Scaling of Magneto-Quantum-Radiative Hydrodynamic Equations: From Laser-produced Plasmas to Astrophysics
The relevant equations of magneto-quantum-radiative hydrodynamics are introduced and then written in a dimensionless form in order to extract a set of dimensionless parameters that describe scale-dependent ratios of all the characteristic hydrodynamic variables. Under the conditions where such dimensionless number are all large, the equations reduce to the usual ideal magnetohydrodynamics and thus they are scale invariant. We discuss this property with regards to the similarity between astrophysical observations and laboratory experiments. These similarity properties have been successfully exploited in a variety of laboratory experiments where radiative processes can be neglected. On the other hand, when radiation is important, laboratory experiments are much more difficult to scale to the corresponding astrophysical objects. As an example, a recent experiment related to break out shocks in supernova explosions is discussed.