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Topology Optimization for Magnetic Circuits Dedicated to Electric Propulsion


Abstract:

In this paper, we present a method to solve inverse problems of electromagnetic circuit design, which are formulated as a topology optimization problem. Indeed, by imposi...Show More

Abstract:

In this paper, we present a method to solve inverse problems of electromagnetic circuit design, which are formulated as a topology optimization problem. Indeed, by imposing the magnetic field inside a region, we search the best material distribution into variable domains. To perform this, we minimize the quadratic error between the prescribed magnetic field and the one computed by a finite element method (FEM). A dedicated software was developed in MATLAB using fmincon routine and FEM Magnetics (FEMM) software; this code is named {\rm ATOP}^{\rm TO} for algorithm to optimization propulsion using topology optimization. To perform the first derivative of the objective function, we implemented an adjoint variable method. Indeed, this approach makes it possible to provide the derivative by only two uses of the finite element tool. Nevertheless, the problem is discrete because we take only two possibilities: with or without material. Thus, the solid isotropic material with penalization method was used to penalize intermediate values to have discrete solutions. Some numerical experiments with 40 and 800 variables concerning circuit designs validated our approach. This represents a first study to design a Hall effect thruster.
Published in: IEEE Transactions on Magnetics ( Volume: 50, Issue: 12, December 2014)
Article Sequence Number: 7401013
Date of Publication: 17 July 2014

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I. Introduction

In space, two technologies are used to move satellites: the chemical propulsion and the electric propulsion. The chemical propulsion consists in producing a thrust by the reaction between a fuel and an oxidizer. This type of propulsion produces a high thrust but requires boarding a large mass of fuel. The electric propulsion consists in accelerating an ionized gas obtained by the collision between atoms of xenon (or krypton) and electrons provided by an electromagnetic field. The electric propulsion needs ten times less gas than liquid chemical propulsion. Then, the satellites equipped with electrical thruster use the electric power provided by the solar panels as a means of propulsion instead of fuel combustion (used by satellites equipped with chemical thruster engine). In the area of space propulsion, the electric propulsion constitutes an attractive technology. In particular, for interplanetary displacements, the electric propulsion becomes the only possible solution (as for example, for smart one or deep space spatial spacecraft). Among the electric propulsion systems, the hall effect thrusters are more and more used on board telecommunication satellites, mainly for keeping some geostationary positions. The operating general principle is to accelerate ions at the output of a plasma channel. An electric field penetrates inside a plasma discharge by reducing the electron conductivity with the help of a transverse magnetic field. An annular geometry is used to create a closed electron drift in the direction, the so-called Hall current. The drift increases the residence time of the electrons inside the channel, which leads to an efficient ionization of the propellant gas. The channel, wherein the discharge is produced, is made with ceramic walls to isolate the plasma from the magnetic circuit. The anode, located at the back of the channel, serves also as a gas distributor. The cathode, located outside the channel, provides primary electrons to initiate the discharge as well as electrons to neutralize the ion beam [1], [2]. Many studies have been made on the anode, the ceramic walls, and the cathode technologies; however, no major modification has been carried out on the magnetic circuit, which represents more than 30% of the total weight. Designed in the 70s in Russian laboratories [3]–[5], the operating magnetic circuit includes magnetic screens (Fig. 2) to guarantee the required magnetic topology. Thus, the effective flux is about 25% of the flux generated by coils. Moreover, the future spatial missions and the board telecommunication satellites need to adapt to the power propulsion. Consequently, a new magnetic circuit must be designed. The design of those magnetic circuits depends on three main constraints. The magnetic circuit is located around the plasma channel that implies two main parts separated by a very large air gap. This allows a significant leakage flux in the plasma channel. The magnetic topology requires, inside and at the output of the plasma channel, a nonuniform magnetic field spatial distribution in the cross section of the channel. For example, an accurate gradient of the flux density at the output of the channel and zones with zero magnetic field in the plasma channel is needed.

Classical magnetic circuit with main elements used for designing a Hall effect thruster.

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