Modeling of the Hall-Effect Thruster Plume
by Combined PIC-MCC / DSMC Method
Ye.A. Bondar , V.A. Schweigert and M.S. Ivanov
Institute of Theoretical and Applied Mechanics
Novosibirsk, 630090, Russia
Abstract. A combined particle method was applied to simulate numerically the ATON Hall-effect thruster
plume. This method employs the Particle-in-Cell / Monte Carlo collisions technique for modeling the plume
ions and the Direct Simulation Monte Carlo method for modeling the neutral species. ATON thruster plume
expansion into the vacuum chamber was simulated, and a comparison with experimental data was performed. The
back-pressure effects of the facility were assessed using two different methods of modeling plume-background
interactions. The importance of accurate modeling of this interactions was demonstrated through a comparison
with total ion current measurements. ATON thruster plume expansion under space vacuum conditions was also
simulated, and the structure of slow ion back flow was studied.
INTRODUCTION
Hall-effect thrusters (HET) form one of the most promising families of electric propulsion devices. The main concern
related to spacecraft integration of these thrusters is the possible undesirable interactions of their plumes with sensitive
spacecraft surfaces. These interactions include direct impingement of fast primary ions (translational energy of about
300 eV), which can occur due to large divergence angles of the HET thruster plume (more than 60 deg), deposition
of non-propellant ions produced by erosion of the accelerating channel walls, and also a back flow of slow secondary
ions arising in the plume in the course of ion-neutral charge exchange (CEX) collisions. In order to understand and
accurately assess the effect of these types of interactions, computational simulations of the HET thruster plume are
required.
Such studies were successfully performed by the PIC-DSMC (Particle-in-Cell / Direct Simulation Monte Carlo)
method (see the review [1]), which is a combination of the Particle-in-Cell (PIC) technique for determining the selfconsistent electric field and describing the motion of particles, and the Direct Simulation Monte Carlo (DSMC) method
for collisional processes. Plume ions, and also atoms of the unionized propellant exhausted from the thruster were
modeled in the form of macroparticles, and the phenomenological model of electrons was used. It was found that the
results of this approach are in good agreement with ion current density measurements in the plume flow fields of the
HET thrusters of different types (SPT-100, D-55, etc.). The approach has been extensively upgraded in recent years in
order to provide a better prediction of other parameters of plasma. The model taking into account the nonuniformity of
the electron temperature in the plume, developed by Van Gilder et al. [2], provided better agreement with experimental
data for the SPT-100 thruster.
The main objective of this work is the numerical simulation of the Hall-effect thruster plume by the combined
PIC-MCC / DSMC (Particle-in-Cell plus Monte Carlo collisions / Direct Simulation Monte Carlo) method. This
method divides the simulation process into two stages: simulation of the neutral flow by the DSMC method [3] and
subsequent PIC-MCC [4] simulation of ions. It was shown in [5] that this method allows a considerable decrease in
the CPU-time cost as compared to the PIC-DSMC method with simultaneous simulation of ions and neutrals.
The object of investigation is a plume of an ATON thruster – a Hall-effect thruster of new generation developed
recently in the MIREA institute in Russia. It was mentioned in [6] that the use of a "buffer chamber" ahead of the
accelerating channel and a special configuration of the magnetic field lines enables one to decrease significantly the
plume divergence angle. The results of plasma measurements were presented in [6], such as the total ion current
CP663, Rarefied Gas Dynamics: 23rd International Symposium, edited by A. D. Ketsdever and E. P. Muntz
© 2003 American Institute of Physics 0-7354-0124-1/03/$20.00
549
Faraday cup measurements and the radial profiles of the normalized current density. In the present study, the ATON
thruster plume flow in the vacuum chamber was modeled and compared with the results [6]. The ATON thruster
plume expansion into space vacuum was also simulated. Special attention was paid in this work to modeling the
ATON thruster CEX ion back flow, which is critical with respect to contamination problems. The influence of the
nonuniformity of the electron temperature on the back flow parameters was analyzed.
NUMERICAL METHOD
The HET thruster plume model used in the present study is described in detail in [5]. It is similar to the model used
in [2]. Ions and neutrals of the plume are governed by the following kinetic equations:
v ∂ f eE ∂ f St
∂x
m ∂v
∂ f2 ∂ f2 2eE ∂ f2 v St2
∂t
∂x
m ∂v
∂ fn ∂ fn v Stn ∂t
∂x
∂f
∂t
(1)
(2)
(3)
Here f , f2 , and f n are the distribution functions of the single charged ions, the double charged ions, and the neutrals,
respectively, e is the charge of an electron, E
∇φ is the electric field, and m is the molecular mass. Collisional
integrals St in the right-hand sides of equations (1), (2), and (3) account for ion-neutral and neutral-neutral elastic and
ion-neutral CEX collisions.
Plume plasma is assumed to be quasi-neutral. That means that the electron density is equal to ion charge density.
Two different electron models are used in the paper.
Uniform Te model. Assuming electrons unmagnetized, collisionless, and isothermal makes it possible to use the
f
Boltzmann relation n e x
nre
e exp φ x Te to determine the electron number density (here T e is the electron
f
temperature in eV and n re
e is the reference number density). Therefore, one can obtain the electric field values from
the electron density:
E x
Te ∇ ln ne x
(4)
Variable Te model. Measurements of the plasma parameters show that, in fact, the electron temperature is not
uniform in the Hall thruster plume. A maximum of about 10-14 eV is observed at the thruster exit, and the value
decreases with the distance to some constant value of about 1-3 eV. An analytical approximation of the measured
electron temperature profile is used in the present work. Writing the momentum equation for unmagnetized and
collisionless electrons, one also obtains the expression for the electric field:
T x ∇ ln n x e
e
E x
∇Te x
(5)
For a numerical solution of system 1, (2), (3), and (4) (or (5)) the combined PIC-MCC / DSMC particle method is
used in the present study. This method implies that the impact of ion-neutral collisions on the flow of the propellant
neutrals is insignificant. This assumption allows one to divide the process of plume modeling into two stages:
simulation of the neutral flow by the DSMC method and subsequent PIC-MCC simulation of ions. At the PIC-MCC
stage, the PIC technique is used for modeling of the ion motion and computation of the electric field. Ion-neutral
collisions are modeled by the Monte Carlo method (null-collision technique) using density, velocity, and temperature
flowfields of the neutrals obtained at the DSMC stage. As was shown in [5], the difference in the results of PIC-MCC /
DSMC and PIC-DSMC simulations is insignificant in studying HET thruster plume expansion into space vacuum. The
use of the PIC-MCC / DSMC method allows a considerable decrease in the CPU-time cost of the simulation process,
which is extremely important for simulations of the thruster plume vacuum expansion, including millions of particles
for a correct modeling of the back flow region where the plasma density is very low.
In modeling the ATON thruster plume exhausting into the vacuum chamber, it is necessary to take into account the
effect of the back pressure on the plume flow. The density in the chamber is large under the experimental conditions [6],
being several times higher than the density of all plume species even in the near vicinity of the thruster exit. This
550
significantly increases the impact of ion-neutral collisions. Note that the standard method of including the effect of
the back pressure in PIC-DSMC simulation implies creating temporary particles at each iteration to represent the
background gas (see [2]). This method assumes uniformity of the background gas; therefore, the impact of the ionneutral collisions on the background gas is neglected. In the PIC-MCC / DSMC method, both the background and the
propellant neutrals are modeled at the first DSMC stage; hence, this impact is not included either. In [5], it was shown
that the results of modeling of vacuum chamber expansion of the HET thruster plume obtained by both methods are
in good agreement.
To take into account the interaction of the thruster plume and the background gas more accurately, full PICDSMC simulation with simultaneous modeling of ions, propellant neutrals, and background neutrals were performed
in addition to the PIC-MCC / DSMC simulations. In the full PIC-DSMC simulation, the background particles are
modeled in the same manner as the propellant neutrals, and the impact of the ion-neutral collisions on the background
gas is included in the simulation. Owing to a large difference in plume and background gas concentrations, the
weighting scheme [3] is used for background particles. The majorant frequency scheme [7] is utilized to model the
collisional processes.
The following cross sections are employed in computations for different types of collisions. The VHS model [3] is
used to model neutral-neutral collisions. The cross section from [8] is assumed for elastic ion-neutral collisions. To
model CEX collisions cross section measured by Pullins et al. [9] is taken.
COMPUTATIONAL PARAMETERS AND FLOW CONDITIONS
A sketch of the axisymmetric computational domain and the coordinate system used in the simulations is shown in
Fig. 1. The origin O is the point of intersection of the thruster centerline (X axis) and the thruster exit plane. The thruster
body is a cylinder of length X L and radius RT . The radius is RT 10 cm in all cases, and the length X L for simplicity is
always defined as the distance from the origin to the left boundary. The inner and outer radii of the ATON accelerating
channel annulus are 2 cm and 3.6 cm, respectively. Three different computational domains are used. In simulations
of a plume exhausting into the vacuum chamber, a small domain (Y U 0 2 m, XR 0 4 m, XL 0 1 m) is used to
compare with available experimental data. To analyze the facility effects, computations that include the full chamber
geometry are performed using YU 0 45 m, XR 2 5 m, and XL 0 5 m. In simulations of a plume exhausting into
space vacuum, a domain with a large part of the back flow region is used (Y U 1 2 m, XR XL 1 m).
The computational domain has boundaries of the following types: open boundaries (or chamber walls for the full
chamber geometry case) a, b, and c; centerline d; thruster exit f; sections of the thruster surface e, g, and h.
The following conditions are imposed at the computational domain boundaries. All particles that reached the
open boundary or the exit of the accelerating channel are eliminated from the simulation process. Fluxes of neutrals
corresponding to the initial steady state of the background gas are set at the open boundaries. Ions that reach the thruster
surface or chamber walls are eliminated (or neutralized and diffusely reflected from the surface at a temperature of
300 K in the full PIC-DSMC simulation). Neutral atoms also experience diffuse reflection from the thruster surface.
It is assumed that the normal component of the electric field equals zero at the open boundaries, at the channel exit,
and at the axis of symmetry. In simulation of the plume exhausting into the vacuum chamber, the thruster boundary and
the chamber walls (for the full geometry case) is assumed to be electrically grounded. In simulation of space vacuum
expansion of the plume, it is assumed that a floating potential is established at the thruster surface. The value of this
potential is determined numerically during the simulation from the condition of equal ion and electron currents at the
thruster surface.
A rectangular mesh refining toward the thruster exit is used in PIC computations. Since the Debye length in the
plume plasma is very small (of the order of 10 5 m at the thruster exit), resolving the plasma at the level of this length
scale is computationally intractable. For this reason, the mesh step is chosen sufficient to reach a good accuracy in
solving the equations of ion motion; the mesh step is 1 mm near the thruster exit plane and has a maximum size of
about 5 cm at the open boundaries. In DSMC computations, rectangular collisional cells are also used; the cell size is
chosen under the condition of small variation of macroparameters within the cell; it is also 1 mm at the thruster exit and
about 5 cm at the open boundaries. The time step is governed by the Courant condition and amounts to 0 5 10 7 s.
Several hundreds of thousands of model ions are used in a typical small domain simulation of the plume exhausting
into the vacuum chamber. In simulation of vacuum expansion of the plume and full chamber geometry simulations,
about two or three million of model ions are used.
Initialization of ions and neutrals at the thruster exit plane is performed using the macroscopic parameters of the
551
Y
YU
b
0.4
0.3
c
Y, m
a
6E+15
1.5E+15
3E+15
0.2
1.2E+16
0.1
g
f
e
h
-X L
O
0
d
XR
1.5E+15
3E+15
3E+16
3E+17
-0.2
0
X
1E+17
0.2
X, m
0.4
0.6
0.8
1
FIGURE 1. Schematic of the computational domain and the coordinate system (left). Plasma density, # m3 , in vacuum chamber
simulation (right)
species, which are determined on the basis of experimental data and prescribed integral input parameters. In the present
work, the ATON thruster is simulated under the following operating conditions: total mass flow rate ṁ=3 mg/s and
discharge voltage U= 300 V and 350 V (for different cases). According to [6] measurements, the translational energy
of single charged ions (in eV) is approximately 50 V lower than the discharge voltage. Therefore, we assume 250 eV
for the 300 V case and 300 eV for the 350 V case (translational energies of double charged ions 500 eV and 600 eV for
those two cases, respectively). The Gaussian profile of the ion current density is employed at the thruster exit plane,
and a 30-deg divergence half-angle of the velocity vector is used. The total ion current value of 2.4 A is assumed for
simulations of plume expansion into space vacuum. In modeling plume expansion into a chamber, a set of different
values of the total ion current is employed. A 12-% double ion fraction is assumed, also based on [6] measurements.
The ion temperature Ti equal to 4 eV is used, which is a reasonable value for Hall-effect thrusters [10].
Propellant neutrals (Xe) are simulated under sonic conditions at the thruster exit plane, based on a stagnation
temperature of 1000 K. Two values of the background gas number density of 0 66 10 19 # m3 and 1 1019 # m3 ,
and the temperature value of 300 K reported in [6] are used in vacuum-chamber computations. The reference value of
the electric potential of 37 V is set at the thruster exit in vacuum-chamber computations, also based on [6] data. An
electron temperature Te of 5 eV, which corresponds to the average plume value of [6] is assumed for the uniform T e
case. The analytical electron temperature profile obtained by approximation of the experimental data of [6] with the
constant 4 eV value in the far field is employed in the variable T e case. The reference number density in space vacuum
simulations is assumed to be equal to the ambient LEO plasma density, which is taken to be 10 10 # m3 .
RESULTS
Plume expansion into a vacuum chamber
The general features of plume expansion into a vacuum chamber are presented first. The plasma density isolines are
shown in Fig. 1. The plume plasma expands both along the plume axis, in the radial direction, and in the back flow
region. The plasma density in the back flow region (X 0) is comparable with the plasma density in the core of the
plume. Such a structure of the plume may be explained only by the presence of a very large number of slow CEX ions.
It is clearly seen in Fig.2, which shows the CEX ion fraction isolines, that CEX ions dominate everywhere in the
plume, even in the vicinity of the thruster exit, and more than 80 % of the plume at a distance of 0.5 m from the origin
is composed of CEX ions. Note, the full chamber computations showed a significant influence of the CEX collisions
on the fast ion flow. For example, at a distance of 1 m from the thruster exit, the density of single charged fast ions
decreases by four orders of magnitude. This is demonstrated in Fig. 2, which also shows the axial profiles of fast and
CEX ion number densities. A slower decrease in density of double charged fast ions may be attributed to the smaller
size of the CEX collisions cross section used for double charged ions. The density of CEX ions also decreases with
distance from the thruster exit but more slowly than that of fast ions.
Thus, the effect of CEX collisions is a governing factor in the flow structure in the case of plume expansion into
the vacuum chamber. One can, therefore, expect a significant inhomogeneity of the background neutral density profile
near the thruster exit, where the CEX collision frequency is maximal. Figure 3 shows the profiles of the background
552
10
18
10
17
10
16
10
15
10
14
10
13
0.3
+
X fast
0.99
Xe2+fast
+
XeCEX
0.98
Xe
2+
CEX
n, #/m
Y, m
3
0.2
0.95
0.1
0.9
0.6
0
0.7
0.6
0
0.1
0.8
0.2
0.3
X, m
0.4
0.5
0
0.25
0.5
0.75
1
X, m
0.6
1.25
1.5
FIGURE 2. CEX ion fraction (left) and number densities of ions of different sorts along the accelerating channel centerline
(right) in vacuum chamber simulation
2.6
1
1
0.9
0.9
2.2
0.8
0.8
1.8
2.4
PIC-MCC / DSMC
Full PIC-DSMC
PIC-MCC / DSMC var. Te
EXPERIMENT
J, A
n/n0
n/n0
2
0.7
1.6
1.4
0.7
1.2
0.6
0.5
0.6
Y = 10 cm
Y = 2.8 cm
0
0.1
FIGURE 3.
0.2
X, m
0.3
0.4
0.5
1
X = 1 cm
X = 20 cm
X = 35 cm
0
0.05
0.1
X, m
0.15
0.8
0.2
0.6
5
10
15
20
X, cm
25
30
35
Axial (left) and radial (center) profiles of normalized density of the background gas. Total ion current (right)
gas number density in the directions parallel and perpendicular to the plume axis, obtained by the full PIC-DSMC
simulation, which takes into account the impact of the ion-neutral collisions on the background gas. These results
show that the number density of background neutrals in the vicinity of the thruster exit predicted by the simulation is
40 % lower than the undisturbed background value.
The effect of this decrease in density of neutrals is demonstrated in Fig. 3, which also shows a comparison of full
PIC-DSMC and PIC-MCC / DSMC simulation results with the data of Faraday cup measurements of the total ion
current [6]. The Faraday cup is a cylinder 11 cm in diameter, which is located coaxially with the thruster and moves
along the centerline on a traversing gear. Note, the total ion current at the thruster exit J=2.85 A is used in these
computations. This value is the largest possible for the above parameters under the assumption of total ionization of
the propellant, the flux of background gas neutrals inside the thruster being taken into account. Therefore, the results
presented are a kind of an upper estimate. For lower values of the ion current density at the thruster exit, both full PICDSMC and PIC-MCC / DSMC profiles are lower than the experimental curve; in any case, full PIC-DSMC simulations
give a better prediction of the total ion current. Hence, one may argue that a correct estimate of background pressure
effects in simulation of the thruster plume expanding into the vacuum chamber requires consideration of the effects
of CEX collisions on the background neutral flow, which can result in a significant increase in the integral plume
parameters such as the total ion current. The profile obtained in simulation with the variable T e model shows that the
effect of the electron-temperature inhomogeneity on the total ion current values is not very significant in the case of
plume expansion in the vacuum chamber.
A comparison of normalized ion current density computational profiles with the data of the Langmuir probe
measurements [6] is shown in Fig. 4. Note that both full PIC-DSMC and PIC-MCC / DSMC simulations underpredict
the expansion of the plume core at an axial distance of 12 cm but somewhat overpredict it at a distance of 32 cm
from the exit plane. In the variable Te case a greater widening of the ion current density profile is observed than in the
uniform Te simulation. Generally, all the simulations predict the ion current density profile at different distances from
the thruster exit quite well.
553
X = 12 cm
1
PIC-MCC / DSMC
Full PIC-DSMC
PIC-MCC / DSMC var. Te
EXPERIMENT
0.8
0.7
1
0.5
0.8
0.8
0.7
0.7
0.6
0.5
0.5
0.4
0.4
0.4
0.3
0.3
0.3
0.2
0.2
0.2
0.1
0.1
0.1
0
-12
-10
-8
-6
-4
-2
0
Y, cm
2
4
6
FIGURE 4.
8
10
0
12
X = 32 cm
0.9
0.6
j/j0
0.6
j/j0
X = 22 cm
0.9
j/j0
1
0.9
-12
-10
-8
-6
-4
-2
0
Y, cm
2
4
6
8
10
0
12
-12
-10
-8
-6
-4
-2
0
2
Y, cm
4
6
8
10
12
Normalized ion current density at different distances from the thruster exit
1.2
0.8
3E+12
Y, m
1E+13
1E+12
3E+13
3E+11
0.4
3E+13
3E+14
1E+15
1E+11
3E+15
1E+16
0
-1
-0.5
0
X, m
0.5
Plasma density, # m3 , in space expansion simulation
FIGURE 5.
0.03
0.99
0.2
0.5
3
n, #/m
Y, m
0.005
0.1
0.03
0.1
18
10
17
10
16
+
0.01
0
10
Xefast
Xe2+fast
+
XeCEX
2+
Xe CEX
0.1
1.0
0
1
0.2
X, m
0.3
1015
10
14
10
13
10
12
10
11
0
0.25
0.4
0.5
X, m
0.75
1
FIGURE 6. CEX ion fraction (left) and number density of ions of different sorts along the accelerating channel centerline (right)
in space expansion simulation
Plume expansion into space vacuum
The plume structure for space vacuum expansion for the ATON thruster may be illustrated by the field of the
plasma density (Fig.5). There is a significant difference in the plume structure from plume expansion into the vacuum
chamber. First, note the presence of characteristic lobe structures in the space vacuum case, which are formed by the
CEX ion flow. The density in the back flow region is by orders of magnitude lower than in the plume core. Recall that
comparable plasma density values in both regions are observed in chamber expansion simulations.
The CEX ion fraction isolines in Fig. 6 demonstrate the difference in the plume structure in space vacuum from the
vacuum chamber case. The region where the densities of CEX and fast ions are comparable is very small in the case
of plume expansion into space vacuum. It separates the plume core, where no more than 1 % of CEX ions are present,
from the rest of the flow, where CEX ions dominate. Recall that CEX ions dominate in the entire flow region in the
554
case of plume expansion into the vacuum chamber (see Fig. 2), except for a very small vicinity of the thruster exit, if
any.
The axial profiles of the number densities of fast and CEX ions (Y 2 8 cm) in Fig. 6 also show that the plume
structure under space conditions qualitively differs from the structure of the plume expanding into the vacuum chamber.
First, note that the number density of fast ions decreases much less rapidly with X than in the chamber simulation. At
a distance of 1 m, it is approximately two orders of magnitude lower than at the thruster exit (in the case of chamber
expansion this decrease amounts nearly to four orders of magnitude for single charged ions and nearly to three orders
of magnitude for double charged ions). The fraction of CEX ions in the plume is low (less than 5 % of the total ion
density), and their density rapidly decreases with distance from the thruster exit (at least by three orders of magnitude
at X 1 m). Note, in vacuum chamber simulation, CEX ions dominate in the whole plume, and their density decreases
much slower than that of fast ions with X.
10
14
200
single, un. Te
double, un. Te
single, var. Te
10
single, un. Te
160
double, un. Te
single, un. Te
5
double, un. Te
single, var. Te
140
double, var. Te
13
6
180
single, var. Te
double, var. Te
double, var. Te
4
T, eV
E, eV
n, #/m
3
120
100
3
80
1012
2
60
40
1
20
10
11
0.3
FIGURE 7.
exit plane
0.5
Y, m
0.7
0.9
1.1
0
0.3
0.5
Y, m
0.7
0.9
1.1
0
0.3
0.5
Y, m
0.7
0.9
1.1
Radial profiles of number density, translational energy, and temperature of the CEX ions 1 cm behind the thruster
Recall that of greatest interest in studying the electric thruster plume is the back flow region. The structure of this part
of the plume is illustrated by the radial profiles of the ion number density (at an axial distance of 1 cm from the thruster
exit plane) shown in Fig. 7. The profiles of both single and double charged ions have a maximum approximately at
Y 15 cm for both cases. The maximum value in the variable T e case is higher than in the uniform Te case by a factor
of 1.5 for single charged ions and by a factor of 2 for double charged ions. With increasing radial coordinate, the
density decreases (for Y 1 m, approximately by an order of magnitude from the maximum value). The qualitative
shape of the profiles is identical for both cases.
A significantly greater difference between the cases considered is observed in the profiles of translational energy of
CEX ions (see also Fig. 7). At small distances from the wall, the energy of single charged ions in the variable T e case
is more than two times higher than the corresponding value for the uniform T e case ( 90 eV vs. 40 eV for single
charged ions). With further increasing distance from the wall, this value decreases down to 60 eV for the variable T e
case and increases to 50 eV for the uniform Te case. The energy of double charged ions in both cases is approximately
twice as high as the energy of single charged ions, and the profiles almost coincide in shape.
The greatest difference between the considered cases is observed in temperature profiles of CEX ions in the same
cross section, which is also shown in Fig. 7. In particular, the temperature for single charged ions in the variable T e case
is greater than the value for the uniform Te case by a factor of 5–6 on the average. For Y 0 3, it reaches a maximum
equal to 2 6 eV for the variable Te case and about 0 35 eV for the uniform T e case. The values of temperature for
double charged ions are approximately twice as high; as in the case of energy and density, there are no qualitative
differences between single and double charged ion profiles.
To demonstrate the change in plume parameters from the very near to deep back flow, the profiles of number density
and mean translational energy of the single charged CEX ions at different distances from the thruster exit for the
uniform Te case are plotted in Fig. 8. The plasma density near the side wall of the thruster decreases significantly with
distance from the thruster exit plane (approximately by a factor of 200 from X
0 01 m to X
0 9 m). At the
upper boundary of the domain, it decreases slower (approximately by an order of magnitude). This means that the ion
flux can be directed predominantly in the radial direction, and only part of ions move in the back direction. The radial
profiles of the mean translational energy in the back flow region, single charged CEX ions accelerate to energies of
about 85 eV near the thruster side wall and about 65 eV at the upper boundary of the domain. Note that the mean
energies of double charged ions are approximately two times higher in the back flow region. Despite the fact that the
values of the plasma density in the back flow region in the case considered are not large, the present study shows that
the predicted CEX ion energies are rather high and may cause some impingement problems on the spacecraft surfaces.
555
10
14
90
- 0.01 m
- 0.1 m
- 0.5 m
- 0.9 m
3
10
n, #/m
n, #/m
3
1013
12
1011
10
- 0.01 m
- 0.1 m
- 0.5 m
- 0.9 m
80
70
60
50
10
0.3
0.5
Y, m
0.7
0.9
40
1.1
0.3
0.5
Y, m
0.7
0.9
1.1
FIGURE 8. Number density and translational energy of single charged CEX ions in the back flow region at different distances
from the thruster exit
CONCLUSIONS
The ATON Hall-effect thruster plume was simulated by the combined PIC-DSMC / MCC method for two cases: plume
expansion into the vacuum chamber with a high value of back pressure and plume expansion into space vacuum. Two
models of plume electrons were used in the simulations: the uniform T e model based on the Boltzmann relation and
the variable Te model, which employs the experimentally measured electron temperature profile. The vacuum chamber
expansion simulations using both models provide ion current density profiles that agree well with the data of Langmuir
probe measurements. The computations show that the slow ions produced by CEX collisions dominate in the entire
plume, and the density of the primary fast ions drastically decreases along the plume axis due to collisions with
background particles.
In order to analyze the facility effects, the full PIC-DSMC simulation was performed, which takes into account the
influence of ion-neutral CEX collisions on the background gas. It was shown that an accurate consideration of the
plume-background interaction results in a 40% decrease in the background gas density near the thruster exit. As a
result of this decrease, higher values of the total ion current were observed, which are in better agreement with the
data of Faraday cup measurements.
The space expansion simulations show the qualitive differences in the plume structure from the vacuum expansion
case. An analysis of the back flow region structure was conducted. Singly charged CEX ions in the back flow region
possess rather high translational energies (more than 40 eV for the uniform T e model and more than 60 eV for the
variable Te model). Translational energy of double charged CEX ions is approximately two times higher. Variable
Te simulations predict significantly higher values of the ion temperature in the back flow than that in the uniform T e
case. The radial profiles of the plasma parameters display significant acceleration of CEX ions with distance from the
thruster exit in the far field of the back flow region.
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