Helicon Plasma Thrusters: prototypes and advances on modeling IEPC

Transcription

1 Helicon Plasma Thrusters: prototypes and advances on modeling IEPC Presented at the 33 rd International Electric Propulsion Conference, The George Washington University, Washington, D.C., USA Jaume Navarro-Cavallé Universidad Politécnica Madrid, Madrid, 284, Spain Eduardo Ahedo and Mario Merino Universidad Carlos III de Madrid, Leganés, 28911, Spain Víctor Gómez and Mercedes Ruiz SENER Ingeniería y Sistemas S.A., Severo Ochoa 4-PTM, Tres Cantos, 2876, Spain and José 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 Helicon Thruster Prototypes, highlighting the main propulsive performances and design parameters. 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, and two independent/matched models of the plasma flow, illustrating consistently all involved physical phenomena. I. Introduction The Helicon Plasma Thruster (HPT) has been presented during the last decade as a novel electric propulsion 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 field has become very useful, providing the understanding of some relevant phenomena, but not enough since the space requirements are by large stricter than those we find in other activities, in terms of efficiencies and device 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 wrapped around 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 RF subsystem, consisting on a power unit, a wave generator/amplifier, and a matching network, which adapts the RF power to the plasma electromagnetic behavior. A feeding system is commonly attached to the back PhD Candidate, Equipo de Propulsión Espacial y Plasmas, UPM, jaume.navarro@upm.es, Professor, Equipo de Propulsión Espacial y Plasmas, UC3M, eduardo.ahedo@uc3m.es. Visiting Professor, Equipo de Propulsión Espacial y Plasmas, UC3M, mario.merino@uc3m.es. Eng. Deg. Candidate, Aerospace Division, SENER, victor.gomez.aero@gmail.com. Project Manager, Aerospace Division, SENER, mercedes.ruiz@sener.es. Section Head, Electric Propulsion.jose.gonzalez.del.amo@esa.int. 1

2 of the chamber. Finally, a set of several electromagnets and/or permanent magnets surrounding the chamber generates the required magnetic field in both inside the chamber (mainly axial) and in the plasma expansion area, forming a divergent magnetic nozzle (MN) topology. Regarding the HPT operation, different physical processes take place, involving among others: the emission 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 a high density plasma; the generated plasma is confined and guided by the magnetic field; forward acceleration of ion is driven by the ambipolar electric field which naturally develops within the plasma to sustain quasineutrality; along the MN, plasma continues expanding supersonically. Thrust is understood as the increment of the momentum of the supersonic beam. The produced thrust is delivered to the thruster thanks to 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 as Hall 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 also expected, since the limited plasma-wall interaction due to the magnetic confinement reduces contamination or 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 propulsive figures and peculiarities. Section III summarizes the current status of development of a 2D axialsymmetric RF wave-plasma interaction code. This code will be coupled with our in-house tools, which deals with the description of the plasma flow dynamics in both the HPS and the MN, attaining a complete image of 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. gas feed Solenoids plasma plume Antenna Cylindrical vessel 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, it is necessary to briefly resume the origins of the HPS. The beginnings of Helicon Sources is attributed mainly 1, 11 to R. Boswell and Chen. During the 9s, the effort was focused on the discussion of wave propagation 12, 13 phenomena within a cylindrical magnetized plasma column. The formation of an electric current-free double layer 14 and the presence of a populations of suprathermal electrons 15 constitute some of the studies carried out by the group of Boswell. Other groups have also contributed to the exploration of the double layer phenomenon. 16, 17 Other aspects being studied include the discussion of the role of landau-damping 8 in RF power absorption. All this HPS heritage has been very useful to provide a basis for the understanding of 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 in which operate. Several research groups have developed HPTs that implement permanent magnets, mostly in the low power range, below 1kW. The Permanent Magnet Expanding Plasma (PEMP) built at the University of Tokyo, 18 the Helicon Plasma Hydrazine COmbined Micro (HPHCOM) funded by the European 7 th FrameWork Program, 4 and the Compact Helicon Plasma Thruster, designed at the Institue of Nuclear Research of the Ukranian National Academy of Sciences, 19 are some examples of HPTs that use permanent magnets to generate the magnetic field. The thrust efficiencies are usually very low in this kind of prototypes: η =1% for the PEMP, 13% for the HPHCOM (although the repeatability of this result has not been 2

3 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. 2 Obtaining a low thrust of 3mN and 5s of specific impulse. This prototype presents a magnetic strength of 2G, the antenna emits at 13.25MHz and its nominal power is 7W. One of the peculiarities of the HPHCOM is the use of a novel resonant antenna, called S-Helicon antenna, which is optimized to operate at the very low power range, below 1W. Frequency was also reduced to 3MHz, increasing plasma density and diminishing losses. Another new feature implemented in the HPHCOM was the use of a diaphragm at the chamber exit, which constricts the flow, increasing the density within the chamber, and consequently improving ionization. A project goal of the HPHCOM project was to operate as a hybrid electric-chemical thruster, using plasma to act as catalyst of the hydrazine decomposition, but this research was dropped out. Different arrangements of permanent magnets were designed during the project development in order to optimize the magnetic topology. The field strength was in the range 4-11G, but the non-uniformity of the topology makes difficult the understanding of all phenomena involved, including both wave propagation and plasma flow behavior. On the other hand, we find the prototypes that use electromagnets. There are several prototypes that use electromagnets, but in this report, only a small subset is described. In the low-to-mid power range stands out the Helicon Double Layer Thruster (HDLT) developed by the Australian National University. 21 It is operated in the 2-8W range, with a magnetic strength of 1-2G and the RF antenna emits at the frequency of 13.25MHz. The thrust efficiency of this device is not higher than 3%, due to the low utilization efficiency η u =25-35%, which means that only a small amount of neutral gas is ionized. This research group has carried out lots of experiments that report the detection of a steady-state current-free double-layer (DL). 14, 21 Direct measurements of thrust suggests that the HDLT delivers up to 6mN of thrust and 8s of specific impulse using argon as a propellant. Recently, they measured separately the magnetic thrust on the coil system and the pressure thrust on the plasma chamber walls. 2 They also demonstrated the ion flow detachment from the magnetic field 22 that occurs in the magnetic nozzle stage. The mini Helicon Thruster experiment (mhtx), 3 designed at MIT, operates with a higher magnetic strength, 15-18G. The nominal power was around 7-1W and uses the same frequency. In contrast to the HDLT, it reaches a higher degree of ionization, with more than 9% of the gas is ionized. Authors claimed that the mhtx presented a thrust efficiency around 12%, with 2s of specific impulse, providing up to 2mN of thrust. The project, even being the one which presented better propulsive performances, was dropped out in 29. In the high power range, the High Power Helicon Thruster (HPHT), 23 developed at the University of Washington. With a nominal power between 2-5kW, they ensure that provides up to 2N, with 14-22s of specific impulse using argon. No DL is detected in the plasma beam, while high density peak n = 1 2 m 3 and high electron temperature 25eV are reported. Antenna operates at a lower frequency.5-1mhz, and also uses a weak magnetic field, 1-2G. Different propellants, such as argon, xenon, hydrogen, nitrogen and even mixtures, were tested obtaining different estimated specific impulses. However, after analyzing the available data in detail, it seems that the flow rate that they use in some studies (16sccm 1 ) is not enough to 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 Magnetoplasma Rocket (VASIMR), 24 developed and patented by the Ad Astra Rocket Co. The reason to review this thruster in this work, is because it uses a HPS to produce plasma, so they provide some interesting data of the HPS operating at high RF powers, 3kW. The whole VASIMR thruster includes an Ion Cyclotron Resonance Heating stage downstream of the HPS, which in fact, energizes the plasma that is finally accelerated along a magnetic nozzle, producing thrust. The complete engine presents a nominal power of 2kW, reaching a thrust efficiency over 5%, providing a thrust higher than 3N and specific impulses above 3s. In this normal mode of operation, the plasma energy remains mainly on ions, the conversion of energy along the magnetic nozzle consists on transforming perpendicular energy into parallel energy, i.e., the inverse magnetic mirror effect. The disadvantage of this technology is the necessity of having ionized ions, so large magnetic fields (>1T, only achievable by superconducting magnets, which are heavy on weight and more extra power is needed to cool down all the system) or light propellants are required. The magnetic field strength in the HPS stage is below 17G, and provides.5n of thrust and 16s of specific impulse, coupling up to 28kW of RF power to the plasma. The plasma ejected by the HPS is almost full ionized, with a propellant efficiency 3

4 of 95%. Table 1 summarizes the main propulsive figures of the above mentioned prototypes, except for the VASIMR-HPS. Prototype Power Thrust I sp (s) η u (%) η(%) HDLT <1.5kW 6mN mhtx 7-15W 2mN HPHCOM 5W 1.5mN PMEP 7W 3mN 5 <5 1 HPHT 2-5kW 1-2N > Table 1. HPT main prototypes: summary of propulsive performances. I sp is the specific impulse (s), η u the HPS 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, a two-dimensional(2d) RF field solver has been developed to obtain accurate results of the wave propagation response within the plasma. The proposed model allows simulating different conditions, varying the 2D magnetic 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 its spatial distribution within the plasma (i.e. identify areas of higher rf-power density), and to determine the plasma 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 timedomain Fourier transform exp(iωt), is given by Maxwell equations, E = iωb, (1) B = µ [iωɛ E + j a ], where the dielectric tensor ɛ carries all the information of the plasma and the surrounding dielectric tube. ω/2π is the RF frequency, and the source term, j a is the electric current density of the RF antenna. Assuming a cold magnetized plasma and excluding any effect of suprathermal electrons, the dimensionless components of the dielectric tensor in a magnetic frame (parallel, azimuthal and perpendicular directions) are the following, ɛ = 1 β ɛ θ = β ɛ = 1 β ω cβ ω ω + iν β ω ω 2 pβ (ω + iν β ) 2 ωcβ 2, ω 2 pβ (ω + iν β ) 2 ωcβ 2, (2) ω 2 pβ ω(ω + iν β ), where ω pβ = e 2 n/ɛ m e, ω cβ = q β B /m β, and ν β are the plasma frequency, the gyrofrequency, and the effective collision frequency for each species β, namely electrons and ions. q β = e is the particle charge. The frequency hierarchy that ensures the RF wave propagation within the plasma is, ω pe ω ce ω ω lh, ν e with ω lh = eb/ m e m i 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 highly dissipative Trievelpiece-Gould(TG) waves. The propagation of these modes is determined by the applied magnetic field B and the plasma properties, such as the density, n, or collision frequency, ν e, etc., all of them included in the dielectric tensor as aforementioned. 4

5 Thanks to the axisymmetric assumption, a θ-fourier expansion for the RF fields E, B, and the antenna current density j a, can be used, {E, B, j a } (r,z,θ) = m {E, B, j a} (r,z,m) exp(imθ iωt), being m the azimuthal mode, and E, B, ja the shape of the electromagnetic field and antenna modes for each azimutal mode in the plane r z. Regarding the geometry, both the dielectric tube (i.e., the HPS source) and the near plasma plume region are contained within a resonator cage of radius radius R c and length L c. In fact, the role of the resonator cage is the same of the Faraday shield that surrounds the HPS in most of the reported experiments. Waves are reflected in this conductive cage, and the boundary condition for the RF fields is invoked there, E 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 the dielectric tensor on the cylindrical frame z, r, θ, using the following transformation, ɛ cos 2 α + ɛ sin 2 α ɛ = ɛ iɛ θ cos α ɛ ɛ 2 sin 2 α iɛ θ cos α ɛ iɛ θ sin α ɛ ɛ 2 sin 2 α iɛ θ sin α ɛ cos 2 α + ɛ sin 2 α (3) where α is the the angle between the local magnetic field B (r, z) and the axis 1 z. 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 problem is using a staggered grid 25, 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, uniform along the axial direction, a good assumption considering the results in Ref. 27. The drop of the plasma density 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: R c =.2m, L c =.1m; The HPS radius is R =.1m. The chosen antenna for this preliminary test is the One loop antenna, of radius R a =.12m, situated in the middle of the cage, only inducing the azimuthal mode m =. The magnetic field is purely axial and uniform, B = 36G. Collisions are defined as in the Annex of Ref. 27. The shape of the RF fields, results provided by this solver are shown in Figure (2). The power density map (r, z) for the given solution is shown in Figure (3) and is calculated as indicated in Ref. 28. The maximum 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 study separately 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 processes occur in different physical places (e.g. power absorption only occurs in the HPS); second, the flow is subsonic 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 which develops within the HPS and in the MN. A. Modeling plasma flows in the HPS Existing models of Cho et al., 29 3, 31 Fruchtman et al. and Ahedo et al., 27 consists on two or three fluid formulations of the plasma flow within the HPS. If we consider an injected flow of neutral gas, ṁ, the applied magnetic field B (z, r), and the absorbed power from the RF wave P a (z, r), the problem consists on solving continuity and momentum equations for all species, in our case, ions, electrons and neutrals (j = i, e, n, respectively): (n e u e ) = (n i u i ) = (n n u n ) = n e n n R ion, (4) (m j n j u j u j ) = p j + q j n j ( φ + u j B ) S j, (5) 5

6 Figure 2. Solution obtained for electric and magnetic field for B = 36G and One Loop antenna configuration Figure 3. Dimensionless power absorption density map, log1(p/pmax ), along the resonant chamber for B = 36G and plasma profile in the form exp( A rr 2 ). Using an annular antenna. p 6 The 33rd International Electric Propulsion Conference, The George Washington University, USA

7 where S j represents binary collisions (e.g. electron-neutral elastic scattering or Coulomb collisions), R ion (T e ) is the ionization rate, and the rest of symbols are conventional. Other hypotheses of this model are the following: it considers an isothermal plasma, with an average temperature T e, immersed in a purely axial magnetic field B = B 1 z. 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 P a. Equations are solved using a variable separation method, 27, 3 thus the 2D model splits into two 1D models (radial + axial) that are coupled through different parameters or eigenvalues. Analyzing Eqs. (4)-(5), it is possible to identify the parameters that control the plasma discharge within the HPS, all of them listed next in dimensionless form. As an hypothesis of this model all these parameters are assumed to be small: (i) the Debye length λ D /R 1, i.e., quasineutral plasma; (ii) the inverse of the Hall Parameter ν e /ω ce 1, i.e., electrons are magnetically confined, with diffusive transport through magnetic lines; (iii) the electron Larmor radius l e /R 1, i.e., electrons are radially confined with no important electron inertial effects; (iv) the ionization mean free path λ ion /L 1, i.e., near full ionization takes place within the source and no further ionization takes place downstream. Note that all these hypotheses are not strictly 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 the dominant mechanisms. The neutral gas, which is injected at the back section, is ionized along the chamber. Near fully ionization (η u 1) is expected for a good chamber design. As mentioned before, plasma is radially confined due to the axial magnetic field. Furthermore, the ambipolar electric field, which develops to maintain quasineutrality, electrostatically confines electrons along the axial direction, but pulls ions forward and backward indistinctly. Sonic conditions are reached at both the back and the exit section of the considered HPS, u ez = u iz = c s = T e /m i, 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 between the expansive plasma pressure ant the confining magnetic force. Plasma flows diffusively to the lateral wall and a diamagnetic azimuthal electron current develops, both due to plasma collisions. The electric field is almost null in the bulk diffusive region, while it increases in the inertial layer, which is a transition to the 32, 33 electrostatic Debye sheath attached to the dielectric wall. This radial shape is the most efficient to reduce plasma losses to the wall, thanks to the drop of plasma density at the edge of the Debye seath, as indicated by the following asymptotic law of the ratio edge density over axis density, n Q 1.25 ν e l e mi. (6) n O ω ce R m e For the high magnetization (large Hall parameter) and colissionless (Boltzmann electrons in the axial direction) regime, an asymptotic law is derived and defines implicitly the utilization efficiency as a function of the dimensionless ionization mean free path, L/λ ion = π/4 π/4 1 tan 2 ξ dξ. (7) 1 η u sin2ξ Note that λ ion depends on the plasma temperature, the injected mass flow, and the geometry, λ ion = (c s u n m i A)/(R ion ṁ). The velocity of the injected neutral gas is u n, A is the area of the cylinder section, and R ion = R ion (T e ) 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 order to describe the full fluid dynamics of the device. The goal of the MN is to increase thrust, transforming internal plasma energy into directed ion kinetic energy, just as in a solid nozzle. However, in contrast to their solid counterparts, a MN operates contactlessly, thereby avoiding plasma-wall losses and erosion. This central 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 accommodate different 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 flow in the MN is the collisionless and fully-ionized limit of Eqs. (4) (5), which is implemented in the DIMAGNO code. 34 In essence, the steady, axysimmetric plasma expansion in the divergent magnetic field is driven by 7

8 r/r z/l u z /c s n z /n n n /n n z/l u r /c s ( ) log nr n(r=) r/r Figure 4. (left) Plasma density 2D map log 1 [n(r, z)/n ] with n = n (ṁ, R, L, T e) a reference value for the density. Here, ṁ = 5 mg/s, B = 15 G, T e = 1 ev, R = 3.5 cm and R/L =.2. z/l = is the back wall and z/l = 1 is the HS exit section. (center) Radial profiles of plasma density log 1 [n(r)/n(r = )] and radial velocity u r/c s (lines that 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), neutral density (thin solid line), and axial plasma velocity (dashed line). the hot electrons, which are considered fully magnetized and follow the magnetic streamtubes. Ions, on the other hand, can have any degree of ion magnetization. In practice, ion magnetization is usually low for actual HPT devices, and ions develop their motion as dictated mainly by the ambipolar electric field that arises within the plasma. This electric field has two central roles, as in the HPS. First, it confines the electron expansion axially, and second, accelerates ions downstream, converting the internal electron energy into 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 between the plasma and the MN field generator: a diamagnetic azimuthal electric current density j θ is induced in the plasma, which receives an axially-outward force j θ B r. In turn, these electric currents create an induced magnetic 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. 2 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 η plume = P zi /P i, which accounts for the fraction of ion kinetic power that is actually in the axial direction (see, for instance, Refs ). As a consequence of the low ion magnetization (or their demagnetization soon downstream of the MN throat), ion trajectories begin to separate from magnetic tubes inward, except at the plasma edge where the global 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 collimated plasma 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 quasineutrality there. This is common among jet based propulsion systems, and when properly controlled does not pose any threats to the spacecraft or the thruster. As the plasma continues to expand downstream, the flow soon becomes hypersonic, and electric and magnetic forces on ions become insufficient to deflect ion trajectories. Consequently, ion streamtubes become nearly conical, as has been illustrated in Fig. 5 for an example simulation. The divergence angle of the resulting plume (measured as the half-angle of the 95%-mass flow tube) is dependent on the shape and strength of the magnetic field, the radial structure of the plasma injected at the MN throat, and the cooling rate of the expanding electron population. 37 The complexity of the processes involved calls for advanced plasma simulation codes such as DIMAGNO and HELPIC. 38 In summary, the MN must guide the expansion of the plasma to generate thrust, without incurring in unnecessary 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 the RF power and the implemented magnetic circuit type. Propulsive properties and design parameters have been discussed for each prototype. The HPT presents some advantages against other plasma thrusters 8

9 r/r % 5% M z/r Figure 5. Ion (solid) and electron (dashed) streamlines for an initially-uniform plasma jet in the magnetic field generated by a single current loop of radius 3.5R located at the nozzle throat. Ions are initially only weakly magnetized erb/ m i T e =.1. The background color displays the ion Mach number. (Hall effect thrusters, gridded ion thrusters...), such as the lack of electrodes, grids or neutralizers, which suggests 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., different prototypes), calls for further work before the HPT can be confirmed as an attractive plasma thruster. This review also suggests the necessity to conduct a more systematic experimental research, focusing the effort on improving the propulsive figures of merit. Regarding the plasma-wave interaction, a new 2D radial-axial axisymmetric model has been developed to solve RF wave propagation and power absorption. The shape of the electromagnetic fields has been obtained for a simplified case, although more complex magnetic fields, non-uniform plasma properties, including the diverging plume region, or other kind of antennas could be simulated after the code being validated (currently in 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 physical processes that take place in the HPT. A discussion on the behavior of the plasma internal flows has been presented according the main results of Ahedo et al. 27 New studies should be focused on the following issues. First, to match the momentum and energy equations in order to solve the spatial distribution of electron temperature. Second, to consider longitudinal electric current density to be nonzero within the source. Third, to include plasma demagnetization caused by the induced magnetic field at high plasma density. Fourth, to deal with 2D magnetic topologies. Taking into account that ions are weakly collisional, a hybrid code of the type used with Hall thruster discharges, 39 with a particle-in-cell formulation for heavy species and a magnetized-fluid one for electrons can be a choice. Further MN modeling must address the electron demagnetization process downstream, the anisotropic part of the pressure tensors, the closure of longitudinal electric currents, and the collisionless cooling of electrons. 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 as HELPIC, 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 /12/NL/CO. Additional support has been provided by the Spain s R&D National Plan (Project AYA ) and FPU scholarship program. References 1 Ziemba, T., Carscadden, J., Slough, J., Prager, J., and Winglee, R., High Power Helicon Thruster, 41th Joint Propulsion Conference, Tucson, AR, edited by A. I. of Aeronautics and W. Astronautics, AIAA , Charles, C. and Boswell, R., Current-free double-layer formation in a high-density helicon discharge, Applied Physics Letters, Vol. 82, 23, pp Batishchev, O., Minihelicon Plasma Thruster, IEEE Transaction on Plasma Science, Vol. 37, 29, pp

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