Criteria for scaled laboratory simulations of astrophysical MHD phenomena

We demonstrate that two systems described by the equations of the ideal mag netohydrodynamics (MHD) evolve similarly, if the initial conditions are geo metrically similar and certain scaling relations hold. The thermodynamic pr operties of the gas must be such that the internal energy density is propor tional to the pressure. The presence of the shocks is allowed. We discuss t he applicability conditions of the ideal MHD and demonstrate that they are satisfied with a large margin both in a number of astrophysical objects, an d in properly designed simulation experiments with high-power lasers. This allows one to perform laboratory experiments whose results can be used for quantitative interpretation of various effects of astrophysical MHD.