Prof. Dr. Wolfhard Möller Fundamentals of Plasma Physics Resume of a lecture held at the University of Technology Dresden Issue: Summer 2006 Prof. Dr. Wolfhard Möller Tel. 0351-260-2245 Forschungszentrum Rossendorf [email protected] 01314 Dresden Postfach 510119 http://www.fz-rossendorf.de/FWI Intention It is the purpose of these notes to present a short display of the physical issues and the main results presented in the lecture "Fundamentals of Plasma Physics". It is not meant to replace a textbook. For details, extended discussions and mathematical derivations, the reader is referred to the literature. Literature 1. F.F. Chen, Introduction to Plasma Physics (Plenum Press, New York 1974) 2. R.J. Goldston and P.H. Rutherford, Introduction to Plasma Physics (Institute of Physics Publ., Bristol 1995) 3. C.K. Birdsall and A.B. Langdon, Plasma Physics Via Computer Simulation (Institute of Physics Publ., Bristol 1991) 4. M.A. Lieberman and A.J. Lichtenberg, Principles of Plasma Discharges and Materials Processing (John Wiley & Sons Inc., New York 1994) 5. R. Hippler, S. Pfau, M. Schmidt and K.H. Schoenbach (Eds.), Low Temperature Plasma Physics (Wiley-VCH, Berlin 2001) 6. B.N. Chapman, Glow Discharge Processes – Sputtering and Plasma Etching (John Wiley & Sons, New York 1980) 7. D.E. Post and R. Behrisch (Eds.), Physics of Plasma Wall Interactions in Controlled Fusion (NATO ASI Series B, Vol. 131, Plenum Press, New York 1986) 8. S. Glasstone und R.H. Loveberg, Kontrollierte Thermonukleare Reaktionen (Verlag Karl Thiemig KG, München 1964) 9. K. Miramoto, Plasma Physics and Controlled Nuclear Fusion (Springer, Berlin 2005) 10. R.E.H. Clark and D.H. Reiter, Nuclear Fusion Research: Understanding Plasma-Surface Interactions (Springer, Berlin 2005) 2 Contents Literature....................................................................................................................... 2 1. Plasma definition and classification…………………………………………………….. 5 1.1 Definitions.............................................................................................. 6 1.2 Maxwellian temperature distribution...................................................... 6 1.3 Debye length.......................................................................................... 6 1.4 Plasma frequency................................................................................... 7 1.5 Classification of plasmas......................................................................... 8 2. Collisions in plasmas…………………………………………………............................. 10 2.1 General definitions.................................................................................. 10 2.2 Binary elastic collision kinematics.......................................................... 10 2.3 Differential cross section........................................................................ 12 2.4 Momentum transfer................................................................................ 13 2.5 Coulomb collisions................................................................................. 14 2.6 Collisions of neutrals.............................................................................. 16 2.7 Resonant charge transfer....................................................................... 17 2.8 Polarization scattering……………………………………………………… 19 2.9 Electron elastic scattering at neutrals…………………………………….. 20 2.10Electron impact ionization………………………………………………….. 20 2.11Electron impact dissociation……………………………………………….. 22 2.12Electron impact excitation………………………………………………….. 22 2.13Penning ionization………….……………………………………………….. 23 2.14Chemical reactions………………………………………………………….. 25 3. Motion of charged particles………………………………………….......................….... 25 3.1 Equation of motion.................................................................................. 25 3.2 Constant magnetic field………................................................................ 25 3.3 Constant electric and magnetic fields...................................................... 26 3.4 Inhomogeneous magnetic field................................................................ 27 3.5 Gravitation and magnetic field................................................................. 30 3.6 Drifts and instabilities............................................................................... 30 3.7 Time-dependent magnetic field………..................................................... 31 3.8 Time-dependent electric field................................................................... 33 3.9 Adiabatic invariants…...………................................................................. 33 4. Plasma as a fluid…………..………………………………………….......................…… 36 4.1 Distribution function and moments........................................................... 36 4.2 Particle, momentum and energy balance………………………………….. 37 4.3 Drifts in fluid description…………............................................................. 40 5. Transport……….…………..………………………………………….......................…... 42 5.1 Drift and diffusion…………………............................................................ 42 5.2 Transport of neutrals……………………...…………………………………. 44 5.3 Ambipolar diffusion………………............................................................. 47 5.4 Diffusion in a magnetic field……………...…………………………………. 48 5.5 Plasma resistivity ………………............................................................ 50 5.6 Electrical plasma heating…………………………………………………….. 51 6. Plasma Boundary ………..………………………………………….......................…... 54 6.1 Electrostatic sheath………………............................................................ 54 6.2 Presheath…………..……………………...…………………………………. 56 6.3 Potential, flux, ion energy………............................................................. 57 6.4 Negatively biased electrode..….………...…………………………………. 58 3 6.5 Collisional sheath ………………............................................................. 62 6.6 Electrostatic probe …………………………………………………………. 65 7. Plasma Surface Interaction………………………………………….............................. 67 7.1 Ion implantation and reemission............................................................. 67 7.2 Collision cascade....……………………...…………………………………. 73 7.3 Radiation damage.……..………............................................................. 74 7.4 Sputtering……………………….………...…………………………………. 74 7.5 Chemical sputtering..……………............................................................ 76 7.6 Surface reactions……………………………………………………………. 77 7.7 Secondary electron emission.…............................................................. 79 8. Particle Waves and Resonances..………………………………….......................…... 82 8.1 Electron oscillations…………….............................................................. 82 8.2 Electron waves…....……………………...…………………………………. 83 8.3 Ion waves………….……..………............................................................ 84 8.4 Electron oscillations in magnetic fields...………………………………….. 84 8.5 Ion waves in magnetic fields...…............................................................ 86 9. Electromagnetic Waves…………..………………………………….......................…... 88 9.1 Non-magnetized plasma……….............................................................. 88 9.2 Magnetized plasma.……………………...…………………………………. 91 10. Plasma Modelling………………..………………………………….......................….... 95 10.1 Global modelling ………...…….............................................................. 95 10.2 Reactive plasmas……………...………...…………………………………. 98 10.3 Fluid modelling... ………...…….............................................................. 100 10.4 Particle-in-cell computer simulation …...…………………………………. 101 11. Low-temperature DC Plasmas..…….…………………………….......................…..... 104 11.1 Breakdown..…… ………...…….............................................................. 104 11.2 Regimes of operation……………………………………………………..... 106 11.3 DC magnetron discharge...…...………...…………………………………. 108 12. Low-temperature RF Plasmas…………………………………………………………... 111 12.1 Capacitively coupled RF discharge........................................................ 111 12.2 Ion energy distribution……………………………………………………… 117 13. Magnetic Confinement Nuclear Fusion Plasma.…………………………………… 120 15.1 Fusion reactions……………………........................................................ 120 15.2 Ignition.…………..….……..………………………………………………… 121 15.3 Machine concepts…………………........................................................ 122 15.4 Transport.………..….……..………………………………………………… 126 4 1. Plasma Definition and Classification 1.1 Definitions A plasma, the so-called 4th physical condition of matter, is defined as a (partly) ionized gas, which is neutral in average ("quasineutral") and exhibits collective properties (the density has to be high enough). Thus, the plasma consists in most cases of neutral atoms or molecules, positive ions and electrons, which interact by collisions. The most efficient mechanism of ionisation is the collision between electrons and neutrals. For this purpose, a fraction of the electrons has to have kinetic energies which exceed the ionization potential, i.e. above a few eV, so that the electrons have to be rather "hot". In a stationary plasma, the rate of ionization has to be compensated by a loss of charged particles to the environment (wall – see Fig. 1.1), if recombination is neglected. This defines a mean residence time (or "confinement time") of the charged particles in the plasma. Fig. 1.1: A quasineutral plasma with