 | Haas F. Quantum plasmas: an hydrodynamic approach. - New York: Springer, 2011. - xiii, 206 p. - (Springer series on atomic, optical, and plasma physics; 65). - Incl. bibl. ref., ind. - ISBN 978-1-4419-8200-1; ISSN 1615-5653
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1 Introduction ................................................. 1
1.1 Classical and Quantum Plasmas ........................... 1
1.2 Debye Shielding in Degenerate and Nondegenerate
Plasmas ................................................. 4
1.3 Plasma Frequency ........................................ 7
1.4 Energy Coupling Parameter ............................... 8
1.5 Kinetic and Fluid Descriptions .......................... 9
1.6 Historical Notes ....................................... 12
Problems .................................................... 12
References .................................................. 13
2 The Wigner-Poisson System ................................... 15
2.1 The Wigner Function .................................... 15
2.2 Mean Field Approximation ............................... 20
2.3 Electrostatic Quantum Plasmas .......................... 24
2.4 The Schrodinger-Poisson System ......................... 28
2.5 Validity of the Wigner-Poisson System .................. 30
2.6 Extensions to Include Correlation and Spin Effects ..... 32
2.7 High Frequency Longitudinal Waves ...................... 33
Problems .................................................... 36
References .................................................. 37
3 The Quantum Two-Stream Instability .......................... 39
3.1 Streaming Instabilities in Quantum Plasmas ............. 39
3.2 Quantum Dawson Model ................................... 40
3.3 One-Stream Plasma ...................................... 41
3.4 Two-Stream Plasma ...................................... 46
3.4.1 Two Counter Propagating Beams ................... 46
3.4.2 Stationary Solutions ............................ 49
3.5 Physical Interpretation of the Quantum Two-Stream
Instability ............................................ 51
3.5.1 Time-Averaged Energy Density of Electrostatic
Oscillations .................................... 53
3.5.2 Fast and Slow Approximate Modes in
Electrostatic Two-Stream Quantum Plasmas ........ 55
Problems .................................................... 61
References .................................................. 62
4 A Fluid Model for Quantum Plasmas ........................... 65
4.1 The Convenience of Macroscopic Models for Quantum
Plasmas ................................................ 65
4.2 Quantum Fluid Model .................................... 66
4.3 Applications to Degenerate Plasma ...................... 74
4.3.1 Linear Wave Propagation ......................... 75
4.3.2 Stationary Solutions ............................ 77
4.3.3 Two-Stream Instability .......................... 79
4.4 Equation of State for a Zero-Temperature Fermi Gas ..... 81
4.5 Landau Damping in a Degenerate Plasma .................. 86
4.6 Decomposing an Equilibrium Wigner Function in Terms
of Ensemble Wavefunctions .............................. 88
Problems .................................................... 91
References .................................................. 92
5 Quantum Ion-Acoustic Waves .................................. 95
5.1 Low Frequency Electrostatic Quantum Plasma Waves ....... 95
5.2 A Quantum Korteweg-de Vries Equation ................... 99
5.3 Nonlinear Quantum Ion-Acoustic Waves .................. 103
Problems ................................................... 107
References ................................................. 107
6 Electromagnetic Quantum Plasmas ............................ 109
6.1 Quantum Fluid Equations with Nonzero Magnetic Fields .. 109
6.2 Quantum Magnetohydrodynamics .......................... 116
6.3 Simplified and Ideal Quantum Magnetohydrodynamic
Models ................................................ 119
6.4 Quantum Ideal Magnetohydrodynamics: Equilibrium
Solutions ............................................. 121
6.5 Quantum Harris Sheet Solutions ........................ 125
Problems ................................................... 130
References ................................................. 131
7 The One-Dimensional Quantum Zakharov System ................ 133
7.1 Quantum Zakharov Equations in One Spatial Dimension ... 133
7.2 Parametric Instabilities .............................. 139
7.2.1 Decay Instability .............................. 139
7.2.2 Four-Wave Instability .......................... 142
7.3 Nonlinear Analysis .................................... 146
7.4 Semiclassical Adiabatic Regime ........................ 148
7.4.1 Small H2 ....................................... 151
7.4.2 Large H2 ....................................... 152
7.5 Time-Dependent Variational Method ..................... 153
7.5.1 The Small H Case ............................... 159
7.5.2 Fully Quantum Case ............................. 164
Problems ................................................... 166
References ................................................. 166
8 The Three-Dimensional Quantum Zakharov System .............. 169
8.1 Collapse of Langmuir Wave Packets ..................... 169
8.2 Derivation of the Three-Dimensional Quantum Zakharov
System ................................................ 170
8.3 Lagrangian Structure and Conservation Laws ............ 176
8.4 Variational Solution in Two Dimensions ................ 178
8.5 Variational Solution in Three Dimensions .............. 182
Problems ................................................... 185
References ................................................. 186
9 The Moments Method ......................................... 189
9.1 Moments Method ........................................ 189
9.2 Electrostatic Case .................................... 190
9.3 Dispersion Relation for Electrostatic Waves ........... 193
9.3.1 Electromagnetic Case ........................... 195
9.4 Gauge Invariant Wigner Function ....................... 195
9.5 Macroscopic Equations ................................. 197
9.6 Electromagnetic Dispersion Relation ................... 200
Problems ................................................... 203
References ................................................. 203
Index ......................................................... 205
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