NUMERICAL STUDY OF A DOUBLE STAGE HALL EFFECT THRUSTERelectricrocket.org/IEPC/137.pdf · 2020. 1....

The 29th International Electric Propulsion Conference, Princeton University,

October 31 – November 4, 2005

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Numerical study of a Double Stage Hall Effect Thruster

IEPC-2005-137

Presented at the 29th International Electric Propulsion Conference, Princeton University, October 31 – November 4, 2005

C. Boniface*, G.J.M Hagelaar†, L. Garrigues‡ and J.P. Boeuf§

CPAT, UMR 5002, Université Pau Sbatier, 118 Route de Narbonne, 31062 Toulouse Cedex 4, France

M. Prioul** Snecma Moteurs DPES Site de Villaroche Nord BP93F 77552 Moissy-Cramayel, France

Abstract: Hall Effect Thrusters (HETs) are ion sources used for satellite station keeping and orbit raising. In Single Stage HETs, the same electric field controls both electron heating and ion acceleration. We present simulations of a new HET concept where ionization and acceleration are separated in two different stages. The ionization chamber is based on an original plasma trap called “Galatheas”. This Double Stage HET allows more versatile operation and a separate control of thrust and specific impulse.

* PhD. Student, CPAT, [email protected]. † Research scientist, CPAT, [email protected]. ‡ Research scientist, CPAT, [email protected]. § Senior research scientist, CPAT, [email protected]. ** Propulsion engineer, Snecma Moteurs, [email protected].



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I. Introduction Hall Effect Thrusters (HETs) are gridless ion engines where a magnetic field barrier is used to slow down the

electron conductivity and generate a large electric field that provides collisionless ion acceleration1. The specific impulse of HETs is in the range 1600-2000 s (i.e. the velocity of ejected xenon ions is on the order of 16-20 km/s) and the thrust to power ratio is about 70 mN/kW.

The thrust and the specific impulse of standard Single Stage HETs (SSHETs) are well adapted to the missions of orbit correction and station keeping, but cannot be easily varied and optimized independently, because the same electric field controls both electron heating and ion acceleration. The next generation of satellites however demands flexible multimode thrusters able to provide high thrust for orbit raising or transfer, and high specific impulse for satellite station keeping. High thrust with high mass flow rate and low voltage reduces the duration of orbit transfers, while high specific impulse with high voltage and low mass flow rate is needed to minimize gas consumption during station keeping. An alternative concept of standard HETs consists of separating the two main functions of a Hall Effect thruster where ionization and acceleration are performed in different stages. For instance, Linear Gridless Ion Thruster (LGIT), based on the magnetic confinement of the plasma, are able to increase the residence time of the electrons and so the ionization of the neutral flux. The main problem of the LGIT is the difficulty to ensure a good control of the ion trajectory in order to extract them properly from the ionization stage into the acceleration stage2.

A new HET concept in which ionization and ion acceleration are controlled independently has been recently proposed 3-5. This Double Stage HET (DSHET) uses a separate chamber to ionize the gas flow, while the ion acceleration is provided by the electric field generated in a magnetic field barrier, as in standard SSHETs. The ionization stage and the classical acceleration stage are shown in the diagram of Fig. 1. The plasma in the ionization stage is confined by a semi Galathea trap6 generated by a special arrangement of coils and magnetic circuit. By imposing appropriate voltage drops between the myxina coil, the separatrix magnetic field line, and the metallic chamber wall (see Fig. 1), a potential well is created that confines the ions and guides them to the entrance of the channel, where they are subsequently extracted and ejected. The minimum potential in the ionization chamber is along the separatrix line, and is close to the potential of the anode of the acceleration stage. The maximum potential (30 to 50 V above the latter) is along the myxina and the chamber wall. In such a configuration, the magnetic field lines tend to be equipotential in first approximation. Electrons coming from the channel into the ionization chamber are confined along the magnetic field lines and then drift slowly, across the magnetic field lines, towards the myxina and chamber wall due to collisions with neutral atoms.

Figure 1. Schematic of the DSHET showing the ionization and acceleration stages. The intermediate electrode serves as the anode of the acceleration stage and the cathode of the ionization stage, where it is intercepted by the separatrix magnetic field line.



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A quasineutral hybrid model, similar to the one described in Ref. 7, has been adapted to the DSHET of Fig. 1. In this model, the ions and neutral atoms are described with a Particle-In-Cell simulation. The electric field is deduced from the electron momentum equation (generalized Ohms’law) and current conservation. The electron energy and ionization rate can be calculated either from fluid equations assuming a maxwellian electron energy distribution, or from a Monte-Carlo simulation of the electron trajectories. The results shown in Fig. 2 have been obtained with the Monte Carlo treatment of the electrons8.

Figure 2: (a,top) Calculated ionization rate (log scale over 3 decades, from yellow to red, maximum 5 1022 m-3s-1) and examples of ion trajectories; (a,bottom) positions of a sample of ions in the simulation; (b) potential distribution inside the thruster (only part of the channel is represented). Conditions: xenon mass flow rate 2.5 mg/s, applied voltage in the acceleration channel 300 V, applied voltage in the ionization chamber 30 V. We see in Fig. 2 (a, bottom part) the trapping of ions in the potential well (b) in the ionization chamber and their extraction and acceleration (a, top) in the channel.

II. Ionization processes in DSHET We focus now on the study of the first chamber of the DSHET as an ion source. The aim of this study is to

help to better understand the electron multiplication in such complex magnetic configuration as well as the spatial distribution of ionisation in the chamber.

We used a Monte-Carlo simulation of electrons based on the “null-collision method” 9 in order to have an accurate description of collisionnal processes. In these simulations, the magnetic and the electric fields and the mass flow rate are given. The magnetic field B, obtained by using the FEMM software10, exhibits a complex structure where its intensity is larger near the internal wall than the external wall. There also is a point of zero B-field near the entrance of the ionization chamber. The potentiel well and the mass flow rate are respectively 30V(cf. fig. 2b) and 2.5mg/s. Neutral gas is injected near the external wall. We inject at the entrance of the chamber an electron flux according to a maxwellian distribution at a given electron temperature Te. We simulate each electron for 10-4s (physical time) which is much longer than the time scale for ionisation, excitation and elastic collisions, after that the electrons are ejected from the simulation. Moreover, we suppose that reflexion with walls are specular. We simulate one thousand primary electrons and the secondary electrons created by ionization in order to have good statistics. The simulation time is four hours with a 2 GHz PC.



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A. Maxwellian electron distribution at Te=1 eV In the first case, we inject a maxwellian electron distribution at Te=1eV. For a 30V potentiel well, we obtain 950

secondary electrons created for 1000 primary electrons, so an electron multiplication near to 2. Fig. 3 shows the rate of collisionnal processes and the mean electron energy in the chamber.

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Figure 3. Collisionnal processes in the ionization chamber: a) Ionization source term, log. scale over 4 decades (m-3s-1), white color where < 5 1018m-3s-1; b) Excitation source term (m-3s-1), log. scale over 4 decades; c) Elastic collisions source term (m-3s-1); log. scale over 4 decades, from blue to red, maximum 1 1026 m-3s-1; Electron mean energy (eV), log. scale over 1 decade. a) and b) at the same scale.

We can see a strongly non-uniform distribution of ionization in the chamber. The maximum (5.1022 m-3s-1) is at

the top of the well near the external wall and the myxina whereas ionization is very weak around the separatrix. This distribution is strongly influenced by the magnetic topology and the neutral gas injection. Indeed, the electron transport across the magnetic field lines is easier in weak magnetic field and high neutral density regions. The electrons are initially trapped on the separatrix where they do not have enough energy for inelastic collisions. When the electrons drift towards the chamber wall and the myxina, they gain energy and start exciting and ionizing the neutral gas particles. The total electron multiplication however is weak and the ionization distribution strongly non-uniform.

B. Maxwellian electron distribution at Te=15 eV In this case, we inject a maxwellian electron distribution at Te=15eV. We obtain an electron multiplication of 3-

4. Fig. 4 shows the ionization source term and the electron mean energy.



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Figure 4. a) Ionization source term, log. scale over 4 decades (m-3s-1); b) Electron mean energy (eV), log. scale over 1 decade.

We note a major difference in the spatial distribution of the ionization in the two cases. Firstly, we have an

important ionization around the separatrix. In the middle of the well, the ionization and excitation rates are about equaled. Finally at the top of the well, there is a strong ionization with electron mean energy near to 20-25 eV. Indeed, the initial electron energy at the entrance of the channel allows them to ionize quickly (mean ionization time 10-9s against 10-7s at Te=1eV) so that it limits the influence of electron energy losses by excitation processes. Concerning the difference between internal and external walls, this is always due to the magnetic topology.

All in all, one condition appears clearly: the initial energy of primary electrons at the entrance of the chamber

wall controls strongly the ionization in the chamber of DSHET. Electrons are more influenced by their initial energy than by potential well. Of course, the magnetic field is still important in so far as the confinement allows to increase the electron residence time. Besides the potential well is essential to trap ions as we have seen in Fig 3.

III. Ion extraction in DSHETs The goal of this study is to describe qualitatively the influence of the magnetic field configuration on the extraction process. In such a configuration, the magnetic field lines tend to be equipotential in a first approximation. We used the Monte-Carlo simulation of the electrons to calculate accurately the ionization source term distribution. Then this distribution is injected in the hybrid model to deduce the neutral density and the electric potential profiles. We repeat the process in order to reach a steady state. In the acceleration channel, we inject the primary electrons following a maxwellian distribution at Te=15eV according to the calculation of the previous section ( cf. Fig. 4).

A. Magnetic field modeling We use the Finite Element Method Magnetic (FEMM) solver to calculate the magnetic field distribution for a

given arrangement of the magnetic circuit and a given value for the coil currents. Different values of current myxina coil have been designed to generate different magnetic field configurations. The magnetic field lines are plotted in Fig. 5 for three different topologies varying only the current in the myxina coil. We also represent the axial



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variations of the calculated radial magnetic field strength along the median line (radial position 3.8 cm) between the channel walls for the different magnetic field configurations. The current of the myxina coil increases from the case 1 to the case 3. Modifying the current on the myxina coil changes the axial position of the zero B-field. The consequences are a strong modification of the magnetic field lines in the ionization chamber, especially the curvature of the lines near the entrance of the ionization chamber, and the magnetic field gradient in the acceleration channel.

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Figure 5. DSHET magnetic field lines calculated with FEMM for three different values of the myxina coil currents (case 1, 2 and 3). The separatrix is in green color. Axial variations of the calculated radial magnetic field strength along the median line between the channel walls for different magnetic configurations.

C. Ion extraction The spatial ion distribution plotted Fig. 6 give information on the shape of the ion beam, especially in the region

situated between the zero B-field and the entrance of the channel. This region is a transition between the ionization chamber and the acceleration channel. The ion distributions in the (x,r) plane are represented in Fig. 6 for the three different topologies of Fig. 5. We also represent the axial variations of the calculated electric potential along the median line (radial position 3.8 cm) between the channel walls for the different magnetic field configurations (cf. Fig. 5).



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Figure 6: Ion distribution in the (x,r) plane for the three different magnetic configurations. Axial variations of the calculated electric potential along the median line between the channel walls for different magnetic field configurations.

As we discussed in the section III.B, we vary the coil current in the myxina for the three different magnetic

configurations. Increasing the coil current in the myxina from case 1, case 2 to case 3 shifts the axial position of the zero-B field near the acceleration channel and so the shape of the magnetic field lines in the ionization chamber as we have shown on Fig. 5.

Case 1 features a wider ion beam in the region of the transition than case 3. This is due mainly to the shape of the magnetic field lines intercepting the oblique wall in this region; many ions hit the oblique wall and so they can recombine to the channel wall leading to a re-ionization in the channel. Case 3 exhibits magnetic field lines practically tangent to the wall which guide the ions correctly from the ionization chamber to the entrance of the acceleration channel. However, in case 3 the position of the zero B-field is closer to the channel than in case 1, and the electric potential drops further in the channel as we can see in Fig. 6. Therefore, many ions have no time to convert their transversal velocity into longitudinal velocity, and hit the channel wall where they recombine into neutrals.

The magnetic configuration of case 2 is a compromise between cases 1 and 3 in order to have a better extraction.

All in all, the ion extraction process is influenced by both the shape of the magnetic field lines near the

transition region (to guide the ions correctly) and the position of the electric field (to correctly convert the transverse velocity into longitudinal velocity). It is possible to control these two features by varying the axial position of the zero B-field.

IV. Conclusion These preliminary simulation results present some features of the DSHET in qualitative agreement with the experiments5. More work is needed to better understand its possibilities and limits, and to optimize the ion extraction from the ionization chamber.

An important issue concerning the ionization stage is the spatial distribution of ionization which is influenced by the magnetic topology. The electron multiplication and so the ionization efficiency are controlled mainly by the maximum electron mean energy (initial kinetic energy and potential energy) that electrons can obtain in the chamber. In the future, it could be interesting to have an experimental estimate of initial energy at chamber entrance, although this is linked to anomalous electron transport occurring in the acceleration channel11.



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The magnetic configuration in the ionization chamber controls the shape of the magnetic field lines in the chamber and the magnetic field gradient in the channel which strongly influences the ion extraction process.

Nonetheless, more work is needed to better understand the different processes in the DSHET, notably by improving the calculation of the electric potential inside the ionization chamber where magnetic field is locally weak and neutral density is locally high. This study is under way.

Acknowledgments This study has been performed in the framework of GDR CNRS/CNES/SNECMA n°2759 “Propulsion Spatiale

à Plasma”. We want to acknowledge too the support from European Space agency (ESA). The authors would like to thank E. Chesta and E. Gengembre for helpful discussions. Discussions with A.I.

Morozov, A. Bugrova and V.V. Savel’ev on the DSHET concept are also gratefully acknowledged.

References 1V. V. Zhurin, H. R. Kaufmann and R. S. Robinson, "Physics of closed drift thrusters", Plasma Sources Sci. Technol. 8, R1-

R20 1999. 2P.Y. Peterson and A.D. Gallimore, “The Performance and Plume Characterization of a Laboratory Gridless Ion Thruster

with Closed Electron Drift Acceleration”, 40th AIAA Joint Propulsion Conference and Exhibit, July 11-14, Fort Lauderdale, FL, paper AIAA-04-3936.

3SNECMA Patent 03 08384, 9 July 2003. 4E. Chesta et al., "Flexible variable-specific impulse electric propulsion systems for planetary missions", 5th International

conference on Low-Cost planetary missions, ESTEC, 24-26 September 2003, ESA SP-542. 5M. Prioul et al., "Development of a Double Stage Hall Effect Thruster", 4th International Spacecraft Propulsion

Conference, Sardinia, June 2004. 6A.I. Morozov and V.V. Savel’ev, "On Galateas magnetic traps with plasma-embedded conductors", Physics – Uspekhi 41,

1049-1089, 1998. 7G.J.M. Hagelaar, J. Bareilles, L. Garrigues and J.P. Boeuf, "Two-dimensional model of a stationary plasma thruster", J.

Appl. Phys. 91, 5592-5598, 2002. 8C. Boniface, G.J.M. Hagelaar, L. Garrigues, J.P. Boeuf and M. Prioul "Modeling of Double Stage Hall Effect Thruster”

IEEE. Trans. Plasma Sci. 33 (2), 522 (2005). 9Jean-Pierre Boeuf , PhD thesis. 10FEMM http://femm.berlios.de, 2002. 11G.J.M. Hagelaar, J. Bareilles, L. Garrigues and J.P. Boeuf, "Role of anomalous electron transport in a stationary plasma

thruster simulation", J. Appl. Phys. 93, 67, 2003.

NUMERICAL STUDY OF A DOUBLE STAGE HALL EFFECT THRUSTERelectricrocket.org/IEPC/137.pdf · 2020. 1....

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