Magneto-Fluid Dynamics

Fundamentals and Case Studies of Natural Phenomena

By: Paul Lorrain, Francois Lorrain, Stephane Houle

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Hardcover | 30 August 2006

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360 Pages

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Magnetohydrodynamics (MHD) concerns the interaction between magnetic fields and conducting fluids. We are concerned here with macroscopic inter- actions and, when the conducting fluid is a plasma, time scales are very much longer than the plasma period. Plasma periods vary widely, but are short, say 10~^^ second. We prefer the term Magneto-F/i^Z(i-Dynamics (MFD) because the disci- pline concerns mostly plasmas, various liquid conductors, and the liquid part of the Earth's core. It seems that the only applications of MFD to water are the induction of electric currents in the oceans by the Earth's magnetic field, and ship propulsion. But even MFD is not quite appropriate because that term also includes solid conductors that move in magnetic fields. This book is meant for graduate and upper-division undergraduate stu- dents in Physics, Geophysics, and Astrophysics, as well as for practicing sci- entists in these fields. This book is no more than a brief introduction to MFD because this vast subject is closely related to many others, namely Astrophysics, Elec- trodynamics, Fluid Dynamics, Geophysics, Oceanography, Plasma Physics, Thermonuclear Fusion, etc. We sketch the fundamentals, and provide many Examples, as well as Case Studies related to natural phenomena. MFD sorely needs a rethink: it must of course be totally compatible with Physics. On the contrary, it is the custom to discuss the shapes of imaginary magnetic field lines, without ever referring to the required electric currents.

Industry Reviews

From the reviews: "This text is an interesting, and clearly structured introduction to dynamo theory inspired from the study of natural dynamos, particularly within the solar environment. It provides an enticing flavour of the modelling of a wide variety of electromagnetic phenomena. ... The text is intended primarily for advanced undergraduates and postgraduates in physics, geophysics and astrophysics. ... The essentially independent case studies make this book ideal to dip in and out of and to use as a source of reference on magneto-fluid phenomena ... ." (Anne Juel, Contemporary Physics, Vol. 51 (1), 2010)

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Non-Fiction Science Physics Applied Physics Astrophysics Nuclear Physics Electricity Atomic & Molecular Physics Astronomy, Space & Time Astronomical Observation & Observatories Materials & States of Matter Plasma Physics

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Paperback

Published: 25th November 2010

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Preface	p. XV
Looking Ahead	p. XXI
List of Symbols	p. XXIX
The Early History
The Early History	p. 3
Magnetism in China	p. 4
Magnetism in Europe	p. 5
Navigation by Compass in Europe	p. 5
Pierre de Maricourt (Petrus Peregrinus)	p. 6
From Gilbert on	p. 7
Faraday	p. 8
The Story of the "Maxwell" Equations	p. 9
Maxwell	p. 10
Heaviside	p. 11
Zeeman, Hale, Gouy, and Larmor	p. 13
Fundamentals
The Maxwell Equations	p. 19
Introduction	p. 20
The Equations in Differential Form	p. 20
Example: The Differential Form of Gauss's Law for Electric Fields	p. 23
Example: The Differential Form of Gauss's Law for Magnetic Fields	p. 23
Example: The Differential Form of the Law of Faraday	p. 23
Example: The Differential Form of Ampere's Circuital Law	p. 23
The Equations in Integral Form	p. 24
Example: The Integral Form of Gauss's Law for Electric Fields	p. 25
Example: The Integral Form of Gauss's Law for Magnetic Fields	p. 26
Example: The Integral Form of the Law of Faraday	p. 26
Example: The Integral Form of Ampere's Circuital Law	p. 27
The Displacement Current Density	p. 27
The Convection Current Density	p. 28
Summary	p. 29
Electric Fields	p. 31
Electric Fields and Forces	p. 31
Electric Currents	p. 33
Example: The Drift Speeds of Charge Carriers	p. 34
The Conservation of Electric Charge	p. 34
Example: The Relaxation Time of a Conductor	p. 35
The Electric Potential V	p. 36
The Equations of Poisson and of Laplace	p. 36
Joule Losses	p. 37
Electric Energy	p. 37
Example: A Proton Beam I	p. 37
Case Study: V at the Surface of the Sun	p. 41
Summary	p. 44
Constant Magnetic Fields	p. 45
Magnetic Field Lines	p. 46
The Magnetic Flux Density B at a Point	p. 46
Example: Calculating the Field of a Coil	p. 47
Magnetic Flux [Phi]	p. 48
Ampere's Circuital Law	p. 48
Example: The Thin Solenoid	p. 48
Example: The Thick Solenoid	p. 49
The Vector Potential	p. 50
Example: The Vector Potential near a Circuit	p. 51
Example: The Thin Solenoid	p. 51
Magnetic Multipoles	p. 51
Case Study: The Earth's Magnetic Field	p. 52
The Magnetic Force	p. 56
Example: The Electromagnetic Pump	p. 57
Magnetic Field Lines Again	p. 57
Magnetic Pressure	p. 59
Example	p. 59
Magnetic Energy	p. 59
Example: A Proton Beam II	p. 60
Summary	p. 61
Time-dependent Magnetic Fields: The Law of Faraday	p. 63
The Electric Field Strength	p. 63
The Law of Faraday	p. 64
Lenz's Law	p. 64
Example: The Thin Solenoid	p. 65
Example: A Secondary on a Long Solenoid	p. 65
Self-inductance	p. 65
Magnetic Energy in a Self-inductance	p. 66
Mutual Inductance	p. 66
Electromagnetic Waves	p. 67
Case Study: The Earth's Magnetic Field	p. 67
Summary	p. 68
Moving Conductors
Ohm's Law for Moving Conductors	p. 73
Reference Frames	p. 74
Special Relativity	p. 74
The Kinematic Transformation Equations	p. 75
The Transformation Equations of Electromagnetic Quantities	p. 75
Example: Straight Wire Carrying a Current	p. 79
The Lorentz Force	p. 79
Ohm's Law for Moving Conductors	p. 79
The Induction Equation	p. 82
The Magnetic Reynolds Number	p. 83
Examples	p. 84
Magnetic Forces on Moving Conductors	p. 85
Summary	p. 86
Charges Inside Moving Conductors	p. 87
Introduction	p. 88
Electric Charges in Moving Conductors	p. 88
Example: Rotating Solid Conductor	p. 90
Time-dependent Situations	p. 91
The Magnetic Field of the Convection Current	p. 92
Example: The Faraday Disk	p. 92
The Faraday Disk with the Switch SW Open	p. 93
The Faraday Disk as a Generator	p. 94
The Faraday Disk as a Motor	p. 95
The Currents in the Axle and in the Disk	p. 96
Example: The Rotating Sphere	p. 97
The Surface Charge	p. 99
Summary	p. 101
Nine Examples: Magnetic Fields in Moving Conductors	p. 103
Introduction	p. 104
The Induced Currents	p. 104
Magnetic Field Lines Once More	p. 105
The Net Magnetic Field	p. 106
The Case of Rotating Conductors	p. 107
The Newcomb Criterion	p. 109
Nine Examples	p. 110
Assumptions	p. 111
Examples 1, 2, 3: The Three Shercliff Cases	p. 111
Example 4: Rigid Conductor	p. 113
Example 5: Rotating Cylinder	p. 114
Example 6: Rotating Solid Sphere	p. 116
Example 7: Moving Plate	p. 117
Example 8: Rotating Fluid Sphere	p. 120
Example 9: The Faraday Disk	p. 122
Summary	p. 123
Case Study: The Azimuthal Magnetic Field in the Earth's Core	p. 125
Introduction	p. 126
The Ratio B[subscript T]/B[subscript P]	p. 127
The Reference Frames S and S'	p. 130
Does the Earth's Magnetic Field Rotate?	p. 131
Does the "Other" Magnetic Field Rotate?	p. 132
Does the Axisymmetric Field B[subscript axi] Rotate?	p. 132
Example: The One-piece Faraday Generator	p. 133
Solid Core	p. 133
The Values of v x B and of Q	p. 134
Differential Rotation	p. 135
Ferraro's Law of Isorotation	p. 136
B[subscript T] with v[subscript [Phi]] a Function of z	p. 137
B[subscript T] with v[subscript [Phi]] a Function of p	p. 141
Summary	p. 143
Natural Dynamos
Case Study: The Disk Dynamo Model for Natural Dynamos	p. 147
Introduction	p. 147
The Self-excited Disk Dynamo	p. 149
The Kinematic Self-excited Disk Dynamo	p. 149
The Dynamic Self-excited Disk Dynamo	p. 153
A Laboratory-sized Dynamo?	p. 156
Summary	p. 157
Three Case Studies: Magnetic Flux Tubes, Flux Ropes, and Flux Coils	p. 159
Introduction	p. 160
Convecting, Conducting Fluids	p. 161
Magnetic Flux Tubes (MFT's)	p. 163
The Magnetic Force Density in MFT's	p. 167
The Gas Pressure Inside MFT's	p. 167
[Phi] B[subscript z], and J[subscript [Phi]]	p. 169
The Magnetic Energy in MFT's	p. 170
Power Dissipation in MFT's	p. 170
The Resistance per Meter in MFT's	p. 170
The Inductance per Meter in MFT's	p. 171
The Time Constant of an MFT	p. 171
Fluctuating MFT's	p. 172
Magnetic Flux Ropes (MFR's)	p. 174
The Axial Current in an MFR	p. 176
Magnetic Forces on MFR's	p. 178
Power Dissipation and Time Constants in MFR's	p. 179
Are Tubes and Ropes Light Guides?	p. 179
Electromagnetic Waves	p. 180
Guided Electromagnetic Waves	p. 180
Electromagnetic Waves in Plasmas	p. 181
Guiding Light in Magnetic Flux Tubes and Ropes	p. 181
Magnetic Flux Coils As Particle Accelerators	p. 184
Summary	p. 187
Case Study: Solar Magnetic Elements	p. 189
Introduction	p. 189
Local Currents in Magnetic Elements	p. 191
A Simple Model	p. 192
The Magnetic Flux Density B	p. 194
The Current Density J and the Conductivity [sigma]	p. 194
The Stored Magnetic Energy	p. 196
The Gas Pressure Inside the Element	p. 196
The Dissipated Power	p. 197
The Time Constant	p. 198
Magnetic Element "Dipoles"	p. 200
Anchoring	p. 200
A More Realistic Approximation	p. 200
Summary	p. 203
Case Study: Sunspots	p. 205
Introduction	p. 206
Our Model	p. 206
Plasma Flows Above and Below Sunspots	p. 207
The Magnetic-flux-tube Dynamo	p. 208
Why Are Sunspots Dark?	p. 210
The Radial Distribution of J[subscript [Phi]]	p. 210
The Magnetic Field Configuration	p. 211
Magnetic Pressure and Gas Pressure	p. 215
The Flux Tube Radius As a Function of z	p. 216
The Radius b Below -36 Megameters	p. 216
The Flux Tube Radius b Above -36 Megameters	p. 219
The Wilson Depression	p. 220
Summary	p. 221
Case Study: Solar Spicules	p. 223
Introduction	p. 223
Devising a Model	p. 226
What Type of Particle?	p. 226
Repulsion and Pinching	p. 227
Channeling	p. 228
Self-excited Dynamos	p. 230
A Self-excited Accelerator for Spicules	p. 231
J[subscript a] in the Accelerator, Self-excitation	p. 233
The Magnetic Force Density in the Accelerator	p. 235
The Proton Energy	p. 236
The Beam Head	p. 236
The Beam Head Speed	p. 237
The Return Current at the Beam Head	p. 238
Summary	p. 238
Case Study: Solar Coronal Loops as Self-Channeled Proton Beams I	p. 239
Introduction	p. 239
Observations	p. 241
What Are They?	p. 242
Loops As Charged-particle Beams	p. 245
The Beam Current and the Beam Power	p. 246
The Magnetic Energy	p. 247
The Proton Energy	p. 247
Our Reference Loop	p. 250
Summary	p. 251
Case Study: Solar Coronal Loops as Self-Channeled Proton Beams II	p. 253
Introduction	p. 253
Channeling a Broad Proton Beam	p. 254
Electric and Magnetic Forces on a Proton Beam, Without Rotation	p. 255
Magnetic Forces on a Beam Proton, with Rotation	p. 259
Diamagnetism of the Proton Beam	p. 261
At the Beam Head	p. 263
Guiding the Proton Beam	p. 264
Near-axial Ambient Magnetic Field	p. 264
Diverging or Converging Ambient Magnetic Field	p. 265
What Determines the Beam Diameter?	p. 266
The Forces Outside the Beam	p. 267
No Interaction Within a Given Family?	p. 268
Two Families of Loops Repel?	p. 270
Summary	p. 270
Appendices
Characteristic Lengths and Times, a Justification	p. 273
Introduction	p. 274
Amplitude and Norm of a Function	p. 275
L and T of a Sinusoidal Function	p. 277
Fourier Expansions	p. 279
Characteristic Time T of a Function	p. 281
Characteristic Length L of a Function	p. 282
The Norm of [down triangle] f (r)	p. 283
Vectors with Complex Components	p. 283
The Norms of [down triangle] . A and of [down triangle] x A	p. 283
The Norms of [down triangle][superscript 2] f, [down triangle][superscript 2] A, and [down triangle] x [down triangle] x A	p. 286
Products of Functions	p. 287
Summary and Discussion	p. 289
SI prefixes	p. 295
References	p. 297
Index	p. 309
Table of Contents provided by Ingram. All Rights Reserved.

Magneto-Fluid Dynamics

Fundamentals and Case Studies of Natural Phenomena

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

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