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Home page > Research Groups > Research Group in Energetics, Plasma and Non-Equilibrium Phenomena > Ongoing projects > Hall effect thrusters for satellite propulsion

Hall effect thrusters for satellite propulsion

23 January 2008

Participants :

Students: J. Pérez-Luna

Post-docs: N. Dubuit

Permanent: L. Garrigues, G.J.M. Hagelaar, J.P. Boeuf

Partners, collaboration and contracts

GREPHE/LAPLACE is part of GDR "Propulsion Spatiale à Plasma", a research group involving several research labs in France together with CNES and SNECMA. GREPHE also coordinates the ANR project TELIOPEH (Electron and Ion Transport in Hall Effect Thrusters) involving 4 research groups: ICARE in Orléans, CPHT at Ecole Polytechnique, LPTP at Ecole Polytechnique, and GREPHE). The aim of TELIOPEH is to develop a better understanding of the electron anomalous transport in Hall effect thrusters.

Background and objectives

A Hall Effect Thruster (HET), also called Stationary Plasma Thruster (SPT), is an ion source used for spacecraft propulsion. A plasma is generated in a channel between two coaxial cylinders, typically covered with a ceramic coating. The propulsive gas (Xenon) is injected at one end of the channel (anode side). A set of coils and an appropriate magnetic circuit create a radial magnetic field at the exhaust (cathode side). The magnetic field is maximum in the exhaust region and decreases near the anode. Electrons are emitted by an external hollow cathode near the channel exhaust. The applied voltage between the electrodes carries some of the electrons from the external cathode to the anode at the end of the channel. Part of the electrons go along with the ion jet and ensure neutrality of the thruster plume. Because of the radial magnetic field, electrons entering the discharge chamber are trapped along the magnetic field lines and create a Hall current in the E×B direction. The resulting increase of the electron residence time in the channel causes an increase of the axial electric field due to the drop in electron conductivity and leads to very efficient ionization of the incoming xenon flow. The xenon ions are accelerated by the axial electric field and provide the thrust.

Fig. 1. Schematic picture of a SPT100

On-going project on anomalous electron transport

There have been different attempts to model HETs. Among these, many have built “hybrid” models in which ions and neutrals are described by particle simulations and electrons by fluid equations. Electron mobility is a crucial parameter in the fluid approach. As described above, electrons are trapped by the E×B field. In strong magnetic field regions, the cross-field electron mobility $\mu_{\perp}$ is proportional to the momentum-transfer frequency of electron-particle collisions $\nu$ m. $\nu$ m in the thruster is actually too small to explain the measured current and “anomalous electron transport” must be invoked. Different phenomena have been proposed to explain this anomalous electron transport. It has been attributed to electron-wall interactions and/or plasma turbulence. Thruster-specific parameters adjusted to provide a best fit to the experimentally determined currents can be determined. While hybrid models constructed in this way do provide considerable insight into thruster operation, they are not yet predictive.

Fig. 2. a) Potential (colors, hybrid code) and magnetic field lines for an SPT100 thruster in its nominal operating regime (2D plots in the $(x,r)$ plane); b) Azimuthal component of the electric field deduced form the PIC simulations of Adam et al. Phys. of Plasmas 11 295 (2004) (2D plot in the $(x,\theta)$ plane).

Adam et al. Phys. of Plasmas 11 295 (2004) have developed a fully kinetic model of a HET in the axial $(x)$ and azimuthal $(\theta)$ directions which has shown the existence of an azimuthal electric field wave, as shows Fig.1b that can increase the electron conductivity across the B field. One aim of our work is to analyze electron motion in the thruster in the presence of such an azimuthal instability. The magnetic field is considered as axisymetric and is computed with a finite element magnetic field solver. The electric field in the axi-radial $(x,r)$ plane is computed using a hybrid model (see Figure 2a). We add to this field a simplified azimuthal potential perturbation defined as follows:

$V(x,r,\theta)=\frac{\alpha f(x,r)rE_0}{k_{\theta}}\sin(k_{\theta}\theta)$

where $k_{\theta}$ is the instability wave number, α a parameter (0< $\alpha$ <1) and $E_0$ the maximum electric field from the hybrid model. $f(x,r)$ controls the amplitude of the perturbation in the $(x,r)$ plane: the perturbation is strongest in the acceleration region and decreases near the anode (Fig.2b).

Two trajectories are represented in Fig.3. Collisions and energy losses are not taken into account. The trajectory on the left was computed with no potential perturbation. We clearly see how the electron is trapped along a magnetic field line and goes back and forth because of the mirror effect. The trajectory on the right was obtained by adding an azimuthal perturbation to the potential ( $k_{\theta}=10^3$ rad $^{-1}$ ) and ( $\alpha=1$ ). The perturbation causes a drift towards the anode and the electron enters the discharge channel. We have computed a large number of these trajectories and added elastic collisions. Our results show that the order of magnitude of the electron mean axial velocity ( $v_{x}\sim10^3m.s^{-1$ ) is in agreement with experimental results. The next step is to identify scaling laws which take into account these turbulent effects in electron fluid equations.

Fig. 3. 3D electron trajectories of an electron injected at the cathode for an SPT100 thruster in its nominal operating regime. On the left no perturbation is added. On the right, an azimuthal perturbation (see text) is added to the potential. Color scale shows the axial electron position (zero at anode, exhaust plane at 2.5cm).

Recent Publications

G.J.M. Hagelaar, J. Bareilles, L. Garrigues, and J.P. Boeuf, "Two Dimensional Model of a Stationary Plasma Thruster", J. Appl. Phys. 91 5592 (2002).

C. Boniface, L. Garrigues, G.J.M. Hagelaar, J.P. Boeuf, D. Gawron, and S. Mazouffre, "Anomalous Cross Field Electron Transport in a Hall Effect Thruster", Appl. Phys. Lett. 89 191503 (2006).

L. Garrigues, G.J.M. Hagelaar, C. Boniface, and J.P. Boeuf, "Anomalous Conductivity and Secondary Electron Emission in Hall Effect Thrusters", J. Appl. Phys. 100 123301 (2006).

J. Perez-Luna, G.J.M. Hagelaar, L. Garrigues, and J.P. Boeuf, "Model Analysis of a Double-Stage Hall Effect Thruster with Double-Peaked Magnetic Field and Intermediate Electrode", Phys. of Plasmas 14 113502 (2007).