Contrib. Plasma Phys. 48, No. 8, 543 – 554 (2008) / DOI 10.1002/ctpp.200810087 The Effect of Magnetic Mirror on Near Wall Conductivity in Hall Thrusters D. Yu 1 , H. Liu ∗ 1 , Y. Cao 2 , and H. Fu 1 1 Plasma Propulsion Laboratory, Harbin Institute of Technology, Harbin, Heilongjiang, 150001, China 2 Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen, Guangdong, 518055, China Received 1 January 2008, accepted 1 June 2008 Published online 10 October 2008 Key words Hall thruster, magnetic mirror, near wall conductivity, simulation. PACS 52.65.Pp, 52.65.Rr, 52.75.Di The effect of magnetic mirror on near wall conductivity is studied in the acceleration region of Hall thrusters. The electron dynamics process in the plasma is described by test particle method, in which electrons are ran- domly emitted from the centerline towards the inner wall of the channel. It is found that the effective collision coefficient, i.e. the rate of electrons colliding with the wall, changes dramatically with the magnetic mirror effect being considered; and that it decreases further with the increase of magnetic mirror ratio to enhance the electron mobility accordingly. In particular, under anistropic electron velocity distribution conditions, the mag- netic mirror effect becomes even more prominent. Furthermore, due to decrease in magnetic mirror ratio from the exhaust plane to the anode in Hall thrusters, the axial gradient of electron mobility with magnetic mirror effect is greater than without it. The magnetic mirror effects on electron mobility are derived analytically and the results are found in agreement with the simulation. c  2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 1 Introduction The Hall thruster is one kind of electric propulsion thrusters under rapid development for space propulsion. In a Hall thruster (Fig. 1), the plasma discharge is sustained in an imposed orthogonal electric (E) and magnetic (B) fields. The electrons are emitted by an external cathode. Electrons are magnetized, moving in a closed azimuthal E × B drift to ionize atoms; whereas the propellant ions (usually xenon) are not magnetized. The electrostatic field is used to accelerate ions to obtain high velocities. Typically, 50-80% of the discharge voltage is utilized to generate efficient thrust. In general, the channel of a Hall thruster can be divided in to three regions according to different physical processes: 1) the near anode region where the ionization is low and the current is carried mostly by electrons or by ion backflow; 2) the ionization zone where the ionization rate approaches its maximum and the current is maintained both by electrons towards the anode and ions going to the outlet; 3) the acceleration zone between the ionization zone and the channel exit where the current is carried predominantly by ions. In Hall thrusters, electron mobility is one of the most important parameters that affect the electric potential distribution. The minimum electron mobility locates in the acceleration region where the magnetic field is max- imal and the atom density rather small, which serves to the majority of the potential drop within this region in order to accelerate ions with high velocities. In the acceleration region, the classical conductivity of electron transport across magnetic field lines caused by collisions between electrons and neutral atoms is much less than the experimental results [1], i.e. the so-called anomalous conductivity phenomena. Various theories have been proposed to explain the anomalous electron transport. Some [2, 3] deemed that the anomalous electron transport is caused by plasma turbulence, which is known to produce a cross field electron mobility that varies like 1 B (described with Bohm-type anomalous conductivity). However, experimental results showed that, if the magnetic field intensity increases towards the outlet, the Bohm conductivity is restrained [4]. Morozov developed a near wall conductivity (NWC) theory to explain this phenomenon [5]. When an electron collides with the wall, the steady Hall drift of the electron ∗ Corresponding author: e-mail: liuhui@hcms.hit.edu.cn, Phone: +86 0451 8640 3142, Fax: +86 0451 8640 3142 c  2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim