Figures ........................................................ xi
Preface ...................................................... xiii
1 Partially Ionized Plasmas Here and Everywhere ................ 1
1.1 Plasma, a Matter of State ............................... 1
1.2 Partial Ionization in the Early Universe ................ 1
1.3 Reionization Phase of the Universe ...................... 6
1.4 Partially Ionized Plasma on Cosmic Scales ............... 7
1.5 Molecular Clouds ........................................ 7
1.6 Accretion Disks ......................................... 8
1.7 Interstellar Partially Ionized Plasma ................... 9
1.8 Solar Atmosphere ........................................ 9
1.9 Cometary Tails ......................................... 14
1.10 The Ionosphere ......................................... 14
1.11 Partially Ionized Plasmas in Laboratory ................ 14
1.12 Cold Plasmas in Medicine ............................... 16
1.13 Summary ................................................ 17
1.14 Problems ............................................... 17
2 Multifluid Description of Partially Ionized Plasmas ......... 18
2.1 Statistical Description ................................ 18
2.1.1 The Maxwellian velocity distribution function .... 19
2.2 Local Maxwell-Boltzmann Distribution Function .......... 25
2.2.1 The Boltzmann equation .......................... 25
2.2.2 The fluid formalism ............................. 28
2.2.3 The stress tensor ............................... 33
2.2.4 Validity of the fluid picture ................... 36
2.2.5 The Boltzmann collision integral ................ 37
2.3 Three-fluid Description of a Partially Ionized Plasma .. 37
2.4 Two-fluid Description of a Partially Ionized Plasma .... 41
2.4.1 The MHD fluid ................................... 41
2.4.2 Restrictions on the MHD fluid ................... 46
2.4.3 The neutral fluid ............................... 47
2.4.4 The two-fluid system ............................ 47
2.5 Single Partially Ionized Fluid—the SPIF ................ 48
2.6 Weakly Ionized Plasma .................................. 54
2.7 Summary ................................................ 56
2.8 Problems ............................................... 57
3 Equilibrium of Partially Ionized Plasmas .................... 59
3.1 The Equilibrium ........................................ 59
3.2 The Equilibrium Velocity Distribution Function ......... 59
3.3 Collisional Forces ..................................... 61
3.4 Collision Frequencies .................................. 64
3.4.1 The electron-ion collision frequency ............ 64
3.4.2 The electron-electron collision frequency ....... 66
3.4.3 The electron-neutral collision frequency ........ 66
3.4.4 The ion-neutral collision frequency ............. 66
3.5 Equilibrium of the Three-fluid System .................. 67
3.6 Hydrostatic Equilibrium ................................ 67
3.7 Hydrodynamic Equilibrium ............................... 69
3.8 Equilibrium with Collisional Forces .................... 73
3.9 Equilibrium of Collisionally Dominated Fluids .......... 76
3.10 Three-fluid Equilibrium with Magnetic Field ............ 78
3.11 Three-fluid Equilibrium with Magnetic and Collisional
Forces ................................................. 79
3.12 Equilibrium in the Two-fluid Description of
a Partially Ionized Plasma ............................. 83
3.12.1 Hydrostatic equilibrium ......................... 83
3.12.2 Hydrodynamic equilibrium ........................ 84
3.13 Equilibrium in Collisionally Dominated Two-fluids ...... 86
3.14 Two-fluid Equilibrium with Magnetic Field .............. 88
3.14.1 With current density  θ ..................... 92
3.14.2 Current density  ........................... 93
3.15 Two-fluid Equilibrium with Collisional Forces .......... 94
3.16 Equilibrium of the SPIF ................................ 95
3.17 Equilibrium of the Weakly Ionized Plasma ............... 95
3.18 Hall Equilibrium of the Weakly Ionized Plasmas ......... 97
3.19 Summary ................................................ 99
3.20 Problems .............................................. 100
4 Waves in Partially Ionized Plasmas ......................... 102
4.1 Waves in a Weakly Ionized Plasma ...................... 102
4.1.1 Transverse waves in weakly ionized plasmas -
the TWIP waves ................................. 107
4.1.2 Polarization of TWIP waves ..................... 113
4.1.3 Energy partition in TWIP waves ................. 114
4.1.4 Dissipation of the TWIP waves .................. 115
4.1.5 Longitudinal waves in weakly ionized plasmas -
the LWIP waves ................................. 117
4.1.6 LWIP waves with  |  0 ......................... 118
4.1.7 Polarization of LWIP waves with | 0 ......... 119
4.1.8 Energy partition for LWIP waves with | 0 .... 119
4.1.9 Dissipation of LWIP waves for | 0 ........... 120
4.1.10 Oblique LWIP waves ............................. 121
4.2 Waves in Single Partially Ionized Fluid—the SPIF ...... 124
4.3 Waves in Two-fluid Picture ............................ 126
4.3.1 Incompressible wave-motions .................... 126
4.3.2 Compressible wave-motions ...................... 135
4.4 Electrostatic Waves in Three-fluid Picture ............ 140
4.5 Electrostatic Waves in Magnetized Three-fluids ........ 149
4.6 Electromagnetic Waves in Three-fluids ................. 161
4.6.1 Electromagnetic waves in unmagnetized three-fluids ... 163
4.7 Electromagnetic Waves in Magnetized Three-fluids ...... 168
4.7.1 Electromagnetic waves with | 0 .............. 170
4.7.2 Electromagnetic waves with  0 .............. 176
4.8 Summary ............................................... 181
4.9 Problems .............................................. 181
5 Advanced Topics in Partially Ionized Plasmas ............... 184
5.1 Equilibrium of Partially Ionized Structures in the
Solar Atmosphere ...................................... 184
5.2 Equilibrium Plasma Structures with Hall Effect ........ 186
5.3 Hall Equilibrium of the Weakly Ionized Plasmas ........ 187
5.4 Hall Equilibrium of the Static Weakly Ionized
Plasmas ............................................... 188
5.5 Dynamical Hall Equilibrium ............................ 189
5.6 Static Equilibrium with Ambipolar and Resistive
Effects ............................................... 193
5.7 Taylor Relaxation in Weakly Ionized Plasmas ........... 194
5.7.1 Taylor relaxation in a single-fluid ............ 194
5.7.2 Taylor relaxation in an ideal single-fluid
with flow ...................................... 197
5.7.3 Taylor relaxation in a two-fluid system ........ 197
5.7.4 Taylor relaxation in a weakly ionized plasma ... 199
5.8 Hall Waves in Rotating Weakly Ionized Plasmas ......... 201
5.9 Exact Non-linear Dispersion Relation .................. 206
5.10 Kolmogorov Dissipation Scales in Weakly Ionized
Plasmas ............................................... 207
5.11 Generation of Magnetic Fields in Partially Ionized
Plasmas ............................................... 213
5.11.1 Mean-field dynamo ............................. 215
5.11.2 Mean-field dynamo in partially ionized
plasma ........................................ 221
5.11.3 Hall dynamo ................................... 222
5.11.4 Mean-field dynamo with ambipolar diffusion .... 225
5.11.5 Hall and ambipolar dynamo ..................... 228
5.11.6 Differential rotation-Hall-ambipolar dynamo ... 229
5.11.7 Magnetic transport via ambipolar diffusion .... 230
5.11.8 Stability analysis of ambipolar diffusion ..... 232
5.11.9 Sweet-Parker current slab in a weakly
ionized plasma ................................ 235
5.11.10 Parker-Sweet reconnection mechanism ........... 235
5.11.11 Parker-Sweet current slab ..................... 237
5.12 Summary ............................................... 241
5.13 Problems .............................................. 242
6 Research Problems in Partially Ionized Plasmas ............. 244
6.1 The Three-fluid Description ........................... 244
6.2 The Two-fluid Description ............................. 245
6.3 The Single-fluid Description .......................... 245
6.4 Weakly Ionized Plasma ................................. 245
6.5 The Equilibrium ....................................... 245
6.6 Waves ................................................. 246
6.7 Continuation of Studies in Chapter 5 .................. 246
Supplementary Matter .......................................... 249
Index ......................................................... 259
|
