Introduction .................................................... 1
1 Magnetic fields of axially symmetrical magnetic systems
used for generation of the strong fields (methods of
calculation, assessment of the edge effects) ................. 8
1.1 Magnetic field of the systems with the given current
distribution ............................................ 8
1.2 The setting of the task for the calculation of
a magntic field at a small penetration depth ........... 13
1.3 The determination of the parameters of the inductor
systems at a strongly-pronounced skin effect
according to the simplified field pattern .............. 18
1.3.1 The field of single-turn solenoids (flat ring)
above the ideally-conducting plane {h « r1) ..... 18
1.3.2 The field of multiwinding solenoid in the form
of a flat spiral above the plane (Figure 1.6b) .. 19
1.3.3 Field of solenoid in off-loading cylindrical
screens ......................................... 20
1.4 Edge effects in single-coil magnets. Modelling of
problems ............................................... 21
1.5 References ............................................. 27
2 Calculating formulas and the results of numerical
estimations of field parameters for typical single-turn
magnets ..................................................... 29
2.1 The field of the flat ring as an example of the
single-turn magnet with sharply pronounced edge
effect ................................................. 29
2.2 The coil of a rounded cross-section (an ideally
conductive toroid) ..................................... 32
2.3 Thin-wall single-turn magnets .......................... 35
2.4 The field of rectangular coils with arbitrary ratios
of characteristic dimensions ........................... 39
2.5 Induction of the one-turn magnet placed near the
coaxial cylinder or the plane .......................... 41
2.6 References ............................................. 44
3 Field diffusion into the conductors and their heating ....... 45
3.1 Adiabatic heating of conductors at a given current
density ................................................ 46
3.2 Linear regime of field diffusion in conductors ......... 50
3.3 The surface impedance. Energy losses in the skin
layer with sinusoidal current .......................... 52
3.4 The asymptotical values of the magnetic field
intensity and current density at the conductor edge
under the condition of a pronounced skin effect ........ 57
3.5 Examples of the diffusion of the uniform pulse
electromagnetic field into a medium with constant
conductivity ........................................... 61
3.6 Energy generation and heating a medium in the case of
diffusion of the pulse magnetic field into the
conductor .............................................. 65
3.7 Heating of a conductor with a current in an external
magnetic field ......................................... 70
3.8 Minimization of a uniform medium heating under
diffusion ofthe pulse magnetic field ................... 76
3.9 One-dimensional diffusion of the field into a medium
with conductivity depending on the coordinate.
Reduction of energy generation in the surface layer .... 78
3.10 One-dimensional nonlinear diffusion ofthe magnetic
field into the conductor heated by the eddy current .... 81
3.11 Approximate description of the surface effect. "The
skin layer method" ..................................... 85
3.12 References ............................................. 89
4 Matching of the parameters of solenoids and power supply
sources ..................................................... 91
4.1 General requirements to the power supply source ........ 91
4.2 Optimization of the parameters of the system of
solenoids - capacity energy storage .................... 92
4.3 Optimization of solenoids according to Fabri ........... 94
4.4 Transformations of energy in a circuit with
alternating inductance ................................. 98
4.4.1 Direct current in the element ofthe electrical
circuit with alternating inductance ............. 99
4.4.2 Energy transformations in the short-circuiting
coil with alternating inductance ................ 99
4.4.3 Railgun powered by energy capacity storage ..... 100
4.5 On the application of inductive storages for
supplying the magnetic systems ........................ 109
4.6 References ............................................ 112
5 Electromagnetic forces and mechanical stresses in
multiturn solenoids. The optimization of multilayered
windings ................................................... 113
5.1 Asimuthal and axial stresses in the thin-wall turn
in the poloidal magnetic field ........................
5.2 Mechanical stresses in the uniform cylinder with
a given current distribution .......................... 117
5.2.1 A winding with constant current density ......... 118
5.2.2 A winding with a current density decreasing
inversely with radius (Bitter's solenoid) ....... 120
5.3 Mechanical stresses in an equilibrium thin-wall
cylinder with current ................................. 121
5.4 Mechanical stresses in two-component winding .......... 125
5.5 Magnets with mechanically separated thin current
layer. Series or parallel connection of layers ........ 129
5.5.1 A winding with a series connection of current
layers ......................................... 129
5.5.2 A winding with parallel-connected layers ....... 130
5.6 Multilayer magnet with equally-loaded winding ......... 131
5.7 Multilayer magnets with equally-loaded internal
reinforcements ........................................ 136
5.8 The plastic deformation and the resource of
multiturn magnets ..................................... 140
5.9 References ............................................ 145
6 Generation of strong magnetic fields in multiturn magnets .. 147
6.1 Traditional constructions of solenoids with spiral
multilayer windings ................................... 149
6.2 Present-day materials used to make windings ........... 154
6.3 Special features of constructions of present-day
multiturn monolithic magnets with held of 60-80 T ..... 159
6.4 The results of tests of multiturn magnets and
investigation of their destruction .................... 164
6.5 Magnets with record fields ............................ 169
6.6 Flat helical solenoids ................................ 175
6.7 References ............................................ 178
7 Solenoids with quasi-force-free windings ................... 182
7.1 Quasi-force-free configurations, an analog of which
is a winding of a quasi-force-free magnet ............. 183
7.1.1 One-dimensional quasi-force-free magnetic
systems: the flat layer and cylinder ........... 183
7.1.2 Two-dimensional force-free configurations
satisfying the characteristic boundary
conditions ..................................... 186
7.1.3 Features of current distribution in the face
zone of a force-free magnet .................... 192
7.2 The methods of realization of a quasi-force-free
winding. The estimates of residual mechanic stresses
in a thin-wall quasi-force-free winding ............... 194
7.2.1 Quasi-force-free winding with pairs ofthe
equilibrium current layers (number of pairs
N » 1) ......................................... 194
7.2.2 Multilayer magnetic systems with variable
direction of current in each layer ............. 196
7.3 Configurations of magnetic systems with equilibrium
windings with zero thickness .......................... 201
7.3.1 One-modular configurations ..................... 202
7.3.2 Multimodular systems ........................... 206
7.4 Thin-wall quasi-force-free magnets with current
removals .............................................. 210
7.4.1 Systems with equally-loaded internal
reinforcements ................................. 210
7.5 Comparative estimates of the residual stresses and
sizes of magnets with a quasi-force-free winding and
loaded outer zone ..................................... 213
7.6 Design methods of quasi-force-free magnets ............ 214
7.7 References ............................................ 217
8 Generation of strong pulsed magnetic fields in single-
turn magnets. Magnetic systems for the formation of
pulsed loads ............................................... 219
8.1 Mechanical stresses in a single-turn magnet
operating under the condition of a sharply
pronounced skin effect ................................ 220
8.2 Assessing the strength of single-turn magnets at
short pulses .......................................... 222
8.3 Thermoelastic stresses in single-turn magnets ......... 227
8.4 The destruction of single-turn magnets. The problem
of erosion ............................................ 231
8.5 Special construction features of single-turn magnets
and their power supplies .............................. 237
8.6 Deformed single-turn magnets restored after the
discharge ............................................. 246
8.7 Magnetic systems used for deformation of solids and
the study of their properties ......................... 247
8.8 Magnetic systems for the acceleration of conductors ... 259
8.9 References ............................................ 266
9 Generation of ultrahigh magnetic fields in destructive
single-turn magnets ........................................ 270
9.1 Physical processes accompanying the generation of
megagauss magnetic field in single-turn magnets ....... 270
9.2 Modeling problems illustrating the role of different
factors leading to the destruction of single-turn
magnets ............................................... 281
9.3 Hydrodynamic flows in single-turn solenoids.
Application of the model of a noncompressible liquid
with ideal conductivity to the description of the
deformation of a thick-wall turn ...................... 283
9.4 Electrical explosion of turns of small thickness.
Evaluation of the induction achieved in the
destruction of turns with small initial dimensions .... 291
9.5 One-dimensional hydrodynamic flow in the wall of
a single-turn magnet. Shock wave in conductors
initiated by superstrong magnetic fields .............. 298
9.6 General information on the electric explosion
of conductors ......................................... 301
9.7 Electric explosion of the skin layer in superhigh
magnetic fields. Ideal model .......................... 311
9.8 The actual processes developing for "slow" and
"fast" electric explosions of a conductor surface
skin layer in a superhigh magnetic field .............. 313
9.9 Computer simulation of a skin layer explosion ......... 320
9.10 References ............................................ 330
10 Magnetic cumulation ........................................ 333
10.1 Initial idea. Brief history. Main trends in
development and research .............................. 333
10.2 MC energy generators .................................. 336
10.3 Physical processes in magnetic cumulation.
Analytical estimates for the MC-1 system .............. 342
10.3.1 Induction amplitude and the radius of
turnaround for flux compression by an ideal
cylindrical shell .............................. 343
10.3.2 Estimation of the pulse duration of
a magnetic field in magnetic cumulation ........ 344
10.3.3 The effect of field diffusion on the
induction amplitude with magnetic cumulation ... 346
10.3.4 Restrictions on the induction amplitude
conditioned by the compressibility of
a medium ....................................... 349
10.3.5 Violation of the stability of a liner at
flux compression ............................... 352
10.4 Flux compression systems not using the explosion
energy for liner acceleration ......................... 355
10.4.1 MDC systems with azimuth current in a liner .... 357
10.4.2 Magnetodynamic cumulation in a Z-θ pinch
system ......................................... 362
10.5 Analytical estimations and simulation of
magnetodynamic cumulation ............................. 365
10.6 Explosion devices and solenoids of an initial field
used in magnetic cumulation ........................... 379
10.6.1 Detonation of the explosive charge ............. 379
10.6.2 Generation of the initial magnetic field ....... 382
10.7 Liners of MC-1 generators ............................. 384
10.7.1 Commonly used metal liners ..................... 384
10.7.2 Metal composite liners ......................... 385
10.7.3 Shock-wave liners with phase transitions ....... 386
10.8 Violation of liner stability in flux compression ...... 390
10.9 Principle of cascading in MC generators of ultrahigh
magnetic fields ....................................... 395
10.10 MC-1 cascade generator. Numerical simulation and
experiment ........................................... 399
10.11 Ways of increasing the induction amplitude. Methods
for control over the pulse shape. Capabilities of
the MC-1 generator ................................... 407
10.11.1 Methods for control over the shape and
amplitude of an induction pulse ............... 407
10.11.2 Capabilities of MC-1 generators of ultrahigh
magnetic fields ............................... 410
10.12 Conclusion ........................................... 416
Supplement S10. Calculation of the skin layer thickness and
of the parameter q, characterizing the energy in the skin
layer ...................................................... 416
10.13 References ........................................... 418
Index ......................................................... 424
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