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Introduction. The method of magnetic-flux compression by shock waves of closed configuration converging to a certain axis and transforming the nonconducting material to a conducting state was independently proposed by the authors of this paper [1][2][3] and K. Nagayama et al. [4, 5]. The method differs from classical magnetic cumulation by the loss of a great portion of magnetic flux that is "trapped" into the conducting material formed behind the shock-wave front. This limits crucially the energy potentials of the method. However, despite the significant flux losses in the compression region, the compression of a magnetic field together with the material offers a number of advantages. These advantages are associated with current generation in a fresh conducting material and with the possibility of using the hydrodynamiccumulation effect to increase the mechanical-energy density and, hence, its related density of magnetic-field energy. Using the shock-wave method, megagauss magnetic fields were generated in low-cost generators of extremely simple design [6, 7]. The highest registered field was 3.5 MGs with a magnetic field amplification factor/3 = B/Be ,~ 90 [8].The general energy estimates of [6] for the simplest model of a material packed to a constant density have shown that the possibilities of the method depend fundamentally on the packing parameter of the material n = p/po. It was found that, in sufficiently rigid materials with packing n ~< 2, retardation of a magnetic field by a shock wave does not lead to a marked loss of energy by the wave, the magnetic energy in the compression region does not increase, and the case of complete closure of shock waves does not contradict the law of energy conservation. In this case, the magnetic energy remains finite, and the magnetic flux completely enters the conductor, while the magnetic-flux density tends theoretically to increase strongly with a limited initial energy of the system. The estimates presented in [6] show that when the material behind the shock-wave front is incompressible, the maximum magnetic field is determined by the conductance and geometrical dimensions of the generator, which enter into the expression for the limiting field in the combination corresponding to the magnetic Reynolds number Re,n, i.e., as in classical magnetic cumulation, the restriction of shock-wave compression possibilities by the finite electrical conductivity of the material appears to be of no principal importance: an increase in the dimensions of the system can ensure high values of Rein, and one can expect the corresponding increase in the generated magnetic field.Among the studied materials, the maximum fields and the highest amplification of the magnetic field were obtained in heterogeneous materials such as an aluminum powder with an initial density of the order of 0.1-0.2 of the monolithic density. Since shock compression of highly porous materials is accompanied by strong heating, one can expect that magnetic compression in these materials occurs with a significant l...