MODELLING OF ION THRUSTER PLUME CONTAMINATION R…erps.spacegrant.org/uploads/images/images/iepc_articledownload... · MODELLING OF ION THRUSTER PLUME CONTAMINATION R. I. Samanta

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MODELLING OF ION THRUSTER PLUME CONTAMINATION

R. I. Samanta Roy* and D. E. Hastingst

Space Power and Propulsion Laboratory, Department of Aeronautics and AstronauticsMassachusetts Institute of Technology

Cambridge, Massachusetts 02139

N. A. GatsonisttApplied Physics Laboratory, The Johns Hopkins University

Laurel, Maryland 20723

Abstract jbi beam ion current density, A/m2

k Boltzmann's constant (MKS)While the potential problems of spacecraft me,i electron, ion mass, kgcontamination by the effluents of electric nbi beam ion density, m-3

propulsion thrusters have been known for nie.n total ion, electron, neutral density, m- 3

some time, the limitations of ground (a further subscript "o" denotes

experiments, and until recently, computational reference)power, have prevented accurate assessments Pe electron pressure, N/m 2

q/m charge to mass ratio of ionsand predictions of spacecraft contamination. Re electron collisional drag term, NWe are developing a hybrid plasma particle-in- r thruster beam radius, mcell (PIC) code to model the plume of an ion rr thruster radius, mthruster and the production of slow charge- Te electron temperature, *Kexchange (CEX) ions in the plume and their Tw thermal wall temperature of neutrals, *Ktransport in the region exterior to the beam. vbi, e beam ion, electron velocity, m/sThese CEX ions have the potential to be 0 Hall parametertransported into the backflow region and Ylp propellant utilization efficiency

present a contamination hazard for the beam divergence angle, radiansspacecraft. We present preliminary 2-D 9 electric potential, V

Ve electron collision frequency, s- 1

axisymmetric results of the plume flow acex CEX cross-section, m2

structure and clearly demonstrate the iondensity enhancement around the spacecraft dueto the slow CEX ions. I. Introduction

Nomenclature For future space missions, advancedB fixed ambient magnetic field, T spacecraft propulsion systems such as various

C neutral thermal velocity, m/s types of electric propulsion thrusters are beingCEX charge exchange (ions) earnestly considered. However, many electricE electric field, V/m propulsion devices have low thruste electron charge, C characteristics and hence must operate forIb thruster beam ion current, A extended periods of time to achieve the

necessary velocity changes. These longthrusting times can introduce a problem with

Graduate Research Assistant, Student Member spacecraft contamination that may becomet AA quite critical. While the backflow efflux of thet Professor Senior Member AIAA thruster may be small, protracted thruster

SPostdoctoral Fellow, Member AIAA operation may aggravate any contamination

IEPC 93-142 situation.

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The potential problems of spacecraft experiments. One problem associated with ioncontamination by the effluents of electric thrusters is that complete ionization can not bepropulsion thrusters have been known for achieved with reasonable levels of power, andsome time. However, due to the limitations of hence, neutral gas is emitted at thermal speeds.ground test vacuum facilities, accurate We are interested in these slow neutralsmeasurements of contamination levels are because they charge-exchange (CEX) with thedifficult to obtain. Simple analytical models fast beam ions producing fast neutrals andcan only provide rough estimates with large slow ions which can be influenced by localuncertainties, and until recently, accurate electric fields in the plume. The electric fieldcomputational models have been non-existent, structure in the plume, as seen in experiments 2

Furthermore, almost all ground tests have and in computational models 3 , is radial, andinvolved thrusters of sizes and power far hence the slow ions are pushed out of the beamsmaller than what are envisioned today for and move back towards the spacecraft. In thistomorrow's ambitious space missions. In paper, we present preliminary results of ouraddition, many previous tests employed modelling efforts of the plume forpropellants like mercury, that are not being contamination assessment. Our work isconsidered for future space mission scenarios, complementing the modelling program for theDue to the quality of present data, to scale up International Topaz Test Program (ITTP),present tests to provide accurate predictions of formerly NEPSTP 4 . Previous studiescontaminants from large-scale multi-thruster regarding contamination have examined theconfigurations is rather problematic. A clear role of CEX ions in the sputtering of ionand fundamental understanding of both the thruster grids5 . However, these numericalplume backflow and the interactions between simulations were on the length scale of the sizethe exhaust products of a thruster and its host of a grid hole. The plume contaminationspacecraft are necessary. Possible interactions problem requires orders of magnitudeinclude sputtering and effluent deposition that increases in domain size to encompass thewill affect such aspects of the spacecraft as plume and a large part, if not the whole,solar arrays, thermal control surfaces, optical spacecraft.sensors, communications, science instrument- In Section II of this paper, we formulateation, general structural properties of materials, our approach to the problem and describe ourand spacecraft charging as depicted in Figure 1. model. Numerical methods are discussed in

Recentlyl, the state of the art in the present Section III, and selected results are presentedunderstanding of spacecraft contamination due and discussed in Section IV. Lastly,to electric propulsion devices was reviewed, conclusions and future work are offered inand a general strategy employing modern Section V.numerical techniques was outlined. Thegeneral problem at hand is that of a thruster II. Physical Modelemitting a plume of ionized and neutral gas. Inaddition, various components of the thruster The plumes of ion thrusters containcan sputter and erode, leading to the presence several major components: 1) fast (>10 km/s)of heavy metal species in the plume. The propellant beam ions, 2) neutral propellant, 3)transport of these species, which dynamically slow (initially thermal) propellant ions createdinteract, from the plume back onto the by charge-exchange processes, and 4) non-spacecraft comprises the backflow which is of propellant efflux, i.e. eroded grid and dischargeprimary concern. The essential question is: chamber material of which some is neutral, andhow much of the plume will come back onto some is charged due to CEX reactions withthe spacecraft? We have been studying the ion beam ions. We consider each of these species,thruster due to its maturity and the existence of along with neutralizing electrons below.a large database of ground and space Currently, our model is formulated in

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cylindrical coordinates (r-z). neutral propellant through the grids.

Beam Ions: CEX propellant ions

The current density of the collimated beam Slow propellant ions are created inside theions can be approximated by a parabolic beam due to charge-exchange reactions of theaxisymmetric profile given by, following type between the fast beam ions and

2 Ib1 _ 2 the slow thermal neutrals:

J(r) = r I1 (1) Xet + Xelo-> Xelw + Xe

which is subject to the normalization that at any The result is a fast neutral that travels in adownstream location in the beam, line of sight manner, and a slow ion that is

Ib = jbi r dr dO (2) easily effected by the local radial electric fieldso Jo in the beam. The volumetric production rate of

where Ib is the ion current being emitted from these CEX ions is given by,the thruster. The beam has a constant icex(r,z) = nf(r,z)nbi(r,z)VbiOccx (6)divergence angle, 4, which is usually 15-20°,and thus the beam radius is: rb = rr + z tan, where the relative collision velocity is taken towhere rr is the thruster radius. The beam the beamon veloc Co sons of

volumetric production rates with ground datacurrent is assumed to be predominantly axial, volumec rates th d data

with the beam velocity remaining approx- are good4 .

imately constant over the length scale of xinterest of several meters, and hence the beamro la Efflux NPEion density is:

S(rd) The presence of sputtered grid andnbi(r,z)= (3) discharge chamber metals in the plume

e Vi presents a serious contamination hazard due tothese species' low vapor pressures. The

Neutral Efflux: production of these species is highly thrusterdependent, and experimental data of sputter

The unionized propellant that diffuses out yields is needed. However, estimates of NPEfrom the discharge chamber, exits in free- CEX production ratesl are orders of magnitudemolecular flow. We use a simple point source less than those of the propellant CEX ions, andmodel "hidden" inside the thruster that thus their perturbative effect on the self-compares reasonably well with Direct consistent potential structures in the plume willSimulation Monte Carlo (DSMC) be almost negligible. Hence, one can use thecalculations 6 : potential fields computed self-consistently

(r) = n (z + rT) from the beam and propellant CEX ions, andn()no [(z + rT)2 + rT]3/2 then track the NPE ions in this field.

Currently, our model does not include theseThe flux of neutrals is the Knudsen efflux, species.nnoC/4, where C= V8kT/rJmi. The neutraldensity at the thruster exit is controlled by the An important consideration for thebeam current and the propellant utilization transport of the slow ions is the ambient andefficiency by the relation, thruster-induced magnetic fields. Table 1

4 I 1 - TP shows the gyroradii for thermal and beam ionsnno= -An (5) in various magnetic field strengths

e C corresponding to a range of orbital altitudes.where An is the flow-through area of the The thermal speed of the CEX ions is the

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minimum speed, and represents ions that have continuity equation,not been accelerated through the potential drop aneof the beam. For the length scales that we are t + V. (nev) = 0 (8)interested in currently, (<2-3 m), the ions can For ion time scale behaviors, the electrons canbe considered unmagnetized. However, be considered to be massless, and thus thedepending on the type of thruster, strong momentum equation reduces to Ohm's law.thruster-induced fields must be taken into The electron drift velocity can then be solvedconsideration. directly, and expressed as,

Table 1 Gyroradii for Xe ions vei =FeLEO GEO m

(B=0.2G) (B=0.001G) . 1 F . I p bxFLThermal CEX 15 m 3 km v e = mion (T=500K) .

Beam ion > 680 m > 136 km where the force terms (parallel and

V>10 km/s perpendicular to a magnetic field) include theelectric field, the pressure gradient, andcollisional drag between the beam and CEX

Electons ions, and the neutrals:

Electrons play a vital role in ion thruster F = -eE Pe + R )operation in neutralizing the ion beam. A very n eimportant issue that remains to be resolved is The magnetic field will play an importantthe role of neutralizer electrons that the role in electron behavior in terms of plumespacecraft emits, and the effect of the ambient expansion. However, since our model iselectrons. A rigorous formulation of the currently axisymmetric to capture the essentialelectron density would involve solving the physics of the CEX ion propagation, anelectron continuity, momentum, and energy ambient magnetic field has been neglected. Forequations and including the physics of a typical orbit raising mission scenarios where aneutralizer, which we will include in the future. nuclear powered spacecraft will spiral outwardHowever, in our initial model, we treat beyond geostationary orbital altitudes, theelectrons as an isothermal neutralizing fluid ambient magnetic fields are quite weak. Futurewith no drift velocity. The appropriate des- work will concentrate on developing a fullycription then is a Boltzmann distribution: three dimensional model to incorporate a

( eP\ magnetic field that will play a dominant role inne = ne exPk- (7) electron transport in LEO orbits.

Since the plume cools as it expands, anNote that in this model, the electron density is a energy equation for the electron temperature isspecified background density when the important to include. The temperature fieldpotential reaches zero, or the reference space will be at a value of 1-5 eV that is typical inpotential far from the beam. The Boltzmann thruster plumes, and will fall off to ambientrelationship, often referred to as the temperatures in the far-field. In the future, we"barometric equation", has been experimentally will model this behavior by incorporating,verified, but only in local regions of the plume. V(3 + V 3Currently, we are assuming an isothermal tiPe) + V(vPee) + pVvc = -V.cQesituation, but it is expected that the expanding (11)plasma will cool making the barometric where the electron heating term is due to ohmicrelationship with a single temperature invalid, dissipation and collisional transfer.

In the future, we will incorporate arigorous electron fluid model comprising of the

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I. Numerical Method production rate in the beam. The bulk of CEXions are produced within 2-3 beam radii

To model the expansion of an ion thruster downstream.plume, we employ the hybrid electrostatic Our model currently is two-dimensionalplasma particle-in-cell (PIC) method. In the (r-z). Figure 2 shows a representativeelectrostatic PIC technique, ions and electrons computational grid which is nonuniform toin a plasma are treated as macro-particles, more efficiently handle the highly nonuniformwhere each macro-particle represents many density distribution in the plume. Since theactual particles. The charge of the simulation grid cell size should be on the order of theparticles is deposited onto a grid and a charge Debye length, we have stretched the grids indensity is computed. From this density, the r-direction to follow the increase in DebyePoisson's equation for the electrostatic potential length away from the centerline due to theis solved, and the particles are moved under the density decrease.influence of this self-consistent electric field. A With the Boltzmann distribution for themajor shortcoming of explicit fully kinetic PIC electron density, the Poisson equation for thecodes where electrons are treated as particles, is electric potential becomes nonlinear. Thisthe very small time step that is required to equation is solved with a Newton-Raphsonresolve the electron motion. Since we are Successive-Over-Relaxation (SOR) scheme.interested in the ion motion, we adopt the For large meshes, grid relaxation techniqueshybrid approach where the ions are treated as are the methods of choice7 . Fixed potentialsparticles, but the electrons are treated as a fluid. are imposed on the spacecraft surfaces, andIn this manner, the time step is now on the ion Neumann boundary conditions are held on alltime scale, which for Xe ions, is about 490 exterior boundaries.times larger than the electron time scale.

The equation of motion of each ion macro- IV. Selected Results and Discussionparticle is integrated:

dvi =q) We have performed a sample calculationd-= ()IE + vixB] (12) for a 15-cm Xe ion thruster operating with a

beam current of 0.4 A, a propellant utilizationwhere, in the electrostatic approximation, fraction of 0.84, and an accelerating potential ofE=-Vtp, and the potential is determined from 1500 V. A beam divergence angle of 210 wasPoisson's equation: used, as well as an electron temperature of 1

V2= e (nc - ni) (13) eV. A background ion density of 1010 m-3

o speces was imposed. The following preliminaryNote that the summation over the ion species results were run almost to steady-state. Figureallows different species such as propellant and 3 shows the potential contours of the beam,non-propellant ions. In our simulation model, and Figure 4 shows the CEX ion densitythe slow CEX ions are treated as particles, with contours in the plume. The propagation of thethe real to macro-particle ratio around 1-2 CEX ions into the backflow region is clearlymillion. Particles are created each time step in seen, as well as the fact that the ion densityeach grid cell based on the volumetric CEX enhancement alters noticeably the beamproduction rate given by Eqn. 6. The velocities potential structure. Even though the CEX ionare those of a Maxwellian distribution with a density is at least two orders of magnitude lesstemperature corresponding to the wall of the than that of the beam ions, it must be self-discharge chamber (usually around 5000 K). consistently accounted for in Poisson'sParticles that reach the simulation boundaries equation, and thus, particle tracking of slowand spacecraft surfaces are removed, and ions in a fixed potential field is not adequate. Itsteady-state is reached when the loss of is interesting to note how the CEX ions leavingparticles at the boundaries balances the the beam form a "wing" structure. The sharp

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potential drop at the beam edge which is the scale problems that will completely harness theaccelerating mechanism for the CEX ions can power of massively parallel computers. Wealso be clearly seen. will also conduct parametric studies of

Figure 5 shows the CEX ion current backflow fluxes for various thruster operatingdensity vector field in the backflow region conditions such as beam current, specificbehind the thruster plane. If, for instance, a impulse, and propellant utilization efficiency.highly biased solar array panel was located on These improvements in our model will resultthe spacecraft in this region, the backstreaming in an accurate numerical model of an ionions would constitute a detrimental current thruster plume that can be used to accuratelydrain, provide estimates of contaminating fluxes so

A number of representative CEX ion that spacecraft designers can treat the problemtrajectories are shown in Figure 6. The CEX of integration with a much higher level ofions that are formed within the beam, leave the confidence.beam at angles almost normal to the beam edgeand are accelerated to a speed corresponding to Referencesthe beam voltage drop, a speed that is greater 1) Samanta Roy, R.I. and Hastings, D.E., Electricthan the Bohm velocity which is only a Propulsion Contamination, AIAA 92-3560, 28th Joint

minimum velocity needed for a stable sheath. Propulsion Conference, Nashville, TN, July 1992.2) Carruth, M.R., A Review of Studies on Ion

As an example, for Te=leV, the Bohm Thruster Beam and Charge-Exchange Plasmas, AIAAvelocity is about 860 m/s. However, the 82-1944, 16th International Electric Propulsionvelocity achieved falling down a potential drop Conference, New Orleans, LA, Nov. 1982..of roughly 11 V, is around 4000 m/s. Figures 3) Samanta Roy, R.I. and Hastings, D.E., Modelling7 and 8 show phase-space plots of the CEX of Ion Thruster Plume Contamination, AIAA 93-2531,

.te r l v y v s 29th Joint Propulsion Conference, Monterey, CA,ions. Figure 7 shows the radial velocity versus June 1993.radial position. At a radial distance of around 4) Gatsonis, N.A., et al, Modelling Induced10 cm, we see a sharp acceleration up to nearly Environments and Spacecraft Interactions for the4000 m/s. This is due to the large potential Nuclear Electric Propulsion Space Test Programdrop at the beam edge. (NEPSTP), AIAA 93-2533, 29th Joint Propulsion

Figure 8 shows a radial and axial velocity Conference, Monterey, CA, June 1993.5) Peng, X., et al, Plasma Particle Simulation ofplot which clearly shows two populations of Electrostatic Ion Thrusters, AIAA 90-2647, 21stions. A low energetic population that is International Electric Propulsion Conference,formed inside the beam, and a more energetic Orlando, FL, July 1990.population that possesses a high radial velocity 6) T. Bartel, Private communication, Sandia

component, as well as a backstreaming axial National Laboratory.component. A small number of ions that 7) Hockney, R.W. and Eastwood, J.W., Computer

component. Simulation Using Particles. Adam Hilger, Bristol,expand around the top of the spacecraft and are 98gg.drawn to the spacecraft can also be seen.

AcknowledgmentsIV. Conclusions This material is based upon work supported under a

National Science Foundation Graduate Fellowship.We have developed a 2-D axisymmetric Any opinions, findings, conclusions or recommenda-

Boltzmann electron hybrid PIC code with a tions expressed in this publication are those of themodel the plume of an ion thruster for authors and do not necessarily reflect the views of

the National Science Foundation. The authors wouldcontamination purposes. We can see sharp like to acknowledge useful discussions with Professorpotential structure in the beam that expels the M. Martinez-Sanchez of MIT, and Dr. Barry Mauk ofCEX ions radially outward, as well as the CEX APL. We would also like to acknowledge theion current density in the backflow region, support of the Office of Technology of the Ballistic

Future work will be devoted to developing an Missile Defense Organization.

electron fluid model that includes a neutralizer,and extending the simulation to 3-D on large-

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IEPC-93-142 132/S Charge-Exchange Plasma

Solar Array Interactions Plume Expansion

Communications .

Interactions .i"

S.Thruster Modelling

y (im)..67I

.00 , ,

Figure 2 Computational Grid

7

1.33 ........

.67

Figure 2 Computational Grid

Figure 3 Plume Potential Contour Plot2-D PLASMA PLUME SIMULATIONPOTENTIAL (Volts)

1325 IEPC-93-142 2.40 POT L (Vo

11.0

10.0

9.0

1.60 8.0

y () 7.0

6.0

5.0

4.0

.803.0

2.0

1.0

.0

.00.00 1.00 2.00 3.00

x ml2-D PLASMA PLUME SIMULATIONCEX ION DENSITY (m-3)

.400E+13

.100E+13

.500E+12

1.60.100E+12

y (m)

.500E+11

.100E+11

.500E+10.80

.100E+10

.500E+09

.100E+09

.00.00 1.00 2.00 3.00

x (m)

Figure 4 CEX Ion Density Contour Plot

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2D PLUME SIMULATIONCEX Ion Current Density IEPC-93-142 1326

2.00

1.33

y(m)

.67

x) * (m)

Figure 5 CEX Ion Current Density Plot2-D PLUME SIMULATIONCEX ION TRAJECTORIES1.00

.33

.00

.00 .50 1.00 1.50 2.00x(m)

Figure CEX Ion CEX Iourrent Density Plotries

2-D PLUME SIMULATIONCEX ION TRAJECTORIES

1.00

.00 .25 .50 .75 1.00x (m)

Figure 6 CEX Ion Trajectories9

2D PLUME SIMULATIONVr - r Phase Plot

10000.

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r (m/s) 4

r (m)

2D PLUME SIMULATION Figure 7 Vr-r phase plotVz - Vr Phase Plot

5000.

3000. +

+ ++

Vr (m/s) +

++

-1000.

600. -2000. 2000. 6000. 10000.Vz (m/s)

Figure 8 Vr-Vz phase plot

1010