UNIVERSITY OF SOUTHAMPTON FACULTY OF ENGINEERING AND THE ENVIRONMENT Aeronautics, Astronautics and Computational Engineering Modelling and Design of Inductively Coupled Radio Frequency Gridded Ion Thrusters with an Application to Ion Beam Shepherd Type Space Missions by Mantas Dobkevicius Thesis for the degree of Doctor of Philosophy June 2017 UNIVERSITY OF SOUTHAMPTON ABSTRACT FACULTY OF ENGINEERING AND THE ENVIRONMENT Aeronautics, Astronautics and Computational Engineering Doctor of Philosophy MODELLING AND DESIGN OF INDUCTIVELY COUPLED RADIO FREQUENCY GRIDDED ION THRUSTERS WITH AN APPLICATION TO ION BEAM SHEPHERD TYPE SPACE MISSIONS by Mantas Dobkevicius Recently proposed space missions such as Darwin, LISA and NGGM have encouraged the development of electric propulsion thrusters capable of operating in the micro-Newton (µN) thrust range. To meet these requirements, radio frequency (RF) gridded ion thrusters need to be scaled down to a few centimetres in size. Due to the small size of these thrusters, it is important to accurately determine the thermal and performance parameters. To achieve this, an RF ion thruster model has been developed, composed of plasma discharge, 2D axisymmetric ion extraction, 3D electromagnetic, 3D thermal and RF circuit models. The plasma discharge model itself is represented using 0D global, 2D axisymmetric and 3D molecular neutral gas, and Boltzmann electron trans- port sub-models. This is the first time such a holistic/comprehensive model has been created. The model was successfully validated against experimental data from the RIT 3.5 thruster, developed for the NGGM mission. Afterwards, the computational model was used to design an RF gridded ion thruster for an Ion Beam Shepherd (IBS) type space debris removal mission. Normally, the IBS method requires two thrusters: one for impulse transfer (IT) and one for impulse compensation (IC). This thesis proposes a novel thruster concept for the IBS type missions where a single Double-Sided Thruster (DST) simultaneously producing ion beams for the IT and IC purposes is used. The advantage of DST design is that it requires approximately half the RF power compared with two single-ended thrusters and it has a much simpler sub-system architecture, lower cost, and lower total mass. Such a DST thruster was designed, built and tested, with the requirements and constraints taken from the LEOSWEEP space debris removal mis- sion. During the experimental campaign, a successful extraction of two ion beams was achieved. The thesis has shown that it is possible to control the thrust magnitudes from the IT and IC sides by varying the number of apertures in each ion optics system, proving that the DST concept is a viable alternative for the LOESWEEP mission. Contents List of Figures ix List of Tables xvii Nomenclature xix Acronyms xxiii Declaration of Authorship xxv Acknowledgements xxvii 1 Introduction 1 1.1 Miniature ion thrusters . 3 1.2 Ion Beam Shepherd . 5 1.3 Motivation for research and objectives . 7 1.4 Overview of the thesis . 8 2 Background 9 2.1 Electric propulsion fundamentals . 9 2.1.1 The rocket equation . 9 2.1.2 Performance of electric thrusters . 11 2.2 RF physics . 14 2.2.1 Electromagnetic fields . 14 2.2.2 Impedance and admittance . 15 2.2.3 Resonance . 17 2.2.4 Transmission lines . 18 2.2.5 Matching . 19 2.3 Plasma physics . 22 2.3.1 Bulk plasma properties . 22 2.3.2 Collisions . 23 2.3.3 Sheaths . 25 2.4 RF thrusters . 28 2.4.1 Geometry and working principles . 28 2.4.2 Plasma generation . 29 2.4.3 Plasma parameters . 31 2.4.4 Plasma extraction . 32 2.5 Inductive discharges . 33 2.5.1 RF thruster research . 33 2.5.2 Transformer model . 34 v vi CONTENTS 2.5.3 Global and thermal models . 36 2.6 Summary . 39 3 RF gridded ion thruster model 41 3.1 Model description . 43 3.2 Solution method . 45 3.3 Ion optics model . 47 3.4 Neutral gas model . 51 3.4.1 Clausing factor . 51 3.4.2 Pressure and density . 52 3.5 Plasma model . 54 3.5.1 Electron transport . 54 3.5.2 Ion density distribution . 57 3.5.3 Plasma conductivity . 61 3.5.4 Power and particle balance . 63 3.6 Electromagnetic model . 65 3.6.1 Geometry and boundary conditions . 66 3.6.2 Main equations and principles . 68 3.7 Thermal model . 72 3.7.1 Geometry and meshing . 73 3.7.2 Main equations and principles . 76 3.8 RF circuit model . 78 3.9 Summary . 81 4 RF gridded ion thruster model: results 83 4.1 Validation . 83 4.1.1 Results and discussion . 85 4.1.2 Summary . 90 4.2 Performance parameters . 90 4.2.1 RFG input power and current . 90 4.2.2 Circuit parameters . 93 4.2.3 Plasma properties . 95 4.3 Ion optics . 97 4.4 Electromagnetic fields . 99 4.5 Thermal behaviour . 100 4.5.1 Temperature distribution without plasma . 100 4.5.2 Temperature distribution with plasma . 102 4.5.3 Temperature effect on performance . 104 4.5.4 Temperature effect on plasma properties . 106 4.5.5 3D thermal plots . 108 4.6 Summary . 110 5 Investigation into a DST concept for IBS missions 111 5.1 IBS mission concept . 112 5.2 Propulsion subsystem requirements . 113 5.3 DST concept . 115 5.3.1 Performance parameters . 117 CONTENTS vii 5.3.2 Thrust control . 118 5.4 DST design . 119 5.4.1 Configurations A and B . 122 5.4.2 Discharge chamber . 124 5.4.3 RF coil . 126 5.4.4 Propellant distribution system . 127 5.4.5 Electrodes . 128 5.4.6 IT ion optics . 129 5.4.7 IC1 ion optics . 131 5.4.8 IC2 ion optics . 133 5.5 DST simulations . 134 5.5.1 Optimisation analysis . 134 5.5.2 Performance and plasma parameters . 136 5.5.3 2D electromagnetic field distribution in plasma . 139 5.5.4 2D neutral gas distribution . 140 5.6 Summary . 142 6 Experimental arrangements and procedures 143 6.1 DST experimental campaign . 143 6.1.1 Configurations and electrical set-ups . 143 6.1.2 Southampton University vacuum facility . 146 6.1.3 Test set-up . 149 6.1.4 Radio frequency generator . 149 6.1.5 Propellant feed system . 150 6.1.6 Power supplies and electrical interfaces . 153 6.1.7 Thermal interfaces . 154 6.1.8 Installation . 154 6.2 RIT 3.5 experimental campaign . 156 6.2.1 Electrical set-up . 156 6.2.2 TransMIT vacuum facility . 157 6.2.3 Radio frequency generator . 158 6.2.4 Propellant feed system . 159 6.2.5 Power supplies and electrical interfaces . 159 6.2.6 Installation . 160 6.2.7 Temperature sensors . 161 6.3 Summary . ..