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Numerical Study of Facility Effects on Gridded Ion
Thrusters through a Multi-GPU PIC-DSMC Solver
IEPC-2024-323
Presented at the 38th International Electric Propulsion Conference, Toulouse, France
June 23-28, 2024
Keita Nishii∗
Tokyo Metropolitan University, Hino, Tokyo, 1910065, Japan
Deborah A. Levin†
University of Illinois Urbana-Champaign, Urbana, Illinois, 61801, USA
This study investigates the facility effects on gridded ion thrusters tested in ground vac-
uum chambers using a Multi-GPU PIC-DSMC solver, CHAOS. The research summarizes
our recent work on contamination by backsputtered particles and the coupling between the
electron source and chamber walls. These results indicate that different sputter models
significantly impact backsputtering rates and that ground-based conditions alter electron
temperatures and potentials compared to space conditions. In addition. dimensional scal-
ing is applied to reduce computational costs for a vacuum chamber simulation, revealing
that potential and electron energy are underestimated. These findings provide fundamental
results useful for future numerical studies on facility effects.
I. Introduction
Gridded ion thrusters are tested in ground vacuum chambers to verify their performance when operated
in space. However, the presence of high background pressure and conductive walls in the vacuum chamber
leads to facility effects that increase uncertainty in the performance of the thruster in space. Typical
operating chamber pressures are approximately three orders or more of magnitude higher than the ambient
gas pressures of 10−9Torr on orbit (at 1000 km). At such high background pressure, the lifetime of ion grid
optics is impacted by erosion driven by charge exchange (CEX) ions. Another limitation is the surrounding
wall of the vacuum chamber. The high energy ion bombardment on the wall sputters wall material, and its
deposition masks erosion caused by CEX backflow ions. Thus, the understanding of backsputtering in the
vacuum chamber is essential, and there are several studies modeling sputtered particles.1,2
In addition, ion beam neutralization depends on the neutralizer to ion beam plasma bridge, which can
be affected by nearby wall surfaces and CEX collisions. For such reasons, it is important to understand
the interaction between the thruster plasma plume and the ground facility. Several numerical simulations
have been performed to understand ion beam neutralion.3–7 Plasma plumes from thrusters are mostly
measured in laboratories, with limited direct measurements in space.8, 9 Therefore, comparing ground-based
and space-based conditions through numerical simulations is a highly effective approach to understanding
facility effects. This method allows researchers to bridge the gap between laboratory measurements and
on-orbit performance, providing insights into the interactions between the thruster plasma plume and the
testing environment.
Investigating facility effects requires accounting for neutral particles, ions, and electrons, and the large
computational domain necessitates significant parallelization for speed. We have developed an in-house code,
Cuda-based Hybrid Approach for Octree Simulations (CHAOS), which features adaptive mesh refinement
with octree mesh and is accelerated using MPI-CUDA parallelization strategies. This code has been employed
not only for the current study but also for simulating multiphase flows10 and investigating electron solitary
∗Assistant Professor, Department of Aeronautics and Astronautics, knishii@tmu.ac.jp
†Professor, Department of Aerospace Engineering, deblevin@illinois.edu
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The 38th International Electric Propulsion Conference, P. Baudis Convention Center, Toulouse, France, June 23-28, 2024
Copyright 2024 by the Electric Rocket Propulsion Society. All rights reserved.
wave dynamics.11 The advanced capabilities of CHAOS make it well-suited for addressing the complex
interactions in ion thruster plume simulations.
In the next chapter, we report our numerical work on contamination due to particles sputtered from a
vacuum chamber wall12 (i.e., backsputtering facility effects) and coupling between the electron source and
the wall13 (i.e., electrical facility effects). For backsputtering, we examine the importance of a sputtering
model for carbon particles when fast xenon ions hit the wall (Section A). For electrical facility effects, we
examine how the amount of current changes with and without the wall surface and with and without the
background gas (Section B).
However, these studies have been performed with plasma densities 10–100 times smaller than those of
actual ion thrusters. This is because it is not possible to perform a full-kinetic simulation of the entire vacuum
chamber on a realistic scale, due to the limitations of current computational resources. To overcome this
limitation, dimensional scaling has been used in a few cases to calculate ion thrusters.4, 14, 15 In this study,
we also discuss what results are obtained when dimensional scaling is applied to an ion thruster plume in a
vacuum chamber (Section IV). These results may be useful for future numerical studies on facility effects.
II. Highlights of our Facility Effect Study
A. Backsputtering Simulation
The work12 simulated an ion thruster plume using both fully kinetic and quasi-neutral Boltzmann models.
Here, the kinetic model means that electrons are treated as particles, and the electric potential is calculated
based on Poisson’s equation. The Boltzmann model treats electrons as fluid, and the electric potential is
calculated based on the Boltzmann relation equation. The work investigated the impact on flux, energy, and
angle of incident ions on chamber walls (see Fig. 10 in Ref.12). For momentum exchange (MEX) ions (top
plots), there was almost no difference between the fully kinetic and Boltzmann cases in terms of flux, incident
energy, and angle. This was because MEX ions had high initial energies, making electric potential differences
less impactful. As distance increased, the flux and energy of MEX ions rose due to their larger zvelocities.
In contrast, CEX ions (bottom plots) showed significant differences between the fully kinetic and Boltzmann
cases. CEX ions, which initially had small velocities, gained energy from the electric potential and moved
along the electric field. The fully kinetic simulation predicted higher incident energy and a wider incident
angle distribution compared to the Boltzmann case, attributed to the potential barrier in the Boltzmann
case, which reduced CEX ion energy, especially near the thruster exit. Additionally, in the Boltzmann case,
CEX ions moved behind the thruster where ion density was lower, affecting their incident angles.
The study12 also explored how different sputter models affect the spatial distribution and deposition rate
of carbon backsputtered onto the ion thruster face. Sputtering, caused by high-energy beam ions impacting
downstream walls, was evaluated using the cosine distribution and Yim’s model.16,17 The work showed that
high-energy ions, such as MEX ions, had sufficient energy to cause sputtering, with no significant difference
between the fully kinetic and Boltzmann cases for these ions (see Fig. 17 in Ref.12). The influence of electric
field modeling on backsputtering was negligible due to the lower flux and energy of CEX ions compared to
beam ions.
In conclusion, the choice of the sputter model significantly impacted predicted carbon backsputtering
rates. Yim’s model,16,17 based on experimental data, appears to offer a more accurate representation,
emphasizing the need for realistic angular dependence in sputtering models to better predict and mitigate
backsputtering effects in ion thrusters. How sputtering models are underdeveloped and will be considered
in the future.18
B. Electrical Facility Effect Simulation
Another work13 investigated the electrical facility effect using a fully kinetic model. The comparison between
space and ground-based conditions showed higher electron temperatures and potential in ground-based sim-
ulations due to electron absorption by chamber walls, contrasting with space simulations where electrons
were reflected back. Table 1 (Table 6 in Ref.13 ) highlighted significant differences in electron currents: the
grounded chamber walls increased electron currents to the plasma screen and decreased currents escaping
the chamber. These findings suggested that ground tests may underestimate the electron currents returning
to the thruster, impacting the accuracy of ground-based thruster performance predictions.
The study also examined the impact of background pressure in a vacuum chamber on ion thruster
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Copyright 2024 by the Electric Rocket Propulsion Society. All rights reserved.
Table 1. Ion and electron current from thruster plume to different locations. (from Nishii and Levin13)
Case Ion Current, Ii/Ib
i0 Electron Current, Ie/Ib
e0
Ine Ith Ips Ivc(= Ivc,end+Ivc,side )Ine Ith Ips Ivc(= Ivc,end+Ivc,side)
Space 0.00 0.00 0.01 0.99 0.39 0.06 0.26 0.29
Chamber (w/o BPa) 0.00 0.00 0.01 0.99 (= 0.99 + 0.00) 0.18 0.01 0.02 0.78 (= 0.59 + 0.19)
Chamber (w/ BPa) 0.00 0.01 0.02 0.96 (= 0.72 + 0.24) 0.14 0.01 0.05 0.79 (= 0.57 + 0.22)
aBP indicates the background pressure.
bSee Fig. 3 in Ref.13 for definitions of the current to each part.
plumes. The presence of neutral particles at typical ground test pressures led to the formation of slow
charge-exchange ions, which increased ion density and reduced the electric potential in the plume, resulting
in improved plume neutralization. Additionally, these ions created ion sheaths near the chamber walls,
altering ion current paths. The study found that background pressure effects must be considered to simulate
and predict ion thruster performance in ground-based tests accurately.
In conclusion, ground-based vacuum chamber tests significantly affect ion thruster plume characteristics,
increasing electron temperature and altering current paths due to grounded walls and background pressure.
Accurate predictions of on-orbit performance require accounting for these facility effects in simulation and
testing methodologies.
III. Simulation Code: CHAOS
A. DSMC and PIC Modules
The CHAOS framework utilizes direct simulation Monte Carlo (DSMC), particle-in-cell (PIC), and gas
surface interaction (GSI) modules to simulate ion thruster plasma plumes accurately.6,7, 12, 13, 19, 20 Figure 1
shows the flowchart between three major modules in the code. The DSMC module is primarily responsible for
modeling three types of collisions: momentum exchange (MEX) collisions between xenon neutral particles and
ions, and CEX collisions between xenon ions and neutral particles. In this module, particle interactions are
performed within the leaf nodes of an octree grid, where particles are mapped to these nodes, and collisions
are computed using a no-time counter (NTC) collision scheme. This method is particularly effective in
accounting for the different timescales and weighting factors of ions and neutrals, ensuring accurate modeling
of collision dynamics within the plasma plume.
The main objective of the PIC module is to calculate the self-consistent electric field based on the
spatial distribution of charged particles. This is achieved by solving Poisson’s equation on an unstructured
octree grid using the preconditioned conjugate gradient (PCG) method. The electric potential is iteratively
computed until convergence is achieved, after which the electric field is derived. The octree grid is refined
adaptively to ensure that the cell size is smaller than the local Debye length, maintaining the accuracy of
the electric field calculations. The PIC module operates in conjunction with the DSMC module, providing
the necessary electric field data to update the velocities and accelerations of charged particles.
In our recent work,12,13 we have extended CHAOS to model ground facility environments, focusing on
two critical plasma-surface interactions: charge absorption and sputtering as the GSI module. When ions
hit the wall, they lose their positive charge and become neutralized. This process significantly affects the
background pressure distribution. Additionally, modeling sputtered particles from the vacuum chamber walls
is a key objective. When high-energy ions impact the walls, they cause material sputtering, which must be
accurately simulated to understand contamination and erosion effects. By incorporating these interactions,
CHAOS can more precisely replicate the conditions and challenges faced by ion thrusters in ground-based
testing environments.
B. PIC-DSMC Coupling
The CHAOS framework employs a sophisticated coupling methodology to integrate the PIC and DSMC
modules effectively.7, 12, 13, 20 This coupling is necessary to handle the disparate time and length scales
associated with collisions and electric field evolution in ion thruster plumes. Key strategies employed in this
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Copyright 2024 by the Electric Rocket Propulsion Society. All rights reserved.
Compute
acceleration
Electric eld
START
Poisson
PCG -> Φ
Compute ρ
New
E-FOT?
Construct
2:1 E-FOT
Partition
E-FOT
Initialize
Particles
Move
Particles
B C
Applied
Gas-surface
Interaction?
Last
timestep?
END
Yes
Yes No
No
No
No
Yes
Yes
Neutralization
Sputtering
DSMC, CEX
MCC
Event
calculation
Surface ux
Calculation
New
C-FOT?
Construct
C-FOT
Mapping
Particles
Collisions
of same part.
Partition
C-FOT
Collisions
Neut.-Ion
Collisions
Neut.-Electron
PIC
MODULE
GSI
MODULE
DSMC
MODULE
Figure 1. Schematic diagram of the relationship between major modules in CHAOS
coupling include as follows.
1. Separated Octree Grids
CHAOS constructs two distinct octree grids for the DSMC and PIC simulations, referred to as the collision-
forest of trees (C-FOT) and electric-field forest of trees (E-FOT), respectively. The C-FOT is designed to
resolve local mean free paths for collision calculations, while the E-FOT resolves local Debye lengths for
electric field calculations. These grids are dynamically refined and linearized to optimize computational
efficiency and accuracy.
2. Species Timestep and Weighting Factors
To handle the different densities and velocities of ions, electrons, and neutrals, CHAOS employs species-
specific timesteps and weighting factors. Neutrals are moved only during DSMC executions, while ions
and electrons are updated every PIC iteration. Weighting factors increase the number of computational
particles for charged species, ensuring sufficient particle counts for accurate collision statistics and electric
field computations.
3. Time-Slicing for Disparate Timescales
Given the significant difference in timescales between collisions and electric field evolution, the DSMC module
is executed less frequently than the PIC module. Typically, the DSMC module is called after several hundred
PIC iterations, allowing the PIC module to update the electric field more frequently and accurately. This
approach ensures that the DSMC collisions are performed over appropriate timescales without unnecessary
computational expense.
4. Decoupled sampling
For steady-state simulations, the electric field is established relatively fast. At that point, the computationally
intensive PIC module, which calculates the electric field based on the spatial distribution of charged particles,
is no longer invoked. Instead, the steady-state electric field is sampled and used for further calculations.
After decoupling, the DSMC module continues to simulate heavy particle collisions with the velocities and
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Copyright 2024 by the Electric Rocket Propulsion Society. All rights reserved.
positions of the charged ions updated using the steady-state electric field obtained earlier. This step allows the
simulation to focus on collision dynamics, such as MEX and CEX collisions, without the need to recalculate
the electric field at every iteration.
IV. Dimensional Scaling
A. Simulation conditions
Dimensional scaling aims to reduce computational costs by using a scaling factor, f, to decrease the actual
dimensions of the computational domains. In this case, for three-dimensional calculation, since the particle
flux is kept constant, the total number of computational particles decreases by 1/f3. Additionally, the
number of time steps required to reach a steady state becomes 1/f, which results in an approximately 1/f4
reduction in computational cost. Note that scaling will change plasma dynamics, especially near the walls,
since the Debye length does not change by this dimensional scaling. When considering collisions of neutral
particles or the effects of external electric and magnetic fields, the scaling scheme in Ref.14 can be used. In
our study, these effects were ignored, and only ions and electrons were simulated.
Generally, the influence of the size and plasma density at the exit of the ion engine is characterized by
the ratio of the thruster exit radius to the Debye length based on the exit plasma density (R0/λ0).13, 15 The
maximum R0/λ0of Ref12 and Ref.13 were 285 and 19, respectively. In our work, to address the actual scale,
the ion density of 2.62 ×1015 m−3was determined based on the ion flux and velocity in Ref.,21 as shown
in Table 2. The electron temperature was set to 2 eV, and the electron density was determined so that the
ion-to-electron current ratio was the same as that of Ref.12 and Ref.13 The Debye length at the thruster
exit was 2.1×10−4m in this condition.
Table 2. Species setting on the thruster exit for scaling study based on Ref.21
Species at thruster exit Xe+e−
Current, mA 80.9 250
Flux, m2·s1.0×1020 3.1×1020
Number density, m−32.62×1015 9.84×1014
Bulk velocity, m/s 38,338 0
Temperature, K 0 (12◦Gaussian dist.) 23,210 (2 eV)
To investigate the effect of dimensional scaling, we set the test geometry shown in Fig. 2. The ion thruster
was placed on the left-hand side at a distance from the vacuum chamber downstream wall of 10 cm, and the
electrical potential of the vacuum chamber and thruster were set at 0 V. Similar to Ref.,12 this study only
simulates a quarter domain due to symmetry to further save computational effort. We tested four scaling
factors: 1 (baseline), 2, 4, and, 8. The dimensions and simulation parameters for each scaling factor are
displayed in Table 3. In the baseline case, since the exit radius was 4 cm, R0/λ0= 1904. Due to the large
number of cells required, the number of computed particles was 520 M/species, and the required resources
were 32 Nvidia A100 GPUs. As a result of scaling, the number of total computational particles decreased
by a factor of 1/f3. At f= 8, R0/λ0= 238, where the Debye length at the thruster exit was still small
enough compared to the thruster dimension. For computational parameters, a timestep of 4.0×10−11 and
Fnum of 6.25×102were selected. Once the number of computational particles reached almost steady (at
100,000 timesteps for the baseline case), we started the steady result sampling.
B. Results and Discussion
Figure 3 shows the two-dimensional electric potential result for all scaling factors. The potential decreased
as fincreased. In the baseline (f=1) case, the maximum potential was approximately 9.5 V. In the f=8
case, the maximum potential was approximately 6 V. Since the mesh size was adjusted to a size slightly
smaller than the Debye length by adaptive mesh refinement, the computational mesh was coarser for larger
scaling factors.
The electric potential, ion number density, and electron number density on the thruster center axis (y/D =
0.0) and cross-stream direction (z/D = 1.875) are shown in Fig. 4 to provide a qualitative comparison. The
5
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Copyright 2024 by the Electric Rocket Propulsion Society. All rights reserved.
z
y
10/f cm
10/f cm
5/f cm 4/f cm
20/f cm
10/f cm
2.5/f cm
Numerical pump
Ion thruster, 0 V
Thruster exit
Chamber walls: 0 V
Figure 2. Geometry for a scaling study.
Table 3. Dimensions and simulation parameters for each scaling factor.
Scaling factor, f 1 (baseline) 2 4 8
Domain size, cm (10, 10, 20) (5, 5, 10) (2.5, 2.5, 5) (1.25, 1.25, 2.5)
Thruster size, cm (5, 5, 10) (2.5, 2.5, 5) (1.25, 1.25, 2.5) (0.725, 0.725, 1.25)
Exit radius, cm 4 2 1 0.5
Pump size, cm 2.5 1.25 0.725 0.3125
R0/λ01905 952 476 238
Total particles / species 520 M 65 M 8 M 1 M
Baseline, =(=)
=(=)
=(=)
=(=)
1.25 1.50 1.75 2.00 2.25 2.501.25 1.50 1.75 2.00 2.25 2.50
z/D z/D
y/D
1.25
1.00
0.75
0.50
0.25
0.00
0.25
0.50
0.75
1.00
1.25
Figure 3. Electric potential contours at scaling factors of 1, 2, 4, and 8.
left plot shows the potential curves. Due to the boundary conditions, the potential along the wall at
z/D = 1.25 and z/D = 2.50 has a fixed potential of 0 V and reaches its maximum value downstream of the
thruster. As can be seen in Fig. 3, the potential becomes lower as the scaling factor is increased. On the
6
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Copyright 2024 by the Electric Rocket Propulsion Society. All rights reserved.
other hand, for the ion and electron densities, the difference due to the scaling factor was small.
In addition, Fig. 5 shows the electric potential, ion number density, and electron number density in the
cross-stream direction (z/D = 1.875). In the left potential plot, a negative potential is seen in the region
outside the ion beam (0.7< y/D < 1.1) in the baseline case. This is due to the formation of an ”electron
pool” because ions have a lower temperature, whereas electrons have a higher temperature and can move
outside the region where the ion beam is present. Interestingly, this negative potential disappears as fis
increased. There are small differences between the ion and electron densities, similar to the results for the
thruster axial direction. For electron density, as fis increased, the gradient at the edge of the ion beam
(y/D ∼0.6) becomes smoother, and abrupt changes in potential are not captured.
Electric potential (V)
Ion number density /m3
Electron number density /m3
z/D z/D z/D
Figure 4. Thruster axis results of potential, ion density, and electron density.
Electric potential (V) Ion number density /m3Electron number density /m3
y/D
y/D
y/D
Figure 5. Y-direction results of potential, ion density, and electron density at z/D = 1.875.
Finally, the electron energy distributions at the center of the plume (y/D, z/D) = (0.0,1.88), and near
the downstream of the wall (y/D, z/D) = (0.0,2.45) were obtained, as shown in Fig. 6. This figure shows
that the mean energy and the width of the electron distribution (i.e., temperature) are greatly reduced by
the scaling process and probably cause the reduction of the potentials in Fig. 3. The scaling-induced changes
observed here are attributed to the smaller length plasma scale without changing the Debye length, which
results in a smaller shielding effect. However, it should be noted that for simulations where the chamber and
thruster walls play a small role (e.g., plume core regions), Figs. 4 and 5 show that such a scaling appears
given a good estimate of species profiles.
V. Conclusion
This research provides critical insights into the facility effects on gridded ion thrusters tested in ground
vacuum chambers. Using the CHAOS code, which integrates DSMC and PIC modules, we explored the
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Copyright 2024 by the Electric Rocket Propulsion Society. All rights reserved.
Energy (eV)
EDF (arb.)
EDF (arb.)
Energy (eV)
Figure 6. Electron energy distribution function sampled by a numerical probe, (a) at y/D = 0.0and z/D = 1.88,
(b) at y/D = 0.0and z/D = 2.45,
impacts of backsputtering and electrical facility effects. Our findings show that different sputter models,
particularly, provide more accurate predictions of carbon backsputtering rates compared to the cosine dis-
tribution. Furthermore, ground-based simulations revealed higher electron temperatures and potentials due
to electron absorption by chamber walls, contrasting with space simulations where electrons are reflected.
The presence of neutral particles at ground test pressures forms slow CEX ions, increasing ion density and
reducing electric potential, thereby improving plume neutralization.
The use of dimensional scaling to reduce computational costs was also examined, showing that potential
and electron energy are underestimated when scaling is applied. These results underscore the importance of
considering facility effects in ground-based tests to ensure accurate predictions of ion thruster performance
in space. For ion beams that already have large bulk velocities, these differences have little effect. However,
since CEX ions have not been calculated in this study, the effect on CEX ions should be considered in the
future.
Acknowledgments
This work was partially supported by NASA through the Joint Advanced Propulsion Institute, a NASA
Space Technology Research Institute, grant number 80NSSC21K1118. This work used Delta at the National
Center for Supercomputing Applications through allocation TG-PHY220010 from the Advanced Cyberinfras-
tructure Coordination Ecosystem: Services & Support (ACCESS) program, which is supported by National
Science Foundation grants #2138259, #2138286, #2138307, #2137603, and #2138296.
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