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1 Introduction 1

2 Characteristic parameters of a plasma 5

2.1 Number density and temperature 5

2.2 Debye Iength 7

2.3 Plasma frequency 10

2.4 Cyclotron frequency 12

2.5 Collision frequency 13

2.6 Number of electrons per Debye cube 15

2.7 The de Broglie wavelength and quantum effects 17

2.8 Representative plasma parameters 18

3 Single particle motions 23

3.1 Motion in a static uniform magnetic field 23

3.2 Motion in perpendicular electric and magnetic fields 26

3.3 Gradient and curvature drifts 32

3.4 Motion in a magnetic mirror field 39

3.5 Motion in a time varying magnetic field 45

3.6 Adiabatic invariants 48

3.7 The Hamiltonian method 60

3.8 Chaotic orbits 68

4 Waves in a coldplasma 75

4.1 Fourier representation of waves 75

4.2 General form of the dispersion relation 84

4.3 Waves in a cold uniform unmagnetized plasma 87

4.4 Waves in a cold uniforn magnetized plasma 94

4.5 Ray paths in inhomogeneous plasmas 127

5 Kinetic theory and the moment equations 137

5.1 The distribution function 137

5.2 The Boltzmann and Vlasov equations 140

5.3 Solutions based on constants of the motion 144

5.4 The moment equations 146

5.5 Electron and ion pressure waves 155

5.6 Collisional drag force 162

5.7 Ambipolar diffusion 166

6 Magnetohydrodynamics 175

6.1 The basic equations of MHD 175

6.2 Magnetic pressure 183

6.3 Magnetic field convection and diffusion 185

6.4 The energy equation 192

6.5 Magnetohydrodynamic waves 195

6.6 Static MHD equilibrium 204

6.7 MHD stability 219

6.8 Magnetic reconnection 240

7 Discontinuities and shock waves 251

7.1 The MHD iump conditions 252

7.2 Classification of discontinuities 255

7.3 Shock waves 258

8 Electrostatic waves in a hot unmagnetized plasma 281

8.1 The Vlasov approach 281

8.2 The Landau approach 290

8.3 The plasma dispersion function 308

8.4 The dispersion relation for a multi-component plasma 311

8.5 Stability 318

9 Waves in a hot magnetized plasma 341

9.1 Linearization of the Vlasov equation 342

9.2 Electrostatic waves 345

9.3 Electromagnetic waves 367

10 Non-linear effects 391

10.1 Quasi-linear theory 391

10.2 Stationary non-linear electrostatic potentials 406

11 Collisional processes 415

11.1 Binary Coulomb collisions 416

11.2 Importance of small-angle collisions 417

11.3 The Fokker-Planck equation 420

11.4 Conductivity of a fully ionized plasma 427

11.5 Collision operator for Maxwellian distributions of electrons and ions 431

Appendix A Symbols 435

Appendix B Vector differential operators 441

Appendix C Vector calculus identities 443

Index 445