Infinitesimal Analytical Approach for the Backscattering Problem

Abstract

W E PRESENT calculations of the backscattered flux of particles from the walls of a large vacuum chamber penetrating through a small circular hole. This task may be of interest for many applications. In the case of ion thrusters (we refer to all engines in which thrust is created by accelerated ions as ion thrusters), the backscattered flux from vessel walls in terrestrial qualification experiments may influence the performance of the thrusters. When particles from the plume of ion thrusters hit chamber walls, new particles can be re-emitted. This backscattered flux can also be deposited inside the acceleration channel of the ion thruster. Macroscopic deposits very close to the exit of the thruster can be formed, also modifying, by such geometrical change, the electric potential profile at this location. As a consequence, the main performance parameters of the thrusters, such as thrust or ion beam divergence, may be altered. To describe quantitatively such wall effects, the simulation has to include both erosion from the walls due to the plasma and deposition of particles from the vessel walls on other parts. Because the vacuum chamber is large compared with a typical ion thruster size, we can split the task into two independent parts. First, the angular distribution of the backscattered particles has to be determined. Second, one has to simulate the erosion-deposition processes at ion thruster surfaces also resulting from this backscattered flux. The current work is limited strictly to the first part. In this paper, we introduce analytical estimates of the backscatterd fluxes from chamber walls. For validation of the analytical approach, Monte Carlo (MC) estimates are presented. MC is a widespread approach for such problems, e.g., MC simulations of sputtering and redeposition are well established in fusion-oriented studies [1] and magnetron sputtering [2,3]. There exist a large number of publications on modeling of ion thrusters (see, for example, Taccogna et al [4,5] and Schneider et al. [6]). The problem of ion thruster erosion was addressed by Matyash et al. [7]. Two collisionless plume models were described by Cai et al. [8]. The fundamental problem of gas flows passing through small circular or annular holes was discussed by Cai and Boyd [9]. II. Description of the Model