The approach is based on Hybrid Plasma Modeling with coupled Particle and Fluid models for different aspects of the physical phenomena § The Hall thruster simulations is a multi-step process with: 1) simulation of magnetostatic fields, 2) modeling of background flow field, 3) modeling of the plasma phenomena § The initial background gas flow is predicted using the particle approach with Xe only flow in the system. Plasma simulation are conducted using a hybrid approach with fluid treatment of electrons, particle treatment of neutrals and ions, under the quasineutral approximation § The model is benchmarked for experimental results of SPT-100 Hall thruster

9 Hybrid Model approach for Hall Thruster • The hybrid plasma solver takes the magnetostatic field and the initial background gas flow as inputs • • Magnetostatics Magnetostatic field is solves using standard FEM formulation within Viz. Glow plasma simulation tool Background Xe flow is simulated using particle approach with Monte-Carlo Collision (MCC) formulation • • • Uses particle approach for Xe neutrals, Xe+ ions, and Xe++ ions Electron density calculated assuming quasineutrality Electron temperature solved using a 1 D magnetized electron energy equation Potential solved using current continuity equation Hybrid solver Particle-MCC: Xe, Xe+, Xe++ Fluid : Electron energy, Potential • Hybrid solver : • Gas flow only (particle-MCC)

10 Magnetostatics – Mathematical model Definition of Magnetic Induction: Magnetostatics governing equations: Definition of magnetic vector potential:

Particle modeling approach – Mathematical model Particle equation of motion: Lorentz force: Particle statistical weights: Each species can carry its own statistical weight, thereby improving the statistics for representing species with disparate densities. 11

Particle modeling approach – Mathematical model (MCC collisions) Particle collision model (Monte-Carlo Collisions (MCC): Gas flow only with MCC collisions: Here the gas is represented with only a single collision reaction, i. e. the elastic collision reaction between the gas molecules. For example in the case of Xe gas flow the reaction (Xe + Xe) is specified with a hard-sphere cross section. 12

13 Fluid Model for Electrons

14 Fluid Model for Electrons

15 Fluid Model for Electrons • Illustration of concept of a “magnetic streamline” and a “magnetic streamtube” Minimum streamline (e. g. anode) Maximum streamline (e. g. cathode) “Magnetic Streamtube” between two streamlines

16 Fluid Model for Electrons

17 Fluid Model for Electrons

18 Fluid Model for Electrons

19 Fluid Model for Electrons

Hybrid model plasma solution approach Fluid Model for Electrons • The solution approach comprises of the following sequential steps: New time step Solve ion dynamics using Particle Approach End time step 20

21 Validation of Viz. Glow Hall Thruster Model for SPT-100

22 35 mm channel 40 mm 45 mm 50 mm inflow 100 mm SPT-100 Geometry Specifications Axis 25 mm Parameter Value Annular area of inflow 4. 254 x 10 -4 m 2 Xe flow rate 5 mg/s

23 Magnetostatics (Simulation Results)

24 SPT-100 Magnetic Field Comparison Literature result Ref: Evaluation of Erosion Reduction Mechanisms in Hall effect Thrusters Joint Conference of 30 th International Symposium on Space Technology and Science, Japan July, 2015 D. Pérez-Grande et. al. Viz. Glow

25 Magnetic field in axial center line Viz. Glow result Literature result Channel exit

26 SPT-100 Flow Specifications Flow parameters Value Annular area of inflow Xe flow rate Inflow location temp. 750 K

27 SPT-100 Operating Conditions Discharge Parameters Value Discharge voltage 300 V Thermal Parameters Value Anode temperature 750 K Channel wall temp. 850 K

28 Literature result From: Hofer et al. Heavy particle velocity and electron mobility modeling in hybrid-pic Hall thruster simulations, AIAA Paper 2006 -4658.

Gas Flow Only results: Comparison with literature(speed comparison) Literature result From: Hofer et al. Heavy particle velocity and electron mobility modeling in hybrid-pic Hall thruster simulations, AIAA Paper 2006 -4658. 29

Experimental Results Experimental parameters Xe flow rate on anode 5 mg/s Anode potential 300 V Cathode flow rate 1 mg/s Pressure(facility) 0. 0018 pa Thruster Performance Discharge current 4. 5 A Power 1. 35 k. W Thrust 86. 9 m. N Specific impluse 1470 efficiency 0. 469 Sankovic J. M. et al. , IEPC-93 -094 30

Viz. Glow simulation results: Simulation Parameters No. of stream tubes 30 Anode line position 0. 006 00425 0. 0 Cathode line Position 0. 075 0. 0425 0. 0 Cathode potential 0. 0 V Anode Potential 300 V Electron temperature (Anode) 5. 0 e 4 K Electron temperature 2. 0 e 4 Wall colli. freq. fact. α 0. 1 Bohm Mob. Fact. 0. 05 Wall energy loss factor αe 0. 01 Wall heat loss threshold potential 31 30 e. V Resonable agreement with trends in experimental data 31

Snap shot of plasma results in steady state Anode line index Stream tube index Electron density Cathode line index Electron temperature 32

Snap shot of plasma results in steady state Xe density Xe⁺⁺ density 33

Snap shot of plasma results in steady state Xe⁺ velocity Xe⁺⁺ velocity 34

35 Hybrid Model Results – Thruster Parameters (Baseline) Beam Power (k. W) Xe+ 1. 71 x 1019 66 - Xe++ 4. 46 x 1018 16 - Xe - 0. 000001 - TOTAL Electrical Parameter Value 4. 75 A (avg. ) Ion beam current 4. 3 A (avg. ) 1. 425 k. W Global Efficiency Metrics Value 1673. 4 s Anode Efficiency(46. 9 % exp. ) 47. 2%

Comparison: Viz. Glow simulation and Experimental results Thruster Performance Viz. Glow model experimental Discharge current 4. 75 A 4. 5 A Power 1. 425 k. W 1. 35 k. W Thrust 82 m. N 86. 9 m. N Specific impluse 1673 s 1470 s efficiency 47. 2% 46. 9% • All discharge properties of thruster match well with experimental SPT-100 results 36

37 Summary § We have developed a high-fidelity hybrid computational modeling tool for the predictive simulation of Hall thruster plasma phenomena § The model is developed on the Viz. Glow Plasma Simulation tool framework § Model has been extensively benchmarked for very well know SPT-100 Hall thruster § We have report on all discharge properties of a thruster and the global performance metrics of the thruster

38 End of Presentation