An introduction to magnetohydrodynamics

Contents......Page 3
Preface......Page 7
1.1 Introduction......Page 9
1.2 The electrodynamic equations......Page 15
1.3 The thermodynamic equations......Page 20
1.4 Thehydrodynamicequations......Page 24
1.5 The energy equation......Page 26
1.6 Boundary conditions......Page 30
1.7 Kinematics......Page 36
Problems 1......Page 41
2.1 The magnetic Reynolds number......Page 43
2.2 Diffusion of field in solid conductors......Page 45
2.3 Convection of magnetic flux by a perfect conductor......Page 51
2.4 Intermediate cases......Page 56
2.5 Notes on the vector potential......Page 65
Problems 2......Page 70
3.1 Formulation of the problem......Page 73
3.2 Simple conclusions......Page 77
3.3 Negative results......Page 83
3.4 Positive results......Page 93
3.5 Heuristic results......Page 103
Problems 3......Page 105
4.1 Preliminaries......Page 109
4.2 Governing equations......Page 110
4.3 Illustrations......Page 113
4.4 Force-free fields......Page 116
4.5 Variational results......Page 118
4.6 Axisynlmetric equilibria......Page 121
4.7 Magnetic stars......Page 123
Problems 4......Page 126
5.1 Transverse wave motion in a perfect fluid......Page 129
5.2 The effect of dissipation: Model 1......Page 133
5.3 The effect of dissipation: Model 2......Page 139
5.4 The limit of zero magnetic Prandtl number......Page 143
Problems 5......Page 146
6.1 The Hartmann layer......Page 152
6.2 The stability of the Hartmann layer......Page 159
6.3 Magnetohydrodynamic Blasius flow......Page 169
Problems 6......Page 177
7.1 Basic considerations......Page 179
7.2 Hartmann flow......Page 180
7.3 Duct flow at large Hartmann numbers......Page 189
7.4 Alfven radiation......Page 198
7.5 Bernard convection......Page 202
Problems 7......Page 216
8.1 The energy method......Page 221
8.2 Computation of delta(*) W......Page 225
8.3 Choice of displacement......Page 236
Problems 8......Page 240
9.1 The linear pinch......Page 243
9.2 Interchange instability......Page 252
9.3 Stability criteria for the general linear pinch......Page 255
Table 1: The principal magnetohydrodynamic parameters......Page 263
Table 2: Approximate values of some commonly occurring parameters......Page 265
Bibliography......Page 266
Index......Page 269