2974 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 45, NO. 11, NOVEMBER 2017 Analytical Modeling of Low Erosion Extraction Grid for Ion Thruster S. E. Rahaman, A. K. Singh, S. K. Shukla, and R. K. Barik Abstract— Ion thruster is the most useful electronic propulsion system in deep space to control the orbit of a satellite due to its high exhaust velocity. Erosion of extraction grid is a critical parameter, which limits the life of an ion thruster. In this paper, an analytical model has been presented to estimate the rate of erosion of the extraction grid. The analytical results show that the rate of erosion can be reduced by about 66% using modified extraction grid as compared with conventional grid. Index Terms—Extraction grid, grid erosion, ion thruster. I. I NTRODUCTION N OWADAYS, satellites have becomean essential medium of communication. The orbit of the satellite in deep space is controlled (keeping and raising) by various types of propulsion systems, such as chemical and electronic propul- sion systems. Recently electronic propulsion systems, such as ion thrusters have been identified to have huge potential due to their high exhaust propellant velocity [1]–[4]. The critical components of an ion thruster are cathode, discharge chamber, extraction grid, and neutralizer, as shown in Fig. 1 [5]. Electrons, emitted from the cathode, collide with inert gas (mainly xenon and argon) through a propellant feed and produces plasma in the discharge chamber. Positive ions of plasma are extracted from the discharge chamber through extraction grid by applying sufficient negative voltage to the grid [6]. The neutralizer is used to neutralize the extracted ions from the discharge chamber [7]. Combination of screen and accelerator grids is called the extraction grid in an ion thruster system. The ions are extracted mainly due to accel- erator grid whereas the screen grid prevents the direct ions bombardment on accelerator grid from discharge chamber, as shown in Fig. 1 [8]. The direct ion bombardment on screen grid is mainly responsible for its erosion, which reduces thruster life [9]–[11]. To reduce the erosion rate, it is proposed to chamfer the conventional cylindrical aperture type grid. Manuscript received July 14, 2017; accepted September 3, 2017. Date of publication September 26, 2017; date of current version November 8, 2017. This work was supported by the Council of Scientific and Industrial Research-Central Electronics Engineering Research Institute, Pilani 333031, India. The review of this paper was arranged by Senior Editor C. A. Ekdahl. (Corresponding author: R. K. Barik.) S. E. Rahaman is with the Department of Electronics Engineering, IIT (ISM) Dhanbad, Dhanbad 826004, India. A. K. Singh, S. K. Shukla, and R. K. Barik are with the Council of Scientific and Industrial Research-Central Electronics Engineering Research Institute, Pilani 333031, India, and also with the Academy of Scientific and Innovative Research, New Delhi 110020, India (e-mail: ranjan.ceeri@gmail.com). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.rg. Digital Object Identifier 10.1109/TPS.2017.2752260 Fig. 1. Schematic of an ion thruster. In this paper, a new mathematical model has been presented to analyze the erosion of the screen grid for the proposed design. II. ANALYTICAL MODELING OF EXTRACTION GRID The rate of erosion of a screen grid is a function of direct ion (discharge loss ions) bombardment on it and inci- dent angle θ [11]. The rate of erosion (γ ) calculated by Jonathan et al. [12] as γ ˙ m = Y (θ)(1 - T S ) I ps ˙ m (1) where, (T S ) is ion transparency, Y (θ ) is sputtered yield, I ps is plasma sheath current (Bohm current), and ˙ m is propellant flow rate. Fig. 2 shows the angular dependence of sputter yield for xenon on molybdenum grid. The sputter yield Y(θ ) of a screen grid increases with incident angle and reaches maximum at an incident angle of around 42° and then decrease drastically as shown in Fig. 2 [13]. From (1) it is clear that the rate of erosion (γ ) can be reduced by increasing ion transparency (T S ) and reducing sputter yield Y(θ ) by the proper choice of incident angle (θ ) using Fig. 2. Increasing of incident angle by modifying con- ventional cylindrical aperture Fig. 3(a) into chamfered shaped aperture Fig. 3(b) of screen grid effectively reduces the sputter yield Y(θ ). In Section II-A, ion transparency (T S ) and sputter yield Y(θ ) have been calculated for the proposed molybdenum- based screen grid. A. Estimation of Ion Transparency of Proposed Screen Grid Ion beam transparency mainly depends on the trajectories of extracted ions due to the penetration of electric field 0093-3813 © 2017 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.