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ОбложкаShneerson G.A. Strong and superstrong pulsed magnetic field generation / G.A.Shneerson, M.I.Dolotenko, S.I.Krivosheev. - Berlin; Boston: de Gruyter, 2014. - x, 429 p.: ill. - (De Gruyter studies in mathematical physics; vol.9). - Bibliogr. at the end of the chapters. - Ind.: p.424-429. - ISBN 978-2-11-025191-3; ISSN 2194-3532
Шифр: (И/З.2-S54) 02
 

Место хранения: 02 | Отделение ГПНТБ СО РАН | Новосибирск

Оглавление / Contents
 
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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