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69th International Astronautical Congress (IAC), Bremen, Germany, 1-5 October 2018.
Copyright ©2018 by the International Astronautical Federation (IAF). All rights reserved.
IAC-18-E2.2.10.x48637 Page 1 of 13
IAC-18-E2.2.10.x48637
Modelling and Characterisation of Plasmadynamic Drag on Gridded Ion Engine Propelled Spacecraft in
Very Low Earth Orbit
Shaun Andrewsa*, Lucy Berthouda#
a Department of Aerospace Engineering, University of Bristol, University Walk, Bristol, BS8 1TR, United Kingdom
* Corresponding Author sa15339@my.bristol.ac.uk
# Supervising Academic lucy.berthoud@bristol.ac.uk
Abstract
This work presents particle-based kinetic simulations of Gridded Ion Engine (GIE) plasma plumes, in an analysis
of the modified spacecraft drag profile, resultant of plume interactions with ambient thermosphere, in Very Low Earth
Orbit (VLEO). VLEO is a highly appealing region for spacecraft operations, as reducing the operational height of
remote sensing payloads improves radiometric performance, whilst reducing size, mass, power, and costs required of
the unit. VLEO operation therefore offers high-performing economical spacecraft platforms, but the mission lifetime
is very limited owing to high drag from the residual atmosphere. Detailed characterisation of plume dynamics is vital
in exploring the feasibility of Electric Propulsion (EP) as a means of continuous drag compensation at such altitudes
and mitigating thruster-self-induced drag mechanisms. This research considers the previously undocumented
interactions between EP plumes and onset plasma flow, while also extending on the detailed studies of in-orbit drag
by including interactions of EP operation.
Investigations are conducted for orbital altitudes of 150-400km, where the highest concentration of ionosphere free
electrons and ions was assumed to cause most critical influence on the flow regime, modelling a prograde firing
T5(UK-10) GIE. The plume expands into a rarefied environment of both neutral and charged particles, which required
implementation of the hybrid ’Direct Simulation Monte-Carlo’ - ’Electrostatic Particle-in-Cell’ (DSMC-ESPIC)
method, with density and species compositions obtained from the International Reference Ionosphere IRA-2012 and
NRLMSISE-00 Atmospheric Model.
It is shown that the flow profile is affected by a combination of collisional and indirect electrostatic field
mechanisms. In the immediate aft region of the spacecraft, the interaction is driven by pick-up of freestream ions within
the charge-exchange cloud. The main effect of the plume is to simply deflect the thermosphere freestream as freestream
ions collide with primary beam propellent and accelerate under the thruster potential. Unbounded ion jets form from
collisional exchange at the primary beam edge, and where the energy of freestream ions was enough to penetrate the
main plume, it was found that the plume ions may couple with the freestream to form collective electrostatic
instabilities. The plume and freestream mix into an isotropic structure, which raises the possibility that far-field
interactions beyond the scale investigated here may occur. The consequences of the observed plasmadynamic
mechanisms on the spacecraft drag profile are theorised, and it is shown that effects of EP plume plasma in VLEO
should be included in future analyses, to ensure drag models are complete.
Keywords: Electric Propulsion, Plasmadynamics, Direct Simulation Monte-Carlo, Electrostatic Particle-in-Cell, Very
Low Earth Orbit, Drag.
Nomenclature
Thermosphere Neutral/Ion
B Magnetic Field Strength [T]
Relative Collision Speed [m/s]
Collision Diameter [m]
Electric Field Strength [V/m]
Orbital Height [km]
Boltzmann Constant [m2kg/s2K]
Particle Mass [kg]
Thruster Mass Flow Rate [mg/s]
or Number Density [#/m3]
Thruster Ionisation Efficiency [%]
Total Pressure [Pa]
Generic Propellent Neutral/Ion
Charge Density [C/m3]
Thruster Radius [mm]
Simulation Time [s]
Absolute Temperature [K]
Gamma Flux function
Horizontal Velocity [m/s]
Vertical Velocity [m/s]
Thruster Exhaust Velocity [km/s]
Spanwise Particle Position [m]
Transverse Particle Position [m]
DSMC Viscosity Index
Plasma Frequency [rad/s]
Plasma Potential [V]
69th International Astronautical Congress (IAC), Bremen, Germany, 1-5 October 2018.
Copyright ©2018 by the International Astronautical Federation (IAF). All rights reserved.
IAC-18-E2.2.10.x48637 Page 2 of 13
Subscript
Thruster Reference
Freestream Reference
Electron Property
Thruster Exit Grid
Fast-Moving Neutral/Ion
Simulation Iteration
Particle Collision Relative Property
DSMC Reference Property
Spacecraft
Slow-Moving Neutral/Ion
Acronyms/Abbreviations
AMU Atomic Mass Unit
CEX Charge Exchange
DSMC Direct Simulation Monte-Carlo
EP Electric Propulsion
ESA European Space Agency
ESPIC Electrostatic Particle-in-Cell
GIE Gridded Ion Engine
GOCE Gravity Field and Steady-State Ocean
Explorer
IRI-2012 2012 International Reference
Ionosphere
LEO Low Earth Orbit
MCC Monte Carlo Collision
NRLMSISE-00 International Standard Atmosphere
NTC No Time Counter
SFU Solar Flux Unit
TSS1 Tethered Satellite System
VHS Variable Hard Sphere
VLEO Very Low Earth Orbit
1. Introduction
Very Low Earth Orbit (VLEO) describes the region
of orbit altitudes below 400km, characterised by high
rates of orbital decay from atmospheric drag. Despite this,
the region remains highly appealing for spacecraft
operations, providing substantial improvements in the
performance of Earth observing payloads [1].
With decreasing orbit height, the spatial resolution of
optical instruments increases for a constant aperture.
Thus, resolution can be increased for the same payload
volume or the payload volume and mass reduced for
equal resolution by operating in a lower orbit. For radar
payloads, reducing the operational altitude can reduce the
transmitted power requirements and minimum antenna
area whilst maintaining a given resolution. Furthermore,
as the distance to the imaging target is reduced, the
radiometric performance is improved according to the
well-known inverse-square law [2]. This is significant for
optical, radar, and communications-based detectors, such
that the sensitivity of a given instrument can be
compromised upon whilst achieving similar radiometric
results. This then leads to reduced instrument cost, size,
and mass.
Communications also benefit from reduced power
requirements and downlink data rates. Operating the
spacecraft at a lower orbit also increases the available
payload mass fraction of the launch vehicle. VLEO
operation therefore offers high-performing economical
spacecraft platforms, but the mission lifetime is very
limited owing to high drag from the atmosphere…
To maintain altitude in VLEO, a spacecraft therefore
requires regular prograde manoeuvres, or a method of
continuous low thrust drag compensation. The high
specific impulses provided by electric propulsion (EP)
systems makes the operation of such systems feasible as
a means of drag compensation in VLEO. EP thrusters can
allow continuous compensation for the variable
deaccelerations experienced by a spacecraft due to
atmospheric drag, without the vibrations and limited
mission lifetime with the use of conventual chemically
powered rocket engines, which are capable only of
restoring the path of the host spacecraft to a purely
inertial trajectory. The use of EP as a means of drag
compensation was demonstrated by the European Space
Agency’s (ESA) Gravity Field and Steady-State Ocean
Circulation Explorer (GOCE), launched in 2009. GOCE
utilised dual-gridded electrostatic ion thrusters to
compensate for the orbital decay losses [3], sustaining an
orbital altitude of 255km for 55 months before expending
its fuel.
The mission lifetime of a VLEO-dwelling spacecraft
is limited by the quantity of propellent carried. The
propellent required is proportional to the thrust and by
extension the drag that the craft experiences. Effects
introduced by the operation of a Gridded Ion Engine
(GIE) have long raised several concerns. This includes
plume backflow contamination and spacecraft
interactions with the plume-induced plasma
environment. Backflow contamination can lead to
material deposition that can affect thermal control
surfaces, optical sensors, photovoltaics, science
instrumentation, and communications. The induced
plasma environment will modify spacecraft charging
characteristics and can lead to subsequent charge
interactions with the ambient environment. The GIE
plume will modify the properties of the VLEO
thermosphere flowing around the spacecraft; directly
from ambient-plume interaction, as well as indirectly via
its effect on spacecraft charge and the near-spacecraft
plasma environment. As a GIE will be operating
continuously in a drag-compensating role, a detailed
characterisation of the plume dynamics in the rarefied
plasma environment of VLEO needs to be carefully
assessed.
Due to the complexity of the problem, the difficulty
of replicating space conditions in a laboratory, and the
lack of prospects to flight test EP/GIE systems, particle-
based simulations are the only suitible means to conduct
research. In particular, Roy et. al. [4] conducted hybrid
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Copyright ©2018 by the International Astronautical Federation (IAF). All rights reserved.
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particle-fluid simulations to study the effluent effects of
the plume region, with detailed study on the interactions
of charge-exchange backflowing propellent. Tajmar [5]
characterised the influence of induced plasma
environments on spacecraft charging, using various
hybrid and full-particle based simulations with floating
potential models of spacecraft surfaces. Merino et al [6]
have developed full-fluid models of both near and far
plume regions. They assessed hypersonic plume
expansion in very high computational resolution. The
fluid simulations were applied to determine the forces
transmitted, by a GIE plasma plume, to a remote object
[7]. Wang and Brophy [8, 9] have developed full-particle
and hybrid models of single and multiple thruster plumes,
extending their studies to the effects of static ambient
environments on plasma-plume development. There
have been no studies concerning other aspects of plasma-
plume interactions, such as GIE operation in the VLEO
thermosphere environment and plume-thermosphere
interactions. To the authors knowledge, there has never
been a study into the effects of GIE operation on its host
spacecraft drag profile.
Fig. 1. The Plasmadynamic Flow Regime of GIE
Propelled Spacecraft in VLEO
For a spacecraft operating in VLEO, the GIE
performs in the tenuous, relatively cold plasma of the
thermosphere, with a hypersonic flow speed, and within
the Earth’s magnetic field. A schematic overview of the
regime is given in Fig. 1. It can be assumed that
mechanisms by which the drag profile is modified can be
categorised into three processes: 1: Particle-particle
collisions between propellent neutrals/ions and
freestream thermosphere neutrals/ions. 2: Accelerations
to thermosphere and propellent ions due to the
electrostatic field induced by GIE plasma plume, as well
as the ambient plasma potential field. 3: Electrostatic
accelerations to thermosphere and propellent ions
because of the spacecraft surface charge potential.
While the literature describing the particle-based
modelling of GIE plumes and the associated plasma
interactions with spacecraft systems is extensive, most
studies conducted so far have concentrated on thruster
operation in vacuum environments. Wang [10, 11] has
investigated the interactions between ion thruster plumes
in the presence of solar wind. It was found that the solar
wind was of too little density to influence the plasma
environment near the thruster. But, far downstream, the
plume ions coupled with those of the ambient wind
plasma to result in a range of instabilities. There have
been no studies concerning aspects of plume interactions
in relatively denser ambient environments, such as that in
VLEO.
VLEO thermosphere couplings have never been
examined in association with GIE firing. The properties
of an ion thruster plume expanding into the VLEO
environment involves much larger number densities than
those seen in solar wind plasma interactions and it is not
immediately clear how significant the interactions would
be in the context of spacecraft drag. There have however
been thorough studies of the interactions between the
Low Earth Orbit (LEO) environment and traditional
chemical thruster plumes, both experimental and
computational.
Bernhardt et al [12] characterised the interactions of
neutral rocket plumes in static charged backgrounds,
supplemented with space-based measurements in the
ionosphere. Analysis by Burke et al. [13] investigated the
charge-exchange backflow of the thruster firing of the
Tethered Satellite System (TSS1), noting high collisional
energies at the craft leading edge, induced by upstream
propellent. It was found that significant scattering
occurred near the thruster exit, as well as after collisions
with the neutral gas and ambient oxygen ion
environment, giving in detail the resulting energy
distributions of freestream particles picked up by the
plume [14]. The development of both the neutral plume
and the freestream were found to be strongly influenced
by the presence of local electromagnetic fields by
Stephani and Boyd [15]. The hybrid-kinetic model that
they developed demonstrated that the local environment
and the magnetic field in LEO resulted in a cross-flow
diffusion of the plume, increasing the density of
propellant upstream and transverse far from the thruster.
It is therefore a reasonable hypothesis to say that the
coupled intra-electrostatic and collisional interactions,
between the VLEO environment and an expanding
plasma-plume, influences the particle collisions and
electrostatic stress seen at spacecraft surfaces, and by
extension the drag force.
Drag calculations were previously performed on
satellite bodies in VLEO, to assess EP drag-
compensating feasibility, by Walsh and Berthoud [16,
17]. The study modelled the VLEO environment as
solely neutral, modelling ionic species as their respective
uncharged particles, using the Direct Simulation Monte-
Carlo (DSMC) method, and the GIE was not modelled.
This research expands that study by fully modelling the
GIE plume within the ambient flow, with consideration
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for the charged species of the ionosphere, to capture the
drag profile resulting from electrostatic mechanisms.
In this paper initial plasmadynamic drag analysis via
particle-based simulations of the interaction of GIE
plumes with the rarefied ambient VLEO thermosphere
are presented. In section 2, an overview of plasma-plume,
spacecraft and thermosphere interactions is given. In
section 3, the particle-kinetic methodology and
simulation setup is explained. In section 4, initial
simulation results are presented. The aim within is to
investigate the mechanisms governing the flow regime
and the theorise the consequence upon the spacecraft
drag profile. This paper discusses a qualitative analysis,
and quantifying the results is ongoing. Lastly, section 5
contains conclusions and initial thoughts towards future
work.
2. Plasmadynamic Interaction Phenomenon
2.1. Spacecraft Plasmadynamics in the Thermosphere
In the tenuous plasma environment of the VLEO
thermosphere, the relative speed of the spacecraft vastly
exceeds the ion thermal speed in the plasma and, due to
the greater mass of incoming ions than electrons, the
thermal speed of electrons is far greater than that of ionic
or neutral species [18]. As consequence, a spacecraft
surface initially experiences a larger flux of electrons
than neutrals and ions, acquiring a net negative charge
compared to the surrounding environment. This work
shall therefore focus on the discussion of negative
spacecraft surface potentials. Negative potential
manifested by the build-up of charge on the spacecraft
surface accelerates near ions and repels electrons. A
dynamic equilibrium is established between the flux of
ions and electrons in the near environment. The
acceleration and repulsion of ions and electrons forms a
plasma sheath; a region of charge discontinuity
surrounding the spacecraft where the plasma is
electrostatically shielded from the spacecraft’s floating
potential. This can be understood as a plasmadynamic
‘boundary layer’.
Fig. 2. Illustration of Mesothermal Flow over a
Negatively Charged Spacecraft in the Thermosphere
The compression of the sheath at the leading edge,
and elongation of sheath in the wake, is a result of the
influence to incoming ion velocity, where hyperthermal
ions are unable to penetrate the wake region aft of the
spacecraft. Sub-thermal electrons however, can fill the
void of the wake, creating a radial negative charge
gradient trailing in the wake that will attract nearby ions
and enhance the fill rate. Such conditions are described
as mesothermal. The mesothermal structure of flow
around a spacecraft body is summarised in the illustration
of Fig. 2. The refill of the wake by deflected ions
generates an ion density gradient travelling radially to the
oncoming flow as ions move to fill the wake. Within the
wake, the focus point of deflected ions can also generate
a positive region of sufficient strength to cause a tributary
deflection. This has been observed to be more prominent
with spacecraft of smaller spanwise dimensions [19].
Finally, depending on where they enter the sheath, ions
within certain energy groups are deflected through the
near wake on unbounded (hyperbolic orbits that form ion
pseudo-waves) or bounded (impact the body) trajectories
[20, 21]. This anisotropic structure of plasma interactions
and associated kinetic phenomena that arise from the
sheath structure are difficult to assess. For such
conditions, it has been common for direct and indirect
plasmadynamic forces to be calculated directly from self-
consistent solutions by measuring the momentum fluxes
through a control surface bounding the spacecraft [22]. A
recent numerical study by Capon et al [23] provides a
thorough characterisation of the direct and indirect
charged plasmadynamic drag mechanisms in the
ionosphere.
2.2. The Gridded Ion Engine Plume
In GIEs, propellant ions are accelerated
electrostatically by a system of grids to form a high
velocity beam. Neutralizing electrons are emitted from a
neutralising cathode. During normal GIE operation,
electron emission can be assumed to keep the global
plume wholly quasi-neutral and prevent the spacecraft
from charging up significantly.
Although GIE systems typically possess ionisation
efficiencies >90%, some proportion of the propellant
will diffuse across the ion optics as a neutral gas. The
neutral gas particles possess slow thermal velocity,
remaining in high density near the thruster exit,
exceeding that of the energetic ions in the primary beam.
Charge-exchange (CEX) is a process which occurs when
outer electron shells of a neutral atom and ion collide,
resulting in electron transfer from the atom to the ion
[24]. CEX collisions occur in the plume near the thruster
exit, resulting in the conversion of slow-moving neutrals
and fast-moving ions into fast-moving neutrals and slow-
moving ions as per
(1)
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where is representative of an arbitrary
monoatomic propellant. In the absence of an
electromagnetic field, the primary beam ions follow line-
of-sight trajectories because the electric field within the
plume is too small to perturb their motion. Hence, the
primary ion beam will keep its coherent structure. The
electrons are much more mobile than ions, so the centre
of the plume has a positive potential. This potential
causes the slowly moving CEX ions to move transversely
out of the plume. The result is the formation of a CEX
cloud, a torus-shaped plasma structure surrounding the
primary beam near the thruster exit. The ions produced
from the CEX interactions have the most detrimental
impact on spacecraft operations; CEX ions scatter to
regions upstream of the thruster exit. The resultant
plasma sheath that forms around the spacecraft becomes
highly influenced by thruster operation. The interactions
of CEX ions can affect optical sensors, attenuate
communication signals, cause surface erosion and
charging, as well as destructive discharge [25].
3. Application of Particle-Kinetic Simulations
2.1. DSMC-ESPIC Framework
The collisions between ambient VLEO particles and
ion thruster plume propellant occur under extremely low-
density conditions, where traditional continuum flow
methods cannot be applied. The most appropriate
numerical method for simulation of the regime is the
Direct Simulation Monte-Carlo (DSMC) method,
originally developed by Bird [26]. It is well suited for
non-equilibrium gas flow problems in which binary
collisions are dominant. It models the evolution of the
particle distribution function through particle collisions.
The charged plasma is subject to self-consistent
electrostatic fields, which requires the Electrostatic
Particle-in-Cell (ESPIC) method [27]. This is a kinetic
method that determines solutions to the Vlasov-Maxwell
equations. In this work, the subsequent system of rarefied
collisional and plasma interactions is therefore simulated
in Starfish, a two-dimensional code for plasma and gas
kinetics problems [28]. It implements the ESPIC method
to model plasmas, with multiple gas injection sources,
and a detailed surface handler for surface interactions.
The species interact with each other via DSMC or Monte
Carlo Collisions (MCC) or by chemical reactions.
This work uses a structured cartesian mesh which
facilitates both the DSMC collisional and ESPIC
electrostatic calculations. The orders of magnitude
spanning the properties of electrons from ions and
neutrals, makes their inclusion complex as particles
within the simulation. If modelled as DSMC
macroparticles, extremely small time-steps would have
been required to resolve the electron behaviour, and an
infeasible quantity of time required for simulations to run
to steady-state. The ESPIC potential solver uses a hybrid
kinetic-fluid approach to model the plasma, and it is
assumed that the plasma is quasi-neutral in nature. Heavy
neutral and ionic species are modelled as DSMC
macroparticles, while the electrons are represented as an
equilibrium fluid through momentum equations. Since
this investigation concerns itself with plasmadynamic
interactions in the near-field of the spacecraft, the
influence of the Earth magnetic field is assumed
negligible, i.e. =0.
At each simulation time-step, first, the total number
of collision pairs, within each mesh cell, is determined by
a multi-species implementation of Bird’s No Time
Counter (NTC) method, with the collision probability
determined with total collisional cross-sections per
Equation 4.63 found in [26].
(2)
Post-collision velocities are assumed to follow
isotropic scattering. With DSMC collisions handled, the
ESPIC approach is used to determine the acceleration on
the charged particle species by the self-consistent electric
field. The electron charge density is interpolated to the
mesh nodes, and the local potential is then determined
through the Boltzmann relationship, which approximates
the plasma potential, under the quasi-neutral assumption,
according to:
(3)
The use of this relation makes several assumptions;
the electron flow is treated as an isothermal, ideal gas,
and the influence of intra-electromagnetic properties is
neglected in the electron fluid momentum equations. The
electric field is then determined as:
(4)
Finally, the consequent acceleration from Newtonian
motion coupled with Maxwell’s equations through the
Lorentz force above is used to advance these macro-
particles through time, using a leap-frog integration
method, by imposing a velocity increment on the ions at
each time step [29].
(5)
3.2. Momentum/Charge-Exchange Collisions
The system can be considered to consist of four
general sets of chemical species: propellent neutral/ions,
referred to generally as , and ambient plasma
neutrals/ions Heavy species collisions are treated
according to standard DSMC collision dynamics, with
the possibility of a charge transfer for neutral/ion
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collision pairs. Analysis by Rapp and Francis [30] has
demonstrated that the elastic momentum exchange cross-
sections and charge-exchange (CEX) cross-sections are
approximately equivalent. This relationship was assumed
true for this implementation, and if the collision under
consideration involved a neutral-ion pair, the probability
of a CEX event was taken to be 0.5, with the collisional
cross-section using the data described within [31]. CEX
collisions were modelled using the Monte-Carlo-
Collision (MCC) method, which differs from the DSMC
in that the source particles are collided with a target
cloud, which does not have its properties updated. The
density of the target neutrals were many orders of
magnitude greater within the system of interest than the
density of the source ion species. Therefore, it was
considered reasonable to assume that the neutrals were
affected by collisions to such a small extent as to be
negligible, and the MCC method valid. The MCC method
is much easier to implement and computationally less
demanding, thus the simulation time was greatly reduced
with this assumption. The full set of permitted
interactions are shown in Table 1.
Table 1: Permitted Collision Interactions
DSMC
DSMC/MCC
DSMC
DSMC/MCC
-
DSMC
DSMC/MCC
DSMC
-
-
DSMC
DSMC/MCC
-
-
-
DSMC
Due to the lack of data available for the representative
gas properties of the species in this system at the energy
levels of interest, the momentum-exchange collisions are
modelled using the Variable Hard Sphere (VHS) method
suggested by Bird [26, 32] with isotropic scattering of
post-collisional velocities. The reference molecular
diameters, reference temperatures and viscosity indices,
required for representation of the species in the DSMC
method, were acquired from Appendix A of [32].
3.3. Numerical Setup
The plume flow examined in this initial study models
the T5 (UK-10) GIE. The T5 was chosen because of the
large repository of experimental data available from
vacuum chamber testing [3, 33, 34], but primarily as it
was the EP system used on the GOCE spacecraft, and
therefore allows simulations to be more easily compared
to GOCE accelerometer data in potential future work.
Under typical operating conditions, using a fuel of
Xenon, the =50mm radius thruster has a mass flow rate
of =0.677mg/s and exit beam velocity of around
=40km/s [35]. Near the thruster exit, the temperature of
the beam ions is assumed to be that of the accelerating
exit grid of =1000K, and the temperature of the
neutralising electron fluid to be on the order of =1eV.
The focus of this paper considers a spacecraft with a
uniform, fixed surface potential of =-10V with
respect to the environment. The influence of self-
consistent charging is the subject of future work.
Ionisation within the GIE chamber can produce
multiple ionised propellent states. The fraction of doubly-
charged ions is typically less than 10% for GIEs, and thus
it was assumed the effect of these higher charge ions was
negligible, and they were neglected in initial simulations.
The thruster exit boundary was defined as a Maxwellian
source; ions generated at a specified mass flow rate and
exhaust velocity, given by the thruster operating
parameters, and then a random thermal velocity is added,
sampled from the Maxwellian according to the
prescribed temperature of the thruster exit grid. The
unionised neutrals are modelled and tracked as particles,
with CEX ions generated directly from collisions
between ions and neutrals. The neutrals, like the primary
beam ions, are sampled with a Maxwellian distribution,
with a mass flow rate determined from the thruster
ionisation efficiency and null non-thermal velocity (i.e.
they drift across the exit with only thermal speed).
Fig. 3. Neutral Species Number Density Variation with
orbital Altitude in VLEO
Fig. 4. Charged Species Composition Variation with
orbital Altitude in VLEO
VLEO conditions were modelled using data from the
International Reference Ionosphere 2012 (IRI-2012) [36]
and the NRLMSISE00 Atmosphere Model [37]. This
model provides temperature and gas species number
densities (for He, O, N2, O2, Ar, H and N) covering all
the range from sea level up to the exosphere. It accounts
for the contribution of non-thermosphere species to the
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drag at high altitudes, such as O+ and hot oxygen
(energetic oxygen atoms resulting from photochemical
processes in the upper atmosphere [38]) by including a
component named ‘anomalous oxygen’. To correctly
illustrate the full electrostatic interactions in detail, this
study does not use the anomalous oxygen parameter, and
instead models each ionic/energetic species individually
from IRI-2012 data.
Fig. 3. And Fig. 4. present the composition
parameters used in initial simulations, in the form of
number density and proportions of species in their
ionised states. Simulations were conducted for 150
450km in increments of =50km. At any given
altitude, the properties of the ionosphere and
thermosphere are not uniform, varying with the solar
cycle as well as the Earth’s ground topology and other
local irregularities. Thus, over a single orbit in VLEO,
the density and composition of the environment can vary
significantly. For the initial simulations presented here, a
3-month average density and composition was calculated
for the NRLMSISE00 default data of 01 Jan 2000 at 55
latitude 45 longitude, with F10.7 solar radio flux of
163.1sfu. This is a first implementation, falling between
the last recorded maximum and minimum solar fluxes of
215sfu and 67sfu.
Fig. 5. Simulation Topology and Boundary Conditions.
Every 5th mesh node shown for clarity.
For simulations presented within, the spacecraft is
taken to be a sphere with radius 0.25m. This allows
mechanisms to be preliminarily calculated within the
context of the classical ‘ion flow over a charged sphere’.
The domain extends m and
m, and its topology is illustrated in Fig. 5. The
spacecraft is located at m and
m. The thruster exit grid centre is
located at m, m, and generates thrust in
the -direction, such that the plume expands in the
+direction. The exit plane boundary conditions were
applied according to T5 observational data from Crofton
[35], and the thruster simulation parameters are shown in
Table 2.
Simulations are half-domain symmetric 2D models of
the spacecraft cross-section, and it is assumed the flow
profile is axisymmetric in the x direction. Thermosphere
flow is from left to right. The flow was taken to have
velocity equal to the orbital speed at the simulated
altitude. A uniform source boundary was applied at the
inlet, with the mass flow rate of each species determined
using the known orbital speed and number density. The
freestream reference electron density and electron
temperature were taken directly from IRI-2012.
Dirichlet potential boundary conditions were applied at
the freestream inlet (reference potential =0), thruster
exit and spacecraft surfaces. At the exit, the potential was
set corresponding to the GIE accelerator grid voltage
=-240V. Neumann conditions were applied at right-
hand and upper freestream boundaries.
Table 2: T5(UK-10) Simulation Parameters [35]
Parameter
Simulation Value
Radius [mm]
50
Mass Flow Rate [mg/s]
0.677
Exhaust Velocity [km/s]
40
Exit Grid Voltage[V]
-240
Ionisation Efficiency
78
Exit Temperature [K]
1000
Reference Potential [V]
0
Electron Temperature [eV]
1
Gas-surface interactions are diffusely reflecting and
neutralising with complete thermal accommodation to a
=500K spacecraft wall; investigation into the effect
of surface temperature and surface interaction models is
planned for future work. Mesh spacing was
==0.01m. The simulation time-step was =
. The time-step chosen such that it resolves ion
oscillations defined by the ion plasma frequency
and ensures that simulated particles spend multiple
time-steps within a single cell
. The
number of particles represented within each DSMC
macroparticle was based on the conservative methods
laid down by Boyd [39], and the simulations contained
approximately 1 million particles in steady-state
conditions. As the DSMC method is stochastic, a large
number of particles is required to obtain meaningful
statistics.
4. Results and Discussion
4.1. VLEO Thermosphere Freestream
Simulation results for the nominal case of
thermosphere freestream are presented in Fig. 6. The
results are given for flow at =400km altitude, where O+
is the dominant species. The wake formed behind the
spacecraft is clearly seen. It is also clear to see the
reflection of ions at the centreline, the line of symmetry.
This reflection corresponds to the influx of particles from
the opposite half of the simulation, and the secondary
deflection of ions due to positive potential build up in the
immediate wake. This is best seen in the plot of the
vertical velocity in Fig. 6a. The focus point of wake ion
deflection occurs at 0.6m, after which ions are
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reflected into the freestream, with inlet conditions
matched at 3m. The plasma sheath is seen to possess
thickness around the order of 5cm at the fore-body.
Fig. 6. a) O+ Ion Vertical Velocity b) O+ Ion Horizontal
Velocity, =400km Thermosphere Freestream
4.2. Vacuum GIE Firing
Fig. 7. shows the contours of plasma potential and the
total Xe+ ion density for the nominal case of the T5 GIE
steady-state firing in a vacuum. The outflow of the CEX
ions form the expected charge-exchange cloud, and the
primary beam has a 14 divergence half angle, agreeing
with the data of Crofton [35]. Once outside the plume,
the CEX ions come under the influence spacecraft sheath.
Outside the region of the primary beam, the CEX ions
begin expansion, drawn upstream by the negative surface
potential of the spacecraft. The result is an anisotropic
scattering in the near exit region to the upstream near the
spacecraft. The resulting expansion fan becomes a
preliminary sheath of plasma downstream of the
spacecraft, which turns the trajectories of the CEX ions
into the upstream direction, until they enter the sheath of
the spacecraft.
Fig. 7. a) Plasma Potential b) Xe+ Number Density
, Vacuum Case GIE Firing
4.3. GIE Firing in VLEO Freestream
Results in this section are presented for the extreme
thermosphere cases simulated: =150km altitude where
the charged environment is dominated by 95% NO+, and
=400km where the composition is 96% O+. The flow
behaviour can thus be more clearly analysed with respect
to the single foremost charged species.
The development of the freestream in terms of the ion
number density is illustrated in Fig. 8. Thermosphere ions
are unable to penetrate the CEX cloud of the thruster, and
the ions are partially “picked up” by the plume. A high-
density concentration of ions forms at the root of the CEX
cloud, and collisions between thermosphere species and
propellent within the CEX structure prevents refill of the
wake. Momentum and CEX collisions between the
relatively fast moving propellent ions and slow moving
ambient, greatly reduces the velocity of the ambient ions,
and they become caught in the radial electrostatic field
that governs the CEX cloud, acting to reinforce the CEX
structure. The result is that the distribution of the
freestream tends away from the initial uniform and
toward the anisotropic Maxwellian of the plume.
Fig. 8. Thermosphere Ion Number Density with
Velocity Streamlines a) O+ =400km , b) NO+
=150km
The freestream couples into a relatively warmer
plasma that expands with the primary beam. The vertical
velocity distribution of the thermosphere ions is shown
in Fig. 9., and it indicates a definitive boundary between
ions that have penetrated the primary plume, and those
deflected transversely via collisions at the beam edge. At
=400km, the comparatively light O+ ions (16amu) are
accelerated to radial velocities on the order of
=5km/s, and this velocity component is not observed
to return to near freestream conditions within the domain
of the simulations. The NO+ ions (30amu), at =150km,
are seen to reach radial velocities of 2-4km/s, and the rate
of deceleration toward freestream uniformity is far
greater than that of the O+, with near-zero vertical
velocity returned at approximately =3m. It is apparent
that with decrease in the charged species weight (and by
extension increase in orbital altitude), the freestream is
more sensitive to plume deflection. It is clear that lighter
species are subject to greater accelerations from kinetic
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collisions at the boundary and the repelling intra-
electrostatic field contained within the plume.
Fig. 9. Thermosphere Vertical Velocity a) O+ =400km
, b) NO+ =150km
Far downstream from the thruster exit, where the
plume density has decreased to a level that the VLEO
plasma can more easily penetrate the plume, it is possible
the plume ions may couple with the ambient plasma
through collective electrostatic effects. Fig. 9. illustrates
a turbulent behaviour in the wake at >1m, that can also
be seen to contain an oscillatory pattern in the spanwise
dimension. Low energy CEX ions and the energetic
primary beam ions can constitute a free energy source,
which may drive one of several electromagnetic
instabilities into the propagation of the freestream. The
instabilities can generate enhanced electrostatic field
fluctuations, leading to significant particle scattering.
This raises the possibility that far-field interactions may
affect the plasma environment near the spacecraft,
beyond the scale of the simulations here.
Fig. 10. Thruster Xe+ Ion Number Density ,
a) =400km, b) =150km
Fig. 10. shows the propellent ion number density
distribution. The typical expansion of the CEX cloud to
the upstream does not occur as is shown in Fig. 6b. The
self-consistent electrostatic field contained within the
tenuous ambient flow acts to damp out the large plasma
potential gradient typically seen between the negative
spacecraft body and the positive structure of the plume,
not unlike the viscosity in continuum flows. The effect is
far slower propagation of the CEX plume compared to
the vacuum case, and the trajectory of CEX propellent
ions appear limited to 95 with respect to the -axis at
=400km, and narrower 82 at =150km. The high
density, heavier flow at lower altitude restricts the
upstream penetration of propellent ions through the
collection of positive freestream ions caught in the CEX
structure; a higher concentration at lower altitude is
immediately apparent in the freestream ion density
comparison in Fig. 8.
4.4. Observed Interactions in the Context of Drag
The nature of the drag in these observations can be
categorised into two forms. First, the direct drag,
resulting from mechanical momentum exchange between
particles and the spacecraft body. Second, indirect drag,
manifesting itself as electrostatic field stress on the
spacecraft surface, related to the Maxwell stress in the
plasma flow. This results in plasmadynamic shear stress
that imparts a force on the spacecraft to reflect the
deformation of fields by the plasma sheath.
The introduction of an ion thruster into the regime
results in a very large spanwise potential gradient across
the distance of the host spacecraft, from the highly
positive potential contained within the primary ion beam,
with direction following the structure of the CEX cloud,
culminating in the negatively charged spacecraft surface.
The consequence is an electrostatic plasmasphere, that
acts to deflect the freestream. Negative potential held by
the spacecraft surface accelerates near ions and repels
electrons, and the plasma sheath is typically compressed
at the leading edge, but at approximately three-quarters
span, couples to the potential field of the plume. The
sheath is therefore effectively elongated to infinity in the
wake and only ions with the very highest of energies can
penetrate the wake region aft of the spacecraft. Electron
in-fill is significantly enhanced. The ions are picked up
by the plume structure and reflected around the plume
boundaries, ending in trajectories parallel to the primary
beam expansion.
Fig. 11. Total Pressure a) =400km, b) =150km
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The process is no longer mesothermal, and the aft-
spacecraft sheath thickness is that of the thruster-plume,
where the momentum collisions at the primary beam
edge represent a potential energy barrier. This potential
barrier no longer allows ion concentration points in the
flow-field where, instead of undergoing small angle
deflections into the wake, ions are deflected into
trajectories around the spacecraft body. This leads to
formation of un-bounded ion jets external to the plume
and ion pseudo-waves at the plume edge and extending
within. The ion jets are clear in Fig. 8, presented as ion
distributions with large radial velocities external to the
plume. The influence of such reflected ion jets may
manifest itself as a direct wake thrust due to momentum
collisions at the freestream-plume interface. The net
effect can be observed in Fig. 11. where at =150km, the
higher proportion of ions deflected with the plume
increases and so too does the magnitude of the spanwise
pressure gradient. This is perhaps counter-intuitive, as at
lower altitudes a reduction in drag from increased wake
thrust is seen despite higher flow density. This suggests
that the drag on GIE propelled craft is dominated by
charged species aerodynamics and not the total
composition. However, the deflection of these ions must
impart an indirect drag countering this direct wake thrust
force. Ions that can penetrate the plume and thus into the
wake also contribute to the indirect wake drag. The
potential structure of the plume hides indirect effects in
this qualitative assessment.
The forebody drag in this shielded flow is dominated
by direct drag from sheath ion collection. Due to the
electric field induced by the thruster, less compression
occurs and the sheath thickness increases, and direct
charged drag forces may be tend to the mechanical
momentum imparted to the fore-body by an equivalently
neutral flow. Indirect forebody thrust is likely to be
caused by accelerated non-colliding ions with such large
sheath thickness.
5. Summary and Conclusions
A DSMC-ESPIC framework for analysis of
plasmadynamic ion thruster plume interactions around
VLEO dwelling spacecraft, in the context of spacecraft
drag, has been established.
It has been shown that the flow profile is affected by
a combination of collisional and indirect electrostatic
mechanisms. In the immediate aft region of the
spacecraft, the interaction is driven by the pick-up of
freestream ions responding to the radial electrostatic
potential and high propellant concentration within the
charge-exchange cloud. The main effect of the plume is
to simply deflect the thermosphere freestream as
freestream ions collide with primary beam propellent and
come under the electrostatic acceleration of the beam
expansion. This manifests as two principal mechanisms.
The formation of ion jets from the collisional exchange
at the primary beam edge, deflecting freestream ions on
unbounded paths and, where the energy of freestream
ions was enough to penetrate the main plume, it was
found that the plume ions may couple with the freestream
through collective plasma effects as cyclic electrostatic
instabilities bounded by an ion pseudo-wave, and causing
turbulence in the plume. The plume and the freestream
couple into an isotropic structure which raises the
possibility that far-field interactions beyond the scale
investigated here may affect the plasma environment
near the spacecraft.
The spacecraft drag has been theorised to exist from
the collisional exchange at the plume-freestream
interaction, electrostatic stress from the increased
transverse ion scattering in the wake, indirect
electrostatic drag from the mixing of plume and ambient
ions that have penetrated the primary beam, direct
momentum exchange with freestream ions impacting the
forebody, and finally indirect thrust from the acceleration
of non-impacting ions around the spacecraft surface by
the plasma sheath.
The qualitative analysis presented in this paper only
addresses the possibility and the mechanisms of VLEO
thermosphere interactions with GIE plumes in the
context of drag but does not attempt to quantify the
effects of the individual hypothesised mechanisms or net
effect on the spacecraft drag profile. Only a fixed
negative spacecraft potential was considered, and the
quasi-neutral model does not fully address the effects of
plasmadynamic instabilities and nonequilibrium effects,
including the exact behaviour of the VLEO and thruster-
neutralising electrons. This will be addressed in future
work, which aims to extend this study to fully-kinetic
simulations, and characterise the spacecraft drag profile
quantitatively, through plasma momentum balance,
whilst including a self-consistent charging model of the
spacecraft surfaces. Further, while the gas-surface
interaction considered in this work was that of a diffusely
reflecting wall with complete thermal accommodation,
the exact nature of ion-surface interactions in VLEO
remains uncertain in literature [40, 41]. Many sources
discuss secondary electron emission, photoelectric
emission and sputtering phenomena may influence both
the momentum exchange between ions and the spacecraft
body, changing the observed direct drag and the sheath
structure, changing indirect drag forces [42].
Investigating the drag dependence on these effects,
among further factors such as space weather and
spacecraft geometry, will build on the frame-work
presented here, all of which represent important steps
toward characterising the interactions between GIE
plumes in the VLEO environment. Understanding of the
plasmadynamics is vital to the design and
implementation of GIE propelled craft, as well as the
feasibility of any VLEO mission, especially with
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IAC-18-E2.2.10.x48637 Page 11 of 13
concepts such as air-breathing propulsion coming of age.
This study has shown that effects of GIE plume plasma
in VLEO should be included in future analyses, to ensure
drag models are complete. These interactions will highly
constrain EP implementation on spacecraft, thus must be
assessed to design and select EP architectures. This study
also hints that, with the deflective nature of the propellent
plasma on the ambient flow, plasmadynamic flow control
with EP systems is possible, and would be a very
achievable means of drag reduction in VLEO.
Acknowledgements
The author would like to express thanks to Prof. Lucy
Berthoud, University of Bristol, for her guidance,
encouragement and useful evaluations in supervision of
this work. Thanks are also given to Mr. Jonathan Walsh,
PhD student, University if Bristol, for the very useful
discussions concerning his work and DSMC simulations.
Further appreciations are given to Dr. Lubos Brieda,
Particle in Cell Consulting LLC, for his assistance and
advice concerning the development of the Starfish
programme.
This paper represents the UK undergraduate entry in
the 46th student conference competition on behalf of the
British Interplanetary Society.
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