Magnetohydrodynamic scaling: From astrophysics to the laboratory

During the last few years, considerable progress has been made in simulating astrophysical phenomena in laboratory experiments with high-power lasers. Astrophysical phenomena that have drawn particular interest include supernovae explosions; young supernova remnants; galactic jets; the formation of fine structures in late supernovae remnants by instabilities; and the ablation-driven evolution of molecular clouds. A question may arise as to what extent the laser experiments, which deal with targets of a spatial scale of ∼100 μm and occur at a time scale of a few nanoseconds, can reproduce phenomena occurring at spatial scales of a million or more kilometers and time scales from hours to many years. Quite remarkably, in a number of cases there exists a broad hydrodynamic similarity (sometimes called the “Euler similarity”) that allows a direct scaling of laboratory results to astrophysical phenomena. A discussion is presented of the details of the Euler similarity related to the presence of shocks and to a special case of a strong drive. Constraints stemming from the possible development of small-scale turbulence are analyzed. The case of a gas with a spatially varying polytropic index is discussed. A possibility of scaled simulations of ablation front dynamics is one more topic covered in this paper. It is shown that, with some additional constraints, a simple similarity exists.