Modeling of physical processes in radio-frequency plasma thrusters

1. Introduction 1 1.1. Electric propulsion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2. Helicon Plasma Thruster . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3. Objectives and Thesis outline . . . . . . . . . . . . . . . . . . . . . . . . . 8

2. Plasma-wave Interaction in Helicon Sources: Literature Review 11 2.1. The early history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2. The dispersion relation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.2.1. The Trivelpiece-Gould mode . . . . . . . . . . . . . . . . . . . . . 13 2.2.2. Non-uniform plasma density . . . . . . . . . . . . . . . . . . . . . . 15 2.2.3. The lower hybrid frequency range . . . . . . . . . . . . . . . . . . . 16 2.3. The power absorption mechanisms . . . . . . . . . . . . . . . . . . . . . . 17 2.4. Antenna types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.5. Simulation tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.6. Typical experimental devices . . . . . . . . . . . . . . . . . . . . . . . . . 23

3. General Plasma-wave Interaction Model 27 3.1. Maxwell equations and dielectric tensor . . . . . . . . . . . . . . . . . . . 27 3.2. The (0D) dispersion relation for a uniform plasma . . . . . . . . . . . . . 30 3.2.1. The helicon conventional frequency regime . . . . . . . . . . . . . . 32 3.2.2. The helicon extended frequency regime . . . . . . . . . . . . . . . 33 3.3. The axisymmetric 2D model . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.4. The radial 1D model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 3.5. Power deposition and antenna impedance . . . . . . . . . . . . . . . . . . 40

4. The 1D Plasma-wave Interaction Model 45 4.1. 1D plasma-wave model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 4.1.1. Analytical solution for uniform plasma density . . . . . . . . . . . 47 4.1.2. Analytical solution in vacuum . . . . . . . . . . . . . . . . . . . . . 49 4.1.3. Boundary and matching conditions . . . . . . . . . . . . . . . . . . 49 4.2. The Fourier transform of the antenna current . . . . . . . . . . . . . . . . 51 4.2.1. Nagoya III antenna . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 4.2.2. Double saddle antenna family . . . . . . . . . . . . . . . . . . . . . 53 4.2.3. Helical antenna family . . . . . . . . . . . . . . . . . . . . . . . . . 54 4.3. Nominal simulation case . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 4.4. The truncation of the Fourier double series . . . . . . . . . . . . . . . . . 55 4.4.1. Nagoya III antenna . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 4.4.2. Double saddle family . . . . . . . . . . . . . . . . . . . . . . . . . . 57 4.4.3. Helical antenna family . . . . . . . . . . . . . . . . . . . . . . . . . 58 4.4.4. Summary for the modes truncation . . . . . . . . . . . . . . . . . . 62

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