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Copyright© 1997, American Institute of Aeronautics and Astronautics, Inc.

The Characteristics of the EP Exhaust Plume in Space

Anatoly G. Korsun, Ekaterina M. TverdokhlebovaTSNIIMASH, Korolev, Moscow region, Russia

Abstract

The paper contains a dynamicalproblem formulation, general and particularsolutions describing evolution of plasmaartificial formations (PAF) injected from aspacecraft and a brief description of algorithmsfor computation of spatial and temporal plasmaproperties distributions. The paper contains alsothe comparison of theoretical results obtainedwith data of measurements in plumes of electricand conventional gas thrusters, comparison ofself- similar solutions obtained with publisheddata of analytical and numerical calculation ofparameters for plasma and gas jets.

a, I

j=en(v-vt))k=(a'm)'2MmNnq

Tx, r, <pu. v

x, y, zV

YKr\ = r/aP,9,<PP.a

Subscripts:it n n H

i » en n

0It H II H

x » r

Nomenclature= transverse and longitudinal

spatial scales of plasma jet= ion charge= electric current density= factor of flow divergency= Mach number= ion mass= particles flow rate= particles concentration= density of energy flux= x- and r- components of

energy flux density= temperature= cylindrical coordinates= x- and r- components of flow

velocity= Cartesian coordinates= flow velocity= specific heat ratio= mean free path= self-similar variable= polar coordinates- gas density= plasma electric conductivity

local electric potential

= ion and electron components= initial quantity= x- and r- components of

vector

Prime and dot denotes spatial along axis x andtemporal derivatives.

Introduction

Generation of highly ionized plasma plumesand plasmoids in space particularly in thevicinity of a spacecraft is the typical result ofoperation (normal or during active experiments)of certain onboard systems such as electricthrusters both of steady state and pulseoperation, plasma contactors for tether systemsand for spacecraft charging control.

Knowledge of these plasma artificialformations behavior under conditions of a spaceflight is important for determination ofcommunication, navigation and targetingconditions, for evaluation of the PAF influenceon a spacecraft environment and consequentlyon sensitive onboard equipment operation aswell as for active experiments planning and dataprocessing.

Currently, there are methods of PAFparameters computation developed essentiallyfor very dense plasmas and using known neutralgas jet models.

Plasma expansion in space is determined notonly by collision processes and the initialconditions but also by inner self-consistentelectric fields. These fields arise due to high

, electron mobility and are proportional to localdensity and temperature gradients. In rarefiedplasmas the distribution of the inner fields isstrongly influenced by the thermal conductivityof electrons providing effective transfer of energyto the periphery of plasma jet or cloudparticularly from points of local energy releases.The ions are accelerated by inner plasma fieldspredominantly in the direction of the maximalgradient (across a narrow jet, along the directionof heat flux, etc.). As a result the densities ofenergy and substance fluxes are sufficientlygreater in expanding plasmas than in gases.

To describe a supersonic ( M* » I) rarefiedplasma flow the model of free molecular outflowfrom a point source [Ref. 1] is often used:


A^v 3 A/ Y • 2nu = —-cos 0-expf-—-—sin d)np 2

u=u0 cos2 6; forFor dense flows the simple Roberts's

approximation [Ref.2] is used:Nvn =

np ucos" e, iorM2»l.

The continual flow models [Ref.3] and[Ref.4] taking into account transport processes ingases require hard numerical calculations. Butmore hard numerical calculations are requiredfor flow models of free expanding gas based onkinetic equations [Ref. 11].

All these flow models are good enough todescribe the dense core of a flow, but do not divean accurate description of peripheral regions ofplasma plumes or plasmoids. This suggestion isconfirmed by direct comparison of theoreticaland experimental distribution of parameters forcertain plasma and gas sources [Ref.5,9].

However these peripheral regions areextremely important since they determine theactual boundaries of arising inhomogeneousdomains where the most really interestingprocesses take place in fact. For instance, mostlythese regions are responsible for RF waverefraction/scattering and for electron collectionability of tether plasma contactors.

Therefore creation of the mathematicalmodel more adequately describing the peripheryof plasma flows is a task of great importancefrom practical standpoint.

1 . General ApproachThe combined equations of a two-component

fully ionized plasma extracted from Ref.6 areused to describe a steady state plasma jet ortemporal plasmoid evolution:

d I<LjLdt

dV - -mn ( —— + V VV ) +

d ten —

i +// = -enV<P- — j + /3nVT. ,a

, +/een -— J - pnVT, .a

"2

-2

AT

-—d t

Vq{

~2

=4-

rlH -"

0t

3«V

ma

ne

-T,)

t V(V -

•(T. -T,)+±-

Here / and W are viscous force and density ofheat release due to viscosity; coefficient 0=0. 71.

In the electron motion equation the inertialterm is omitted.

Right-hand sides of the energy and motionequations describe ions interaction with electronsdue to collisions and self-consistent electric fieldwhich tends to keep electrons in the vicinity ofthe flow core and in contrary accelerates ionsalong the potential gradient - Vd>.

Set of equations (1) may be simplified ifdissipative effects due to relative motions ofelectrons and ions, i.e. due to electric current andalso due to viscosity, are relatively weak. It wasfound that all dissipative effects mentionedabove may be evaluated using the onlydimensionless criterion

Here "a" is a spatial scale of plasma jettransverse size.

The numerical evaluation assumes thatequation terms listed above may be neglected ifFl-a/l < 1 that corresponds to a rather dense jetof moderate temperature.

In a smooth expanding jet, when a ~ a/l«l,the relative impacts of transversal andlongitudinal heat fluxes are quite different since:

Here additionally involved value of IT is a spatialscale of sufficient temperature change.

In dependence on values of flow parametersinvolved in criterion ITq the different thermalmodes of jet expansion can be realized:adiabatic one - for IJgx « 1 and Hqr « 1 ;isothermal one - for U^ > 1 and I7qr> 1 andfor Uqx < 1 and J7gr £ 1 - the mode when thetemperature is transversely uniform and changesadiabatically along the jet axis.


Initial set of equation (1) may be simplifiedin the way of composition of equations forcomponents, and for the case of IJ-aA « I itmay be reduced.

2. Problem Statement

The self-similar form of solution for system(1) on the analogy with Ref. 7 may be writtenas:

v ='' (2)

r = Tc(x) • r(/7); nu = N v/ira2 .f(r}\where a(x) is a certain flow line. Figure 1illustrates a representative flow current linea(x) and the expected view of functions f(rj),y(rj) and r(r\).

Fig.l

Let us assume thatf(O) =y(0) = r (0) =1, and vis a numerical multiplier defined fromthe condition:

00

rdr = N or v"1 = [f2rj drj.0 0

Substitution of relationship (2) into set (1)reduces the equation of continuity to anidentity and rearranges other equations to thefollowing forms:

*-

r q• = 1+-*-..i r>

(3)

^<MC*')-I

Nv rr-u^ fr =

Set of equations (3) is the basic one toobtain self-similar solutions for certainthermal modes of plasma or gas jet. In generalonly two equations of motion may be reducedto a separable form subject to variables x andtj with corresponding separation constants Qand C2.

Therefore for three functions uc(x), Tc(x)and a(x) there are three ordinary nonlineardifferential equations and algebraic one.

The self-similar solution of set (1) exists ifthe latter is consistent with the differentialequations or its substitution reduces one of thedifferential equations to an identity.

Now, taking into account set (3) thefunction a(x) may be specified. The properchoice for free separation constant C/is as: C/= C2 that provides compact expressions forfunctions f(tj) and y(ij). This choice alsodetermines the flow current line r = a(x)(Fig.l) where both pressure and velocity heatare given parts of those on the flow axis:

A J_ j^_ i'*--&

nT

"CTC

Particular CasesAdiabatic Plasma or Gas Jet ExpansionThere are two typical particular cases of

adiabatic flow.The first situation is typical for rarefied

plasma flows and suggests that temperature isuniform in the flow across its cross-section inthe vicinity of the flow pole due to the highheat conductivity of plasma3Tldr=Q, Tc = Tc(x) or r (17 ) = L

The second case is usual for dense flowswhen enthalpy is constant in a cross sectionalplane of a plasma jet.

I 1 ) 2 5 71 +vz = const; y*(l + a'*q) = LIV2- =


With r = 1 the problem solution may bewritten as:

xa2um ( l+r2 /<72y'1

a « aa + am (x - x0); (am )2 = (a0 )2

For a dense flow with J1"2 = const we obtain:

-.£*•;

JCG is axial position of the effective pole of aconical flow (Fig. 1).

Actually the initial values of a0 and x0 areinsufficient for calculation since cross sectionsat x » x0 (where a» a0) are the mostinteresting in practice.

The formulas assume that the distributionsof plasma flow parameters in the distantregion of a jet where a» a^are defined by

the particles flow rate, N,the ultimate plasma velocity, um,

k-if <2the factor of flow divergency, ~"" "*

Isothermal Expansion of an Ion BeamOperation of onboard Stationary plasma

(SPT) or Anode layer (TAL) electric thrustersresults in generation of an expanding ionbeam with the following standard initialparameters [Ref.12, 14*16]: N~ 2-1019 c1 ,T~ 1+5 eV, c = 10'*10^ Om-»-m, a ~ 0.1, a' ~0.2 corresponding to criterion II = 20 * 100.

Laboratory measurements [Ref.17] assumethat the electron temperature in the beam ispractically constant ranging within 1*10 eV.

For this isothermal modes of plasma freeexpansion, the solution of combined equations(3) may be written as:

— =l 2 m2

«oao

»«,2,1 Wo*o =~^~

MH

-=-«o

2-C

\l+C/2; r=l.

20 .

1O .

•

-10.

0

20 .

10 .

0

-11

-20

«

r/x0

^&-^^ I_

End-u=2l

5

rl*0

- -SE2>---

"""u=;

Adiabatif; mode

0.01^-\;

^_^-/;

;

Hall plasfna sourcin/sec. Nf 1<r°cTP

i X(J=0.1

0 10 1

Isothermal nr

i

ojoi.--.TITS ——— ...-— *

----- TAJJr-B-55---0 km/sec N=2 10

• xo=0.1m

n/no=0.(

B EPICUF0.1 eV

mI 2

ode

n/no=0.0(——— —

——— —

c.T=2.5«

01

E

X/Xo

0

........

1——— —

— —— -

V

Xfc0

s.m 10 is 20

The initial part of SPT or TAL plume isdescribed (see Ref. 9,10,12,14) by thefollowing conditions:

7M02~500*100»1

»

so that uAiQ = / and a'=a0.


Resulting parameter distributions inconically expanding beam are as follows:- transverse size:

a2=x2/k;- factor of flow divergency:

- concentration:N

2micx2(l+r2/a2)'- beam current density:

eN k2xx2(l+kr2/a2f2'

- impulse flux density along x-axis:2mnu -

InTransverse parameter distributions in

isothermally expanding beam are more sharpthan those of adiabaticafly expanding jet sothat peripherial energy and substance fluxes inthe beam are relatively greater (see Fig. 2).

3. Plasmoid Expansion into Vacuum

The first stage of plasmoid expansion inspace when its dynamics is not perturbed dueto interaction with the Earth magnetic fieldand environment yet, may be described withsystem of dynamic equations (3). In this casethe inner self consistent electric fields may betaken into account in the way of adding aterm of electron gas pressure in the equationof ion motion.

On the analogy with the two-dimensionalplasma jet expansion described above one canwrite down the expression for plasmaconcentration within a plasmoid as:

n - Nv/8abc •/} (x/a)f2 (y/b)f3 (z/c)where vis a normalization factor defined fromthe integral

The most simple and visual solutioncorresponds to the case of uniformtemperature throughout the plasmoid i.e. t=land Vq=0. This case is realized for a "hot"plasmoid when the role of heat conductivityin plasma is sufficient, especially undercondition of no energy exchange between theplasmoid and the environment. In this case:

In Fig.3 there is a typical illustration ofthis problem solution. The main property ofthis 3D expansion is non-uniform increase ofplasmoid sizes. If initial velocities are weaklycomparable to the mean random velocity, VT~VTo /m,thc resulting velocity is maximalalong the coordinate where the initial size of aplasmoid is minimal. Consequently, resultingsize of a plasmoid along this coordinate finallyoccurs to be maximal. Thus, inversion of sizestakes place.

For example, a plasmoid initiallygenerated as a "knitting needle" stretchedalong axis x, later transforms in a disk withminimal x-dimension. In contrary, a densedisk may transform in a long "knittingneedle". The reason of this inversion is clearenough: the thermal energy initiallyaccumulated by a plasmoid, transformsgradually in kinetic energy of expansionpredominantly in the direction of maximalgradient of electric potential or in other wordsalong the maximal gradient of total innerpressure

-VfnTi + nTe)»-VnTi -enVQThe presented above self-similar solution

describes a 3D plasmoid expansion. Manyfeatures of this expansion particularly theshape inversion are similar to the numericalresults for a gas cloud [Ref. 8].


4. Comparison of Results Obtained withAvailable Data on Free Plasma Expansion

4.1.Comparison with Home ExperimentalData

Through measurements of free plasmaexpansion characteristics were made in theplume of the test arcjet plasma sourceEPICURE [Ret. 13] developed to conductspace experiments on RF-signal interactionwith an electric thruster plume.

The device basic characteristics are:- input power ..............<2 kW (28V x 70A);- propellant ................................. caesium;- total propellant load...................... 0.3 kg;- mass flow rate............... up to 30-10-6 kg/s.

Two operating modes were chosen forcomparison of experimental and theoreticaldata. The first one with discharge current of35 A corresponded to the adiabatic flow withcriterion I1<1 and the second one of 65Acorresponded to the isothermal flow withcriterion n> 1.

Table 1operating

modedistance R,

mdensity n,

cm-3

tempera-ture T, eV

Machnumber,

M

35 A

0.3

6- 10"

0.3

2.5

0.7

10»-

1.2

2.5-1010

0.26

2.6

65 A

0.3

2- ion

1.8

2.5

0.7

3- lO'o

-

1.2

7-109

1.6

2.6

The plasma plume basic characteristics -electron density n, temperature T, and Machnumber M, - were measured by Langmuiroriented cylindrical probes located along thevacuum chamber axis at the distances R, of0.3; 0.7; and 1.2 m from the plasma sourcenozzle exit. Table 1 accumulates the plasmaparameters measured at the flow axis for thetwo operating modes mentioned above.

The plasma source was mounted on arotating gear to scan the plasma plume.

In Fig.4 the comparison of theoretical[Ref.1,2] and experimental [Ref.5] results oftransverse plasma parameters distribution areshown. The parameters n=n(p,6) andT-T(p,0) are measured with a plasmaapparatus for two distances R of 0.7 and 1.2mfrom the nozzle exit.

The curves R, N and A correspond to theRoberts's approximation [Ref.2], Narasimha's

formula [Ref.l] and the self-similar model.The latter one is obtained from set (3) and iswritten as:

(nc Tc /nTcos2 0)1/r =l+k tg2 0All these flow models are good enough to

describe the dense core of a flow, but do notgive accurate description of the peripheralregions of plasma plumes orplasmoids.

N A11=1.9 k=3,4

Fig.4

Comparison of the theory and experimentpresented above, confirms that the mathmodel of free plasma expansion correctlydescribes not only a conical flow with ultimatevelocity and straight flow lines in a distantregion but also in the region adjacent to thenozzle flow where plasma heat energyaccelerates the flow and flow lines diverge.

4.1 Comparison with Published Result.4.2.1. Traditional Thrusters

Ref. 9 concerns distributions of gas densityp, and substance pV and impulse fluxes pV2,in simulated RSC plumes. Measured andcalculated data are presented as angulardependencies in polar coordinates with theorigin at the center of the nozzle exit. Themeasurements were made at a relatively largeconstant distance R from the nozzle.

Comparison of the measurement resultswith calculated data, based on some mathmodels of gas flow, suggests that experimentalangular distributions of gas density andsubstance and impulse fluxes are more sharpin the vicinity of flow axis and more smoothat the periphery than the calculated ones.

In Fig.5 the self-similar angulardistributions are added to those derived fromRef.9 with corresponding values of Mach


APRIL 1975Calia V.S. and Brook J.W., "Measurements of a Simulated Rocket

Exhaust Plume Near the Prandtl-Meyer Limiting Angle.", 207

Self-similar model • 'M=4.28;Y=1.4;k=7.1

METHOD Of CHARACTERISTICSCALCULATION; ' '

LIHII

• 50 100ANGLE FROM CENTEM.IKE. DEC

Fig. 2 Normalized mass flux and velocity measurements in (he plumeof * 1/10-scale Lunar Module RCS engine.

sinews' CODU <>UBL' /U '-«' • °-tsl

10-u I) *>!,'• 0.136. •'/• • 0.5W. f. • 200 PSIflII! '•••;, • 0.112. «V« • 0.531. P. • 650 PSIA

Self-similar modelM=3.95;y=1.31;k=7.9M=4.28;y=1.4;k=7.1

AKLE FHflfl CUITEKLIIE. DECFig. 4 Comparison of measured density ratio with predictions fromSimons' model.

10°

£ jO-21

10'-

10'

—— NOZZLES. REF. 1° MzV*SO (F IG- 2)

- - - I N V I S C I D P R O F I U (FIC-. ?)

10°

Self-similar modelM=3.95;y=1.31;k=7.9 .

INVISCID \ TURBW.EKTCOLD KALI

SO 100ANGLE FROM CEKTERLIHE. OEG

Fig. 3 Comparison of measured dynamic pressure profile with Boyn-ton's predictions.

SlIWNS'/MODEL CUjL'/U.,, • 0.75)I) «*, • 0.189. «V » • 0.569. P, • J.2 PSIA

4', m 0.115- '"/• • 0.180. Pt • 17.5 PSIA

Self-similar modelM=6.2y=1.4k=12.5

. o 15050 100AKLE FROM CENTERLINE. DEG

Fig. 5 Comparison of Chiriveila's measured flux ratios with predic-ted density ratio from Simons' model.

ig,5 The self-similar model followsthe experimental distribution of flow parametersmore accurately than simple Robert's approximation or even more tediousnumerical methods of general used.


number. The curves of pVand p are obtainedfrom self-similar angular distribution pV2

using experimental dependence V(6) of Fig 2from Ref. 9.

One can see that the self-similar angulardependencies, displayed in Fig.5, follow moreaccurately the experimental distribution offlow parameters than the simple Robert'sapproximation or even more tediousnumerical methods generally used.Particularly, all the self-similar angulardependencies of fluxes are more sharp in thevicinity of flow axis, 6 < 45°, and moresmooth at its periphery, 9 > 60°, than thosecalculated using other flow models of freeexpanding gas. That is the general differencebetween experimental and numerical results ofRef. 9.

Really, the expression pV2 suggests that inthe vicinity of flow axis, 20°<e<45°, i. e. 1/k <tg20 < 1, the order of magnitude for pv isgiven by pV* ~ (ktg*Q )-<P+I> . Whereas at theflow periphery, where 9 > 60° and tg*9 » 1,the angular dependence of pv is moresmooth:

eNk

4.2.2. Electric Thrusters' PlumesOperation of onboard Stationary plasma

(SPT) or Anode layer (TAL) electric thrustersresults in generation of an ion beamexpanding in space with the following initialparameters :ion energy

electron temperature

values of square Mach number-60;

corresponding to criterionU = (ffenna'/e2N~ 20 + 1000.

Consequently the ion beam expansion isisothermal under the condition of M2-*».

Taking into account that for the nearestflow regiona? =const = l/Jt, foro/fl0 «exp(/»Vo I2T0)we obtain a conical beam expansion.

Ref. 10 represents the distribution of ionbeam current density j(x,r) measured incylindrical coordinates. There is a self-similarrelationship for this quantity:

Theoretical and experimental dependenciescan be compared using two independentmethods. The ion beam current density roundthe axis is expressed via total ion beam current/, = eN, and factor of flow divergency k:

The measured transverse dependence of jxcan be re-plotted in the special coordinates

so that the inclination of the final straight linegives the value of flow divergency factor, k.

o k<

2/3

X(m)

(11)V

JO I ,'K* 9,5

/S

w X = 0,52mO X * 0,67 mD X •= i ,71 m« X « 2,1 mA X =

0

kr2

2A2i 2 ' A •

-I

-2

-3

-4 X(m)1 2 3 4 5

Hg.6

Function f2 is plotted in Fig.6a for a fewtransverse sections of an ion beam for xranging from 0.52 to 3.7 m. Fig.6b displaysjc(x) curve calculated for k=9.5 andexperimental points for axial values of jc.Experimental and calculated lines of equalvalues of jx. are plotted in Fig.6c.


All the three figures suggest thatexperimental and calculated data correlate forx<3m satisfactorily. Under the conditions ofthe ambient pressure in experiments of Ref.1 0, the free path length of charge exchange forXe+ ions is evaluated at about 3m. Thereforethe observed difference between experimentaland calculated data for x>3m, is seemed to becaused by ion beam scattering in the ambientgas.

In Ref. 10 the angular distributions of ionbeam current density j(Q), and ion energy,E(0), for SPT-70 electric thruster plume aremeasured in polar coordinates at constantdistance R from the exit orifice plane. The self-similar solution gives the following angulardependencies for these quantities:

_ (l + tg20)2env

Again the appropriate function f3 can beplotted in special coordinates so that theinclination of resultant straight line gives thevalue of flow divergency factor k. Theresultant value of k = 9.6 from Fig.6 ispractically equal to that (k - 9.5) determinedfor another SPT version of the same design[Ref. 10]. Although in Refs. 10 and 12 the SPTelectric thrusters of the same design werestudied, the measuring methods and alsovacuum facility conditions were different.Coincidence of the processed laboratorymeasurement results for those different casesverify the used analytical method validity.

Let us compare the experimental data onion beam expansion reported in Refs. 12 and14 for SPT-100 and TAL D-55 electricthrusters of different design under the sameconditions of operation: accelerating voltageof 300 V, discharge current of 4.5 A and equalXe mass flow rate. Value of electrontemperature Te, is arbitrary taken at its upperlimit of 5 eV.

Self-similar ion beam current density isgiven

eNk 1

Again the appropriate function f4 beingplotted in the special coordinates, gives thevalue of flow divergency factor k. Fig.7 showsthat the both resultant values of k are equal to26. This suggests that the two ion acceleratorsusing almost the same physical principlesdespite of different design, provide actuallythe same beam focusing with characteristicdivergence half-angle of about arctg(a*)=ll °.

It is also shown that plumes of SPT orTAL producing a high velocity ion beam, arecharacterized with more spread substancefluxes than gas flows due to action of radialelectric fields produced by the electronicspecie.

,2/3

40

30

20

10

Comparison of experimental datafor SPT-70. SPT-100 and TAL D-55 electric engines

plumes with the self-similar flow model orIsothermal expansion mode

• SPT-70 experiment„ SPT-100 experiment, ' TAL D-55 experiment——— self-similar model

Flg.7

In the similar way the analytical modelswere compared to the experimental results[Ref. 20,21] on SPT-100 jet (see Figs. 8 and9). Those experiments [Ref. 20,21]areinteresting because there were not measuredthe current density but plasma concentration.

In the test of Ref. 20, n{r,0) was directlymeasured. The measured values are plotted inspecific co-ordinates in Fig. 8. There is alsothe analytical curve, calculated with Carney'sapproximation [18] having selected values ofcoefficients « and L The comparison showsthat within the angles 0 £ 40° one can selectsuch values of the two coefficients for theCarney's approximation that there will be agood coincidence with experimental data. Inthe self-similar solution only one coefficientcan be varied. That is the divergence of a flowk. It can be evaluated from the initial data oronly once with use of any from measuredvalues: plasma density n{0), current density


j{0), density of impulse flow or density ofenergy flow.

30 H

20 „

10.

Fig.8

In Fig 9 there are the values of n{0),measured in more wide range of angles - 0 <60° [Ref. 21]. Coefficients for Carney'sapproximation are taken from Ref. 19. Onecan see that both self-similarsolution andfrequently used Carney's approximationdescribe the core of flow very well but todescribe the periphery the. self-similar modelshould be taken.

Conclusion

The dynamical problem describingevolution of both fully ionized stationarysupersonic plasma jet and plasmoid injectedfrom a spacecraft is formulated and solved ina self-similar form.

Because of the self-similar approach andreasonable simplification the initial combinedpartial differential equations of twocomponents plasma dynamics wererearranged in a set of separable equations sothat the problem was reduced to quadraturesand to solution of ordinary nonlineardifferential equations.

Analytic forms of the solution wereobtained for really interesting ultimatethermal modes of plasma flows includinghypersonic adiabatic plasma or gas jetexpansion and isothermal expansion of ahighly accelerated ion beam.The dynamical problem solution obtained,properly describes either the region of non-linearly expanding flow adjacent to anozzle orthe distant region of inertial expansion.

The most noticeable feature of threedimensional plasmoid expansion is theinversion of its shape.

Validity of theoretical result obtained isconfirmed in the way of comparison withhome experimental and/or published data.Good coincidence of experimental andtheoretical data is demonstrated for bothtraditional and electric thrusters plumes. It isalso shown that presented mathematicalmodel of free expanding plasma jet follows theexperimental data more precisely thanRobert's and Narasimha's approximationsoften used.

Acknowledgments

The work described in this paper wassupported particular by European Office ofAerospace Research and Development(HOARD). The authors gratefullyacknowledges personally Viki Cox.

Fig.9


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Thruster Plasma Plume on DownlinkCommunication in Space Experiments //AIAA 91-2349, 27th JPC, June 24-26, 1991/Sacramento, Ca. I Ip.14. Manzella D.H., Sankovic J.M. ,"HallThruster Ion Beam Characterisation", 31stJPC San Diego, CA, July 10-12, 1995, AIAA-95-2927.15. Sankovic J.M., Haag T.W., ManzellaD.H., "Performance evaluation of a 4,5 kWSPT Thruster", IEPC-95-3016. Semenkin A.V. et. al., "ExperimentalStudy of Exhaust Beam of Anode LayerThruster", IEPC-95-51.17. Bugrova A.I., Morozov A.I., "Influence ofVacuum Conditions on SPT Operation",IEPC-95-46.18. Lynnette M. Camey, "Evaluation of theCommunications Impact of a Low PowerArcjet Thruster", 24th JPC, AIAA-88-3105.19. Dickens J.,"Communication Impact ofHall Effect Plasma Thruster", DoctoralThesis, TTU, 1995.20. Myers, R.M., Manzella, D.H. "StationaryPlasma Thruster Plume Characteristics",IEPC-93-096.21. Lyon B.King, Alec D.Gallimore,"Ionicand Neutral Particle Transport PropertyMeasurements in the Plume of an SPT-100",32ndJPC,AIAA-96-2712.

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