Physics of Hot Plasmas

HE ninth Scottish Universities' Summer School in Physics, sponsored T jointly by the Scottish Universities and NATO was held at Newbattle Abbey from 28th July to 16th August 1968. This was the first Scottish Summer School to be devoted to plasma physics, the exact title for the School being the Physics of Hot Plasmas. Forty-three students were accepted, fourteen of these being resident in the United Kingdom. In addition there were eleven lecturers and seven other participants. The choice of lecturers, particularly in experimental plasma physics, was limited to some extent by the fact that an international conference on con­ trolled fusion was held at Novosibirsk during the first week in August. Not­ withstanding this, it was possible to arrange a programme of lectures reasonably well balanced between theoretical and experimental plasma physics. The topics chosen included kinetic theory, waves and oscillations, instabilities, turbulence, collisionless shocks, computational methods, laser scattering and laser generated plasmas, plasma production and containment. Several semi­ nars on special topics were given by invited speakers and by students.

1. Introduction to Kinetic Theory of Plasma.- 1. Introduction.- 1.1. Object.- 1.2. Levels of description.- 1.3. The B.B.G.K.Y. (Bogoliubov, Born, Green, Kirkwood, Yvon) hierarchy.- 1.4. The Boltzmann equation.- 2. Application of the Boltzmann Equation to Plasmas.- 3. Transport Coefficients for Simple Gases.- 3.1. Simple kinetic theory.- 3.2. Normal solution.- 4. The Relaxation Approximation.- 5. The Lorentz Gas (I).- 6. The Lorentz Gas (II).- 7. The Kinetic Equation for the Plasma.- 8. Some Properties of the Kinetic Equation.- 8.1. The drag coefficient.- 9. The Electron Correlation Function and Radiation Scatter.- 2. Advanced Kinetic Theory.- 1. Introduction.- 2. The Balescu-Guernsey-Lenard Equation and its Properties.- 3. Klimontovich Equations of Plasma.- 4. Solution of the Linear Equations and Conventional Kinetic Theory.- 5. Justification of an Expansion of the Non-Linear Equations.- 6. Wave Kinetic Equation to Lowest Order.- 7. Particle Kinetic Equation.- 8. Non-Linear Modifications.- 8.1. Corrections due to the time dependence of the Vlasov operator.- 8.2. A diagrammatic systematization of the iteration.- 8.3. General form of wave kinetic equation.- 8.4. Description of the non-linear mechanisms of absorption.- 8.5. Description of the non-linear mechanisms of emission.- 8.6. Synchronization of the rate of emission by Cerenkov radiation.- 8.7. Effects of mode-coupling on the evolution of the one-particle distributions.- 9. Formulation of the Problem of a Test Particle in a Magnetic Field.- 9.1. The explicit form of the diffusion tensor.- 9.2. The drag force.- 9.3. The coefficient of spatial diffusion across a uniform magnetic field.- 10. Conclusions.- 3. Plasma Waves and Oscillations.- 1. Introduction.- 2. Magnetohydrodynamic Waves.- 2.1. Ideal magnetohydrodynamics.- 2.2. Wave propagation in a medium with varying properties.- 2.3. Effect of transport processes on magnetohydrodynamic waves.- 2.4. Magnetohydrodynamic waves in a bounded medium.- 2.5. Large amplitude magnetohydrodynamic waves.- 3. Oscillations of a Two-Fluid Plasma.- 3.1. Basic equations.- 3.2. Wave propagation in a uniform medium.- 4. Oscillations of a Cold Plasma.- 4.1. Introduction.- 4.2. Wave propagation—special cases.- 4.3. Transition to a hot plasma.- 5. Oscillations of a Hot Plasma.- 5.1. Introduction.- 5.2. Oscillations in the absence of an external magnetic field.- 5.3. Oscillations in an external magnetic field.- 5.4. Anisotropic hydromagnetic waves.- 4. Plasma Instabilities.- 1. Introduction.- 2. Macroscopic Instabilities.- 2.1. The hydromagnetic equations.- 2.2. Kink and sausage instabilities of the pinch.- 2.3. The Kelvin-Helmholtz instability.- 2.4. The Rayleigh-Taylor instability.- 2.5. Flute instabilities.- 2.6. The interchange stability criterion in fields with closed lines of B.- 3. Microinstabilities.- 3.1. Dispersion relation for a homogeneous plasma in a uniform magnetic field.- 3.2. Instabilities with k parallel to B0.- 3.3. Quasi-electrostatic instabilities.- 3.4. Gradient-driven instabilities.- 4. Non-Linear Effects.- 4.1. Quantum theory of electrostatic waves and their interaction with particles.- 4.2. Quasi-Linear theory.- 5. Finite Plasma Effects.- 5. Computational Problems in Plasma Physics and Controlled Thermonuclear Research.- 1. Introduction.- 2. Numerical Studies of Pinch Experiments.- 2.1. Infinite conductivity calculations.- 2.2. One-dimensional, fully ionized model.- 2.3. Difference methods.- 2.4. One-dimensional, partially ionized model.- 2.5. Two-dimensional, fully ionized model.- 3. Resistive Instability Calculations.- 3.1. Basic equations and assumptions.- 3.2. First-order equations.- 3.3. Sheet pinch model.- 3.4. Difference equations for the sheet pinch.- 3.5. Cylindrical model.- 4. Computation of Finite-Beta Equilibria.- 4.1. Basic method.- 4.2. Open ended, minimum-B systems.- 4.3. Toroidal equilibria with scalar pressure.- 4.4. Toroidal equilibria with anisotropic pressure.- 4.5. Helical equilibria with anisotropic pressure.- 4.6. Method of solution of the difference equations.- 5. Numerical Solution of the Fokker-Planck Equations for a Plasma.- 5.1. Time-dependent, two-species, isotropic velocity distributions.- 5.2. Energy and angular dependent ion distribution, Maxwellian electrons.- 6. Numerical Solution of the Vlasov Equation.- 6.1. One-dimensional models.- 6.2. Two-dimensional models.- 6. Turbulence.- 1. Introduction.- 2. Stochastic Acceleration.- 3. Weak Turbulence.- 4. The Experimental Situation.- 5. Conclusion.- 7. Collisionless Shocks.- 1. Introduction.- 2. Shock Formation.- 2.1. Continuum flow.- 2.2. Shock-formation and steepening.- 3. Laminar Shocks.- 3.1. Low ? shocks propagating perpendicular to B.- 3.2. Low ? oblique shocks.- 3.3. High ? perpendicular shocks.- 4. Turbulent Shocks.- 4.1. High Mach number shocks.- 4.2. Turbulent high ? parallel shocks.- 8. Collisionless Shock Waves.- I: A General Review.- 1. Relevance of Shock Studies.- 1.1. Occurrence of shocks.- 1.2. Theoretical significance.- 2. Nature of the Shock Transition.- 2.1. Gas-dynamic shock.- 2.2. Collisions in a plasma.- 2.3. Plasma shock.- 3. MHD Classification of Shocks.- 4. MHD Shock Structures.- 5. Critical Mach Number for Resistive Shocks.- 6. Non-Fluid Models.- 6.1. Vlasov treatment.- 6.2. Wave kinetics.- 7. Parameters for the Classification of Shocks.- 7.1. State of the initial plasma.- 7.2. Initial plasma parameters.- 7.3. Piston and compression.- 7.4. Shock conditions.- 8. Review of Main Experiments and Results.- 8.1. Perpendicular shocks with low ?l, and MAMA.- 8.3. Perpendicular high ? shocks.- 8.4. Oblique low ? shocks.- 8.5. Shocks without magnetic field.- II. The Tarantula Experiment.- 1. Introduction.- 2. Initial Plasma.- 2.1. Axial discharge.- 2.2. Experimental methods.- 2.3. Results.- 3. Dynamics of Compression.- 3.1. Pinch device.- 3.2. Magnetic field measurements of piston and shock.- 3.3. Comparison with MHD computation.- 4. Macro-Structure of Shock.- 5. Shock Heating.- 5.1. Thomson scattering of laser light.- 5.2. Measured electron temperatures and comparison with computations.- 6. Collisionless Shock.- 6.1. Inadequacy of classical transport coefficients.- 6.2. Collisionless mechanism for low MA.- 7. Micro-Structure of Shock from Forward Scattering.- 7.1. Description.- 7.2. Results.- 7.3. Local enhancement.- 7.4. Inferred effective collision frequency.- 9. Laser Produced Plasmas.- 1. Introduction.- 2. Gas Breakdown.- 3. Properties of Laser produced Plasmas in Gases.- 4. Laser produced Plasmas using Solid Targets and Single Particles.- 10. The Production and Containment of High Density Plasmas.- 1. Introduction.- 2. The Theta-Pinch.- 3. Shock Heating and Joule Heating.- 4. Radiation and Conduction Losses.- 5. Plasma Focus.- 6. Containment Problems.- 7. Axial Losses.- 8. Consequences for Thermonuclear Systems.- 9. Toroidal Systems.- 11. Light Scattering Experiments.- 1. Introduction.- 2. Scattering from a Free Electron Gas.- 2.1. Thomson scattering.- 2.2. Effect of the motion of the electrons.- 3. Scattering from a Plasma.- 3.1. Phenomenological description.- 3.2. Salpeter theory for scattering from a thermal plasma.- 3.3. Effect of a magnetic field.- 3.4. Collisions.- 3.5. Drifts.- 4. Experimental Considerations.- 4.1. Light source.- 4.2. Scattered flux.- 4.3. Plasma radiation.- 4.4. Time resolution.- 4.5. Choice of scattering angle.- 4.6. Temperature range and wavelength resolution.- 4.7. Rayleigh scattering.- 4.8. Perturbation of the plasma.- 5. Experimental Results.- 6. Technique.- 6.1. Ruby laser.- 6.2. Stray light.- 6.3. Forward angle scattering detection system.- 6.4. 90° scattering detection system.- 6.5. Intensity calibration.- 12. Plasma Diagnostics Based on Refractivity.- 1. Refractivity of Plasma.- 1.1. Propagation in the absence of a static magnetic field.- 1.2. Propagation in the presence of a static magnetic field Bz:.- 1.3. Propagation in partially ionized plasma.- 2. Review of Methods and Techniques in Refractivity Diagnosis.- 3. Some Limitations to these Methods.- 4. Interferometric Measurements.- 5. Laser Interferometry.- 6. The Schlieren Method.- 7. The Shadowgraph.- 8. Application of Holography in Optical Plasma Diagnostics.- 8.1. Holographic interferometry.- 8.2. Fourier-transform spectroscopy with stationary interferometers.- 8.3. The statistical approach.