De Gruyter Studies in Mathematical Physics -- Title Page -- Copyright Page -- Table of Contents -- Introduction -- Bibliography -- 1 Magnetic fields of axially symmetrical magnetic systems used for generation of the strong fields (methods of calculation, assessment of the edge effects) -- 1.1 Magnetic field of the systems with the given current distribution -- 1.2 The setting of the task for the calculation of a magntic field at a small penetration depth -- 1.3 The determination of the parameters of the inductor systems at a strongly-pronounced skin effect according to the simplified field pattern -- 1.3.1 The field of single-turn solenoids (flat ring) above the ideally-conducting plane (h ≪ r1) -- 1.3.2 The field of multiwinding solenoid in the form of a flat spiral above the plane (Figure 1.6b) -- 1.3.3 Field of solenoid in off-loading cylindrical screens -- 1.4 Edge effects in single-coil magnets. Modelling of problems -- 1.5 References -- 2 Calculating formulas and the results of numerical estimations of field parameters for typical single-turn magnets -- 2.1 The field of the flat ring as an example of the single-turnmagnet with sharply pronounced edge effect -- 2.2 The coil of a rounded cross-section (an ideally conductive toroid) -- 2.3 Thin-wall single-turn magnets -- 2.4 The field of rectangular coils with arbitrary ratios of characteristic dimensions -- 2.5 Induction of the one-turn magnet placed near the coaxial cylinder or the plane -- 2.6 References -- 3 Field diffusion into the conductors and their heating -- 3.1 Adiabatic heating of conductors at a given current density -- 3.2 Linear regime of field diffusion in conductors -- 3.3 The surface impedance. Energy losses in the skin layer with sinusoidal current.

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 -- 3.5 Examples of the diffusion of the uniform pulse electromagnetic field into a medium with constant conductivity -- 3.6 Energy generation and heating a medium in the case of diffusion of the pulse magnetic field into the conductor -- 3.7 Heating of a conductor with a current in an external magnetic field -- 3.8 Minimization of a uniform medium heating under diffusion of the pulse magnetic field -- 3.9 One-dimensional diffusion of the fieldinto a medium with conductivity depending on the coordinate. Reduction of energy generation in the surface layer -- 3.10 One-dimensional nonlinear diffusion of the magnetic field into the conductor heated by the eddy current -- 3.11 Approximate description of the surface effect. "The skin layer method" -- 3.12 References -- 4 Matching of the parameters of solenoids and power supply sources -- 4.1 General requirements to the power supply source -- 4.2 Optimization of the parameters of the system of solenoids - capacity energy storage -- 4.3 Optimization of solenoids according to Fabri -- 4.4 Transformations of energy in a circuit with alternating inductance -- 4.4.1 Direct current in the element of the electrical circuit with alternating inductance -- 4.4.2 Energy transformations in the short-circuiting coil with alternating inductance -- 4.4.3 Railgun powered by energy capacity storage -- 4.5 On the application of inductive storages for supplying the magnetic systems -- 4.6 References -- 5 Electromagnetic forces and mechanical stresses in multiturn solenoids. The optimization of multilayered windings -- 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 -- 5.2.1 A winding with constant current density -- 5.2.2 A winding with a current density decreasing inversely with radius (Bitter's solenoid) -- 5.3 Mechanical stresses in an equilibrium thin-wall cylinder with current -- 5.4 Mechanical stresses in two-component winding -- 5.5 Magnets with mechanically separated thin current layer. Series or parallel connection of layers -- 5.5.1 A winding with a series connection of current layers -- 5.5.2 A winding with parallel-connected layers -- 5.6 Multilayer magnet with equally-loaded winding -- 5.7 Multilayer magnets with equally-loaded internal reinforcements -- 5.8 The plastic deformation and the resource of multiturn magnets -- 5.9 References -- 6 Generation of strong magnetic fields in multiturn magnets -- 6.1 Traditional constructions of solenoids with spiral multilayer windings -- 6.2 Present-day materials used to make windings -- 6.3 Special features of constructions of present-day multiturn monolithic magnets with field of 60-80 T -- 6.4 The results of tests of multiturn magnets and investigation of their destruction -- 6.5 Magnets with record fields -- 6.6 Flat helical solenoids -- 6.7 References -- 7 Solenoids with quasi-force-free windings -- 7.1 Quasi-force-free configurations, an analog of which is a winding of a quasi-force-free magnet -- 7.1.1 One-dimensional quasi-force-free magnetic systems: the flat layer and cylinder -- 7.1.2 Two-dimensional force-free configurations satisfying the characteristic boundary conditions -- 7.1.3 Features of current distribution in the face zone of a force-free magnet -- 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.

7.2.1 Quasi-force-free winding with pairs of the equilibrium current layers (number of pairs N ≫ 1) -- 7.2.2 Multilayer magnetic systems with variable direction of current in each layer -- 7.3 Configurations of magnetic systems with equilibrium windings with zero thickness -- 7.3.1 One-modular configurations -- 7.3.2 Multimodular systems -- 7.4 Thin-wall quasi-force-free magnets with current removals -- 7.4.1 Systems with equally-loaded internal reinforcements -- 7.5 Comparative estimates of the residual stresses and sizes of magnets with a quasi-force-free winding and loaded outer zone -- 7.6 Design methods of quasi-force-free magnets -- 7.7 References -- 8 Generation of strong pulsed magnetic fields in single-turn magnets. Magnetic systems for the formation of pulsed loads -- 8.1 Mechanical stresses in a single-turn magnet operating under the condition of a sharply pronounced skin effect -- 8.2 Assessing the strength of single-turn magnets at short pulses -- 8.3 Thermoelastic stresses in single-turn magnets -- 8.4 The destruction of single-turn magnets. The problem of erosion -- 8.5 Special construction features of single-turn magnets and their power supplies -- 8.6 Deformed single-turn magnets restored after the discharge -- 8.7 Magnetic systems used for deformation of solids and the study of their properties -- 8.8 Magnetic systems for the acceleration of conductors -- 8.9 References -- 9 Generation of ultrahigh magnetic fields in destructive single-turn magnets -- 9.1 Physical processes accompanying the generation of megagauss magnetic field in single-turn magnets -- 9.2 Modeling problems illustrating the role of different factors leading to the destruction of single-turn magnets.

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 -- 9.4 Electrical explosion of turns of small thickness. Evaluation of the induction achieved in the destruction of turns with small initial dimensions -- 9.5 One-dimensional hydrodynamic flow in the wall of a single-turn magnet. Shock wave in conductors initiated by superstrong magnetic fields -- 9.6 General information on the electric explosion of conductors -- 9.7 Electric explosion of the skin layer in superhigh magnetic fields. Ideal model -- 9.8 The actual processes developing for "slow" and "fast" electric explosions of a conductor surface skin layer in a superhigh magnetic field -- 9.9 Computer simulation of a skin layer explosion -- 9.10 References -- 10 Magnetic cumulation -- 10.1 Initial idea. Brief history. Main trends in development and research -- 10.2 MC energy generators -- 10.3 Physical processes in magnetic cumulation. Analytical estimates for the MC-1 system -- 10.3.1 Induction amplitude and the radius of turnaround for flux compression by an ideal cylindrical shell -- 10.3.2 Estimation of the pulse duration of a magnetic field in magnetic cumulation -- 10.3.3 The effect of field diffusion on the induction amplitude with magnetic cumulation -- 10.3.4 Restrictions on the induction amplitude conditioned by the compressibility of a medium -- 10.3.5 Violation of the stability of a liner at flux compression -- 10.4 Flux compression systems not using the explosion energy for liner acceleration -- 10.4.1 MDC systems with azimuth current in a liner -- 10.4.2 Magnetodynamic cumulation in a Z-Θ pinch system -- 10.5 Analytical estimations and simulation of magnetodynamic cumulation.

10.6 Explosion devices and solenoids of an initial field used in magnetic cumulation.