helicon plasma thrusters: prototypes and...

Helicon Plasma Thrusters: prototypes and advances

on modeling

IEPC-2013-285

Presented at the 33rd International Electric Propulsion Conference,The George Washington University, Washington, D.C., USA

October 6–10, 2013

Jaume Navarro-Cavalle∗

Universidad Politecnica Madrid, Madrid, 28040, Spain

Eduardo Ahedo† and Mario Merino‡

Universidad Carlos III de Madrid, Leganes, 28911, Spain

Vıctor Gomez§ and Mercedes Ruiz¶

SENER Ingenierıa y Sistemas S.A., Severo Ochoa 4-PTM, Tres Cantos, 28760, Spain

and

Jose Antonio Gonzalez del Amo‖

European Space Agency, ESTEC, TOS-MPE, Noordwijk aan Zee, The Netherlands

The first part of this work inquires into a review of a selection of some existing HeliconThruster Prototypes, highlighting the main propulsive performances and design parame-ters. New advances on the simulation of the helicon plasma discharge are also detailed.These new and improved tools include a novel 2D code of the plasma-wave interaction, andtwo independent/matched models of the plasma flow, illustrating consistently all involvedphysical phenomena.

I. Introduction

The Helicon Plasma Thruster (HPT) has been presented during the last decade as a novel electric propul-sion device.1–4 The transfer of the know-how on Helicon Plasma Source (HPS),5–7 mainly acquired in

either the plasma physics research or in the industry of material processing, to the space propulsion fieldhas become very useful, providing the understanding of some relevant phenomena, but not enough since thespace requirements are by large stricter than those we find in other activities, in terms of efficiencies anddevice optimization.

The HPT is composed of the following parts (see Fig.1). A cylindrical chamber, where plasma is produced,typically slender and made of dielectric material, i.e., Pyrex glass. A radio-frequency (RF) antenna wrappedaround the chamber, that emits within the range 1-27MHz, with a wide assortment of topologies: annular,Nagoya-III type, helical, as presented in Ref. 8. The RF power is supplied to the antenna thanks to the RFsubsystem, consisting on a power unit, a wave generator/amplifier, and a matching network, which adaptsthe RF power to the plasma electromagnetic behavior. A feeding system is commonly attached to the back

∗PhD Candidate, Equipo de Propulsion Espacial y Plasmas, UPM, [email protected], http://ep2.uc3m.es†Professor, Equipo de Propulsion Espacial y Plasmas, UC3M, [email protected].‡Visiting Professor, Equipo de Propulsion Espacial y Plasmas, UC3M, [email protected].§Eng. Deg. Candidate, Aerospace Division, SENER, [email protected].¶Project Manager, Aerospace Division, SENER, [email protected].‖Section Head, Electric [email protected].

1The 33rd International Electric Propulsion Conference, The George Washington University, USA

October 6–10, 2013

of the chamber. Finally, a set of several electromagnets and/or permanent magnets surrounding the chambergenerates the required magnetic field in both inside the chamber (mainly axial) and in the plasma expansionarea, forming a divergent magnetic nozzle (MN) topology.

Regarding the HPT operation, different physical processes take place, involving among others: the emis-sion and propagation of the wave from the antenna to the plasma; the absorption of the RF wave energy,which is deposited mainly on the electrons; these energized electrons bombard the neutral gas, producing ahigh density plasma; the generated plasma is confined and guided by the magnetic field; forward accelera-tion of ion is driven by the ambipolar electric field which naturally develops within the plasma to sustainquasineutrality; along the MN, plasma continues expanding supersonically. Thrust is understood as the in-crement of the momentum of the supersonic beam. The produced thrust is delivered to the thruster thanksto the interaction of plasma currents with the applied magnetic field.9

The attractiveness of these devices is that in comparison with other electric propulsion devices, such asHall thrusters, ion engines, MPDs, or arcjets, this concept does not need any electrode, grids or neutralizers.The lack of these components suggests that the HPT is a simple and robust device. A long lifetime is alsoexpected, since the limited plasma-wall interaction due to the magnetic confinement reduces contaminationor sputtering of sensitive components, e.g. the cathode in Ion or Hall thrusters.

Section II provides a detailed review of some relevant existing HPT prototypes, highlighting their propul-sive figures and peculiarities. Section III summarizes the current status of development of a 2D axial-symmetric RF wave-plasma interaction code. This code will be coupled with our in-house tools, which dealswith the description of the plasma flow dynamics in both the HPS and the MN, attaining a complete imageof all physical phenomena involved. This fluid description of the plasma discharge is resumed in section IV.Conclusions and future work are detailed in section V.

Solenoids

Cylindricalvessel

Antenna

plasmaplume

gasfeed

Figure 1. Sketch of the HPT with the main parts.

II. Review of prototypes

To introduce the review of HPT prototypes and get an enriching point of view of this novel application, itis necessary to briefly resume the origins of the HPS. The beginnings of Helicon Sources is attributed mainlyto R. Boswell and Chen.10,11 During the 90s, the effort was focused on the discussion of wave propagationphenomena within a cylindrical magnetized plasma column.12,13 The formation of an electric current-freedouble layer14 and the presence of a populations of suprathermal electrons15 constitute some of the studiescarried out by the group of Boswell. Other groups have also contributed to the exploration of the doublelayer phenomenon.16,17 Other aspects being studied include the discussion of the role of landau-damping8

in RF power absorption. All this HPS heritage has been very useful to provide a basis for the understandingof helicon discharges, but in general all these works do not explore the HPS propulsive capabilities.

HPT prototypes are often classified according to the magnetic circuit they use and the power range inwhich operate. Several research groups have developed HPTs that implement permanent magnets, mostlyin the low power range, below 1kW. The Permanent Magnet Expanding Plasma (PEMP) built at the Uni-versity of Tokyo,18 the Helicon Plasma Hydrazine COmbined Micro (HPHCOM) funded by the European7th FrameWork Program,4 and the Compact Helicon Plasma Thruster, designed at the Institue of NuclearResearch of the Ukranian National Academy of Sciences,19 are some examples of HPTs that use permanentmagnets to generate the magnetic field. The thrust efficiencies are usually very low in this kind of proto-types: η =1% for the PEMP, 13% for the HPHCOM (although the repeatability of this result has not been


October 6–10, 2013

demonstrated yet).Regarding thrust, direct measurements are not provided by the HPHCOM group. On the contrary,

pressure or thermal thrust and magnetic thrust contributions have been accurately measured for the PEMP.20

Obtaining a low thrust of 3mN and 500s of specific impulse. This prototype presents a magnetic strength of200G, the antenna emits at 13.25MHz and its nominal power is 700W.

One of the peculiarities of the HPHCOM is the use of a novel “resonant” antenna, called S-Heliconantenna, which is optimized to operate at the very low power range, below 100W. Frequency was alsoreduced to 3MHz, increasing plasma density and diminishing losses. Another new feature implemented inthe HPHCOM was the use of a diaphragm at the chamber exit, which constricts the flow, increasing thedensity within the chamber, and consequently improving ionization. A project goal of the HPHCOM projectwas to operate as a hybrid electric-chemical thruster, using plasma to act as catalyst of the hydrazinedecomposition, but this research was dropped out. Different arrangements of permanent magnets weredesigned during the project development in order to optimize the magnetic topology. The field strengthwas in the range 400-1100G, but the non-uniformity of the topology makes difficult the understanding of allphenomena involved, including both wave propagation and plasma flow behavior.

On the other hand, we find the prototypes that use electromagnets. There are several prototypes thatuse electromagnets, but in this report, only a small subset is described. In the low-to-mid power rangestands out the Helicon Double Layer Thruster (HDLT) developed by the Australian National University.21

It is operated in the 200-800W range, with a magnetic strength of 100-200G and the RF antenna emitsat the frequency of 13.25MHz. The thrust efficiency of this device is not higher than 3%, due to the lowutilization efficiency ηu =25-35%, which means that only a small amount of neutral gas is ionized. Thisresearch group has carried out lots of experiments that report the detection of a steady-state current-freedouble-layer (DL).14,21 Direct measurements of thrust suggests that the HDLT delivers up to 6mN of thrustand 800s of specific impulse using argon as a propellant. Recently, they measured separately the magneticthrust on the coil system and the pressure thrust on the plasma chamber walls.20 They also demonstratedthe ion flow detachment from the magnetic field22 that occurs in the magnetic nozzle stage.

The mini Helicon Thruster eXperiment (mHTX),3 designed at MIT, operates with a higher magneticstrength, 1500-1800G. The nominal power was around 700-1000W and uses the same frequency. In contrastto the HDLT, it reaches a higher degree of ionization, with more than 90% of the gas is ionized. Authorsclaimed that the mHTX presented a thrust efficiency around 12%, with 2000s of specific impulse, providingup to 20mN of thrust. The project, even being the one which presented better propulsive performances, wasdropped out in 2009.

In the high power range, the High Power Helicon Thruster (HPHT),23 developed at the University ofWashington. With a nominal power between 20-50kW, they ensure that provides up to 2N, with 1400-2200sof specific impulse using argon. No DL is detected in the plasma beam, while high density peak n = 1020m−3

and high electron temperature 25eV are reported. Antenna operates at a lower frequency 0.5-1MHz, andalso uses a weak magnetic field, 100-200G. Different propellants, such as argon, xenon, hydrogen, nitrogenand even mixtures, were tested obtaining different estimated specific impulses. However, after analyzing theavailable data in detail, it seems that the flow rate that they use in some studies (160sccm1) is not enoughto couple such a high RF power to the plasma, and the thrust frequency they claimed 55% seems, in fact,overestimated.

The last prototype, which in fact is not exactly a HPT, is the VAriable Secific Impulse MagnetoplasmaRocket (VASIMR),24 developed and patented by the Ad Astra Rocket Co. The reason to review this thrusterin this work, is because it uses a HPS to produce plasma, so they provide some interesting data of the HPSoperating at high RF powers, ∼ 30kW. The whole VASIMR thruster includes an Ion Cyclotron ResonanceHeating stage downstream of the HPS, which in fact, energizes the plasma that is finally accelerated alonga magnetic nozzle, producing thrust. The complete engine presents a nominal power of 200kW, reachinga thrust efficiency over 50%, providing a thrust higher than 3N and specific impulses above 3000s. In thisnormal mode of operation, the plasma energy remains mainly on ions, the conversion of energy along themagnetic nozzle consists on transforming perpendicular energy into parallel energy, i.e., the inverse magneticmirror effect. The disadvantage of this technology is the necessity of having ionized ions, so large magneticfields (>1T, only achievable by superconducting magnets, which are heavy on weight and more extra poweris needed to cool down all the system) or light propellants are required. The magnetic field strength in theHPS stage is below 1700G, and provides 0.5N of thrust and 1600s of specific impulse, coupling up to 28kW ofRF power to the plasma. The plasma ejected by the HPS is almost full ionized, with a propellant efficiency


October 6–10, 2013

of 95%.Table 1 summarizes the main propulsive figures of the above mentioned prototypes, except for the

VASIMR-HPS.

Prototype Power Thrust Isp(s) ηu(%) η(%)

HDLT <1.5kW 6mN 800 25-35 1-3

mHTX 700-1500W 20mN 2000 90 10-20

HPHCOM 50W 1.5mN 1200 90 13

PMEP 700W 3mN 500 <50 1

HPHT 20-50kW 1-2N >2000 ∼100 55

Table 1. HPT main prototypes: summary of propulsive performances. Isp is the specific impulse (s), ηu theHPS utilization efficiency, and η the thrust efficiency.

III. Modeling the 2D plasma-wave interaction

In order to reach a better understanding of the RF wave generation and plasma-wave interaction, atwo-dimensional(2D) RF field solver has been developed to obtain accurate results of the wave propagationresponse within the plasma. The proposed model allows simulating different conditions, varying the 2D mag-netic field topology/strength, the plasma dielectric properties, or accounting for different kinds of antennas.The goal of this model is to obtain the amount of RF power absorbed by the plasma, describing also itsspatial distribution within the plasma (i.e. identify areas of higher rf-power density), and to determine theplasma electric impedance, since both are necessary to properly design the RF subsystem.

The solution of the RF wave propagation through a magnetized plasma column, considering a time-domain Fourier transform ∝ exp(iωt), is given by Maxwell equations,

∇×E = −iωB, (1)

∇×B = µ0[iωε ·E + ja],

where the dielectric tensor ε carries all the information of the plasma and the surrounding dielectric tube.ω/2π is the RF frequency, and the source term, ja is the electric current density of the RF antenna.

Assuming a cold magnetized plasma and excluding any effect of suprathermal electrons, the dimensionlesscomponents of the dielectric tensor in a magnetic frame (parallel, azimuthal and perpendicular directions)are the following,

ε‖ = 1−∑β

ω + iνβω

ω2pβ

(ω + iνβ)2 − ω2cβ

,

εθ = −∑β

ωcβω

ω2pβ

(ω + iνβ)2 − ω2cβ

, (2)

ε⊥ = 1−∑β

ω2pβ

ω(ω + iνβ),

where ωpβ =√e2n/ε0me, ωcβ = qβB0/mβ , and νβ are the plasma frequency, the gyrofrequency, and the

effective collision frequency for each species β, namely electrons and ions. qβ = |e| is the particle charge.The frequency hierarchy that ensures the RF wave propagation within the plasma is,

ωpe � ωce � ω � ωlh, νe

with ωlh = eB/√memi the lower hybrid frequency. Under these conditions, the solution within the plasma

consists in two pairs of waves: the long-wavelength Helicon waves and the short-wavelength and highlydissipative Trievelpiece-Gould(TG) waves. The propagation of these modes is determined by the appliedmagnetic field B0 and the plasma properties, such as the density, n, or collision frequency, νe, etc., all ofthem included in the dielectric tensor as aforementioned.


October 6–10, 2013

Thanks to the axisymmetric assumption, a θ-Fourier expansion for the RF fields E, B, and the antennacurrent density ja, can be used,

{E,B, ja}(r,z,θ) =∑m

{E∗,B∗, j∗a}(r,z,m) exp(imθ − iωt),

being m the azimuthal mode, and E∗,B∗, j∗a the shape of the electromagnetic field and antenna modes foreach azimutal mode in the plane r − z.

Regarding the geometry, both the dielectric tube (i.e., the HPS source) and the near plasma plume regionare contained within a resonator cage of radius radius Rc and length Lc. In fact, the role of the resonatorcage is the same of the Faraday shield that surrounds the HPS in most of the reported experiments. Wavesare reflected in this conductive cage, and the boundary condition for the RF fields is invoked there, E0 ⊥ ~s,being ~s the parallel vector to the conductive surface.

Because of the magnetic field is not purely axial, as considered in Ref. 25, it is necessary to define thedielectric tensor on the cylindrical frame z, r, θ, using the following transformation,

ε = ε0

ε‖ cos2 α+ ε⊥ sin2 α −iεθ cosαε⊥−ε‖

2 sin2 α

iεθ cosα ε‖ −iεθ sinαε⊥−ε‖

2 sin2 α iεθ sinα ε⊥ cos2 α+ ε‖ sin2 α

(3)

where α is the the angle between the local magnetic field B0(r, z) and the axis 1z.After defining the chamber geometry and plasma properties, Maxwell equations are solved using a finite

difference scheme in the plane r−z. Thanks to the structure of the equations the best way to solve the problemis using a staggered grid25,26 instead of a regular one. This method allows reducing the computational cost.

The solver developed in this research has been tested for a given plasma profile, which is, in fact, uniformalong the axial direction, a good assumption considering the results in Ref. 27. The drop of the plasmadensity close to the dielectric wall is approximated by the following radial profile,

n(r) = exp(−A(r/R)2),

where A is an adjustable positive constant. The test case uses the next dimensions for the resonance cage:Rc = 0.02m, Lc = 0.10m; The HPS radius is R = 0.01m. The chosen antenna for this preliminary test is the“One loop” antenna, of radius Ra = 0.012m, situated in the middle of the cage, only inducing the azimuthalmode “m = 0”. The magnetic field is purely axial and uniform, B0 = 360G. Collisions are defined as in theAnnex of Ref. 27.

The shape of the RF fields, results provided by this solver are shown in Figure (2). The power densitymap (r, z) for the given solution is shown in Figure (3) and is calculated as indicated in Ref. 28. Themaximum density of power absorption is focused at the section where the annular antenna is placed.

IV. Modeling the 2D plasma flow

In order to analyze the plasma behavior from a fluid dynamics point of view, it is very convenient to studyseparately the process that occur within the plasma source from those that take place along the expansion(i.e., in the MN). Three strong hypotheses are required to establish this separation: first, different processesoccur in different physical places (e.g. power absorption “only” occurs in the HPS); second, the flow issubsonic within the chamber and supersonic in the MN; third, the expansion will be considered collisionless.Each one of the following subsections summarizes our latest results on the stationary plasma structure whichdevelops within the HPS and in the MN.

A. Modeling plasma flows in the HPS

Existing models of Cho et al.,29 Fruchtman et al.30,31 and Ahedo et al.,27 consists on two or three fluidformulations of the plasma flow within the HPS. If we consider an injected flow of neutral gas, m, the appliedmagnetic field B0(z, r), and the absorbed power from the RF wave Pa(z, r), the problem consists on solvingcontinuity and momentum equations for all species, in our case, ions, electrons and neutrals (j = i, e, n,respectively):

∇ · (neue) = ∇ · (niui) = −∇ · (nnun) = nennRion, (4)

∇ · (mjnjujuj) = −∇pj + qjnj(−∇φ+ uj ×B0)− Sj , (5)


October 6–10, 2013

Figure 2. Solution obtained for electric and magnetic field for B0 = 360G and One Loop antenna configuration

Figure 3. Dimensionless power absorption density map, log10(P/Pmax), along the resonant chamber for B0 =360G and plasma profile in the form ∝ exp(−A r

rp

2). Using an annular antenna.


October 6–10, 2013

where Sj represents binary collisions (e.g. electron-neutral elastic scattering or Coulomb collisions), Rion(Te)is the ionization rate, and the rest of symbols are conventional. Other hypotheses of this model are thefollowing: it considers an isothermal plasma, with an average temperature Te, immersed in a purely axialmagnetic field B0 = B01z. The temperature is obtained from a global energy balance of the whole thruster(also including the expansion stage), and it is related with the absorbed power Pa. Equations are solvedusing a variable separation method,27,30 thus the 2D model splits into two 1D models (radial + axial) thatare coupled through different parameters or eigenvalues.

Analyzing Eqs. (4)-(5), it is possible to identify the parameters that control the plasma discharge withinthe HPS, all of them listed next in dimensionless form. As an hypothesis of this model all these parametersare assumed to be small: (i) the Debye length λD/R� 1, i.e., quasineutral plasma; (ii) the inverse of the HallParameter νe/ωce � 1, i.e., electrons are magnetically confined, with diffusive transport through magneticlines; (iii) the electron Larmor radius le/R � 1, i.e., electrons are radially confined with no importantelectron inertial effects; (iv) the ionization mean free path λion/L� 1, i.e., near full ionization takes placewithin the source and no further ionization takes place downstream. Note that all these hypotheses are notstrictly fulfilled everywhere, as in the Debye electrostatic sheaths or within the inertial layers.

This model presents the shape of axial and radial plasma structures (see Figure 4) and discusses thedominant mechanisms. The neutral gas, which is injected at the back section, is ionized along the chamber.Near fully ionization (ηu ∼ 1) is expected for a good chamber design. As mentioned before, plasma isradially confined due to the axial magnetic field. Furthermore, the ambipolar electric field, which developsto maintain quasineutrality, electrostatically confines electrons along the axial direction, but pulls ions for-ward and backward indistinctly. Sonic conditions are reached at both the back and the exit section of theconsidered HPS, |uez| = |uiz| = cs =

√Te/mi, and a section of zero axial velocity coincides with a peak

of plasma density. The radial response consists on a θ-pinch structure, which is an equilibrium betweenthe expansive plasma pressure ant the confining magnetic force. Plasma flows diffusively to the lateral walland a diamagnetic azimuthal electron current develops, both due to plasma collisions. The electric field isalmost null in the bulk diffusive region, while it increases in the inertial layer, which is a transition to theelectrostatic Debye sheath attached to the dielectric wall.32,33 This radial shape is the most efficient toreduce plasma losses to the wall, thanks to the drop of plasma density at the edge of the Debye seath, asindicated by the following asymptotic law of the ratio “edge density” over “axis density”,

nQnO' 1.25

νeωce

`eR

√mi

me. (6)

For the high magnetization (large Hall parameter) and colissionless (Boltzmann electrons in the axialdirection) regime, an asymptotic law is derived and defines implicitly the utilization efficiency as a functionof the dimensionless ionization mean free path,

L/λion =

∫ π/4

−π/4

1− tan2ξ1− ηusin2ξ

dξ. (7)

Note that λion depends on the plasma temperature, the injected mass flow, and the geometry, λion =(csun0miA)/(Rionm). The velocity of the injected neutral gas is un0, A is the area of the cylinder section,and Rion = Rion(Te) is the ionization rate.

B. Modeling plasma flows in the MN

The HPS model described above needs to be matched to a 2D model of the MN plasma expansion in orderto describe the full fluid dynamics of the device. The goal of the MN is to increase thrust, transforminginternal plasma energy into directed ion kinetic energy, just as in a solid nozzle. However, in contrast totheir solid counterparts, a MN operates contactlessly, thereby avoiding plasma-wall losses and erosion. Thiscentral advantage favors the use of MN in plasma thrusters like the HPT and in other plasma applications.Additionally, the MN brings up the possibility of varying either MN shape or field strength to accommodatedifferent in-flight requirements.

MN modeling must address two main aspects: (1) plasma acceleration and thrust generation, and (2)plasma detachment from the magnetic field downstream. A reasonable model of the supersonic plasma flowin the MN is the collisionless and fully-ionized limit of Eqs. (4)–(5), which is implemented in the DIMAGNOcode.34 In essence, the steady, axysimmetric plasma expansion in the divergent magnetic field is driven by


October 6–10, 2013

z/L

r/R

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

−1.5

−1

−0.5

0

0.5

0 0.2 0.4 0.6 0.8 1−1

0

1

2

z/L

nz/n0

uz/cs

nn/nn0

0 0.2 0.4 0.6 0.8 1

−2

−1

0

1

r/R

log(

nr

n(r=0)

)

ur/cs

Figure 4. (left) Plasma density 2D map log10[n(r, z)/n0] with n0 = n0(m,R, L, Te) a reference value for the density.Here, m = 5 mg/s, B0 = 150 G, Te = 10 eV, R = 3.5 cm and R/L = 0.2. z/L = 0 is the back wall and z/L = 1 is theHS exit section. (center) Radial profiles of plasma density log10[n(r)/n(r = 0)] and radial velocity ur/cs (linesthat increase close to the lateral wall r/R → 1); at the HS back section (solid lines) and at the exit section(dashed lines). (right) Axial profiles of radial averaged properties: plasma density (thick solid line), neutraldensity (thin solid line), and axial plasma velocity (dashed line).

the hot electrons, which are considered fully magnetized and follow the magnetic streamtubes. Ions, onthe other hand, can have any degree of ion magnetization. In practice, ion magnetization is usually lowfor actual HPT devices, and ions develop their motion as dictated mainly by the ambipolar electric fieldthat arises within the plasma. This electric field has two central roles, as in the HPS. First, it confines theelectron expansion axially, and second, accelerates ions downstream, converting the internal electron energyinto directed kinetic energy of ions (a mechanism termed ambipolar ion acceleration).

The generation and transmission of thrust in the MN relies completely on magnetic forces acting betweenthe plasma and the MN field generator: a diamagnetic azimuthal electric current density jθ is induced in theplasma, which receives an axially-outward force −jθ ×Br. In turn, these electric currents create an inducedmagnetic field on the MN generator, which receives the reaction magnetic force. These azimuthal currents,which occur naturally in a hot magnetized plasma, are therefore essential for the operation of the device;34

the magnetic character of thrust has been recently confirmed by Takahashi et al.20

The 2D nature of the plasma plume is revealed by the existence of strong radial gradients in density,velocity, and electric potential, and can be measured with the divergence efficiency ηplume = Pzi/Pi, whichaccounts for the fraction of ion kinetic power that is actually in the axial direction (see, for instance, Refs.34–36).

As a consequence of the low ion magnetization (or their demagnetization soon downstream of the MNthroat), ion trajectories begin to separate from magnetic tubes inward, except at the plasma edge where theglobal current-free and quasineutrality conditions demand that ion and electron/magnetic tubes coincide.This causes most of the mass flow to detach from the magnetic field, ensuring the formation of a collimatedplasma plume,36 and hinting a possible solution to the detachment problem.35 Naturally, a small fraction(< 1%) of the plasma flow near the plasma edge remains attached to the MN to comply with quasineutralitythere. This is common among jet based propulsion systems, and when properly controlled does not pose anythreats to the spacecraft or the thruster.

As the plasma continues to expand downstream, the flow soon becomes hypersonic, and electric andmagnetic forces on ions become insufficient to deflect ion trajectories. Consequently, ion streamtubes becomenearly conical, as has been illustrated in Fig. 5 for an example simulation. The divergence angle of theresulting plume (measured as the half-angle of the 95%-mass flow tube) is dependent on the shape andstrength of the magnetic field, the radial structure of the plasma injected at the MN throat, and the coolingrate of the expanding electron population.37 The complexity of the processes involved calls for advancedplasma simulation codes such as DIMAGNO and HELPIC.38

In summary, the MN must guide the expansion of the plasma to generate thrust, without incurring inunnecessary radial losses. Ideally, this is achieved with well-magnetized electrons, and low-magnetized ions.Clearly, the use of heavy propellants facilitates meeting these requirements with a mild magnetic field.

V. Conclusions and Future Work

A review of the HPT technologies has been conducted, establishing a natural division according to theRF power and the implemented magnetic circuit type. Propulsive properties and design parameters havebeen discussed for each prototype. The HPT presents some advantages against other plasma thrusters


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95%

50%

M

r/R

z/R0 10 20 30 40 50

0

1

2

3

4

5

0

5

10

15

20

25

30

Figure 5. Ion (solid) and electron (dashed) streamlines for an initially-uniform plasma jet in the magnetic fieldgenerated by a single current loop of radius 3.5R located at the nozzle throat. Ions are initially only weaklymagnetized eRB/

√miTe = 0.1. The background color displays the ion Mach number.

(Hall effect thrusters, gridded ion thrusters...), such as the lack of electrodes, grids or neutralizers, whichsuggests HPT to be reliable, simple and robust. Nevertheless, the low maturity level of this technology,which is indicated by the disparity on the results presented by the different research institutes (i.e., differentprototypes), calls for further work before the HPT can be confirmed as an attractive plasma thruster. Thisreview also suggests the necessity to conduct a more systematic experimental research, focusing the efforton improving the propulsive figures of merit.

Regarding the plasma-wave interaction, a new 2D radial-axial axisymmetric model has been developed tosolve RF wave propagation and power absorption. The shape of the electromagnetic fields has been obtainedfor a simplified case, although more complex magnetic fields, non-uniform plasma properties, including thediverging plume region, or other kind of antennas could be simulated after the code being validated (currentlyin process). This code will be coupled, on one side, to an equivalent electromagnetic circuit of the RFSS, and,on the other side, to the fluid dynamic models of the HPS+MN, showing a complete image of all physicalprocesses that take place in the HPT.

A discussion on the behavior of the plasma internal flows has been presented according the main resultsof Ahedo et al .27 New studies should be focused on the following issues. First, to match the momentumand energy equations in order to solve the spatial distribution of electron temperature. Second, to considerlongitudinal electric current density to be nonzero within the source. Third, to include plasma demagne-tization caused by the induced magnetic field at high plasma density. Fourth, to deal with 2D magnetictopologies. Taking into account that ions are weakly collisional, a hybrid code of the type used with Hallthruster discharges,39 with a particle-in-cell formulation for heavy species and a magnetized-fluid one forelectrons can be a choice.

Further MN modeling must address the electron demagnetization process downstream, the anisotropicpart of the pressure tensors, the closure of longitudinal electric currents, and the collisionless cooling ofelectrons. This last aspect is currently object of preliminary research.37 Introduction of additional effects,such as collisions, ionization in the MN, etc., may be facilitated by advanced PIC/fluid codes such asHELPIC,38 which in addition is able to simulate the whole HPS+MN system in a unified way.

Acknowledgments

The research has been sponsored by ESA, under contract 4000107292/12/NL/CO. Additional support hasbeen provided by the Spain’s R&D National Plan (Project AYA-2010-61699) and FPU scholarship program.

References

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2Charles, C. and Boswell, R., “Current-free double-layer formation in a high-density helicon discharge,” Applied PhysicsLetters, Vol. 82, 2003, pp. 1356.

3Batishchev, O., “Minihelicon Plasma Thruster,” IEEE Transaction on Plasma Science, Vol. 37, 2009, pp. 1563–1571.


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helicon plasma thrusters: prototypes and...

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