Principles of Plasma Physics for Engineers and Scientists

Cover......Page 1
Half-title......Page 3
Title......Page 5
Copyright......Page 6
Dedication......Page 7
Contents......Page 9
Preface......Page 15
CHAPTER 1 Introduction......Page 17
1.1 Speed, energy, and temperature......Page 24
1.2 Quasi-neutrality and plasma oscillations......Page 26
1.3 Debye shielding......Page 29
1.4 Problems......Page 34
References......Page 35
CHAPTER 2 Single-particle motion......Page 36
2.1 Motion in a uniform B field: gyration......Page 37
2.2 E x B drift......Page 42
Example 2-1 Hall thruster......Page 45
2.3 Particle motion in non-uniform B fields......Page 46
2.3.1 Gradient drift......Page 47
2.3.2 Curvature drift......Page 49
2.3.3 Other gradients of B......Page 52
2.4 Adiabatic invariance of the magnetic moment......Page 53
2.5.1 Polarization drift: slowly varying E field......Page 58
2.5.2 Particle motion in static B and arbitrary E fields......Page 60
2.6 Summary......Page 64
2.7 Problems......Page 65
References......Page 68
3.1 Introduction......Page 69
3.2 Comparison of properties of gases and plasmas......Page 71
3.3 Velocity distribution function......Page 73
3.4 The Boltzmann equation......Page 76
3.5 The Maxwell–Boltzmann distribution......Page 80
3.5.1 Number density......Page 82
3.5.2 Temperature......Page 83
3.5.3 Velocity in one dimension and speed......Page 84
3.5.4 Degree of ionization: the Saha equation......Page 87
3.6 The Vlasov equation......Page 89
3.6.1 The convective derivative in physical space and in phase space......Page 91
3.7 Equivalence of the particle equations of motion and the Vlasov equation......Page 93
3.8 Summary......Page 96
3.9 Problems......Page 97
References......Page 99
4.1 Introduction......Page 100
4.2 The zeroth-order moment: continuity equation......Page 102
4.2.1 Closer consideration of collisions and conservation of particles......Page 104
4.3 The first-order moment: momentum transport equation......Page 106
4.3.1 The pressure and collision terms......Page 111
4.4 The second-order moment: energy transport equation......Page 115
4.5 Systems of macroscopic equations: cold-and warm-plasma models......Page 116
4.5.2 The warm-plasma model......Page 118
4.6 Summary......Page 119
4.7 Problems......Page 120
References......Page 121
5.1 Introduction......Page 122
5.2 Complete set of two-fluid equations......Page 123
5.3 Fluid drifts perpendicular to B......Page 126
5.4 Parallel pressure balance......Page 129
5.6 Problems......Page 130
References......Page 131
6.1 Introduction......Page 132
6.2 Single-fluid equations for a fully ionized plasma......Page 133
6.2.2 Equation of motion......Page 135
6.2.3 Generalized Ohm\'s law......Page 136
6.3 Magnetohydrodynamics plasma model......Page 139
6.4 Simplified MHD equations......Page 140
6.4.1 Frozen-in magnetic flux lines......Page 144
6.5 Force balance in MHD......Page 148
6.5.1 Magnetic forces......Page 150
6.6 Magnetohydrostatics......Page 154
6.6.1 The theta-pinch......Page 155
6.6.2 The cylindrical pinch......Page 157
6.7 Collisionless plasmas with strong magnetic field......Page 160
6.7.1 Mirror equilibrium......Page 162
6.8 Summary......Page 164
6.9 Problems......Page 165
References......Page 166
7.1 Introduction......Page 168
7.2.1 Weakly ionized plasmas......Page 170
7.2.2 Fully ionized plasmas: Coulomb collisions......Page 171
7.2.3 Specific resistivity......Page 173
7.3.1 DC conductivity......Page 175
7.3.2 AC conductivity......Page 179
7.3.3 Conductivity with ion motion......Page 180
7.5 Problems......Page 181
References......Page 182
8.1 Introduction......Page 183
8.2.1 Ambipolar diffusion in an unmagnetized plasma......Page 186
8.2.2 Free diffusion across a magnetic field......Page 188
8.3 Diffusion in fully ionized plasmas......Page 190
8.4 Summary......Page 191
8.5 Problems......Page 192
9.1 Introduction......Page 194
9.2 General properties of small-amplitude waves......Page 196
9.3.1 Plasma oscillations......Page 199
9.3.2 Transverse electromagnetic waves......Page 200
9.3.3 Electrostatic electron and ion waves......Page 205
9.4 Problems......Page 206
10.1 Introduction......Page 208
10.2 The dispersion relation......Page 209
10.3 Waves in magnetized plasmas......Page 211
10.3.1 Principal modes......Page 214
10.3.2 Oblique propagation at an arbitrary angle theta......Page 221
10.5 Problems......Page 223
References......Page 225
11.2 Effects of collisions......Page 226
11.3 Effects of positive ions......Page 227
11.3.1 Parallel propagation (theta = 0)......Page 228
11.3.2 Perpendicular propagation (theta = pi/2)......Page 231
11.3.4 Hydromagnetic (MHD) waves......Page 232
11.4.1 Parallel propagation (theta = 0)......Page 236
11.4.2 Perpendicular propagation (theta = pi/2)......Page 238
11.6 Problems......Page 239
12.1 Introduction......Page 241
12.2 Waves in a hot isotropic plasma......Page 242
12.2.1 Longitudinal waves (k parallel E)......Page 244
12.2.2 Transverse waves......Page 251
12.2.3 The two-stream instability......Page 255
12.3 Waves in a hot magnetized plasma......Page 256
12.4 More on collisions in plasmas......Page 260
12.4.1 The Krook collision model......Page 262
12.5 Summary......Page 264
12.6 Problems......Page 265
References......Page 266
13.2 Particle flux......Page 267
13.3 Sheath characteristics......Page 268
13.4 The Langmuir probe......Page 273
13.5 Problems......Page 275
Appendix A: Second moment of the Boltzmann equation......Page 277
B.1 Definitions and identities......Page 279
B.3 Relations in cylindrical coordinates......Page 280
B.4 Relations in spherical coordinates......Page 281
Index......Page 283