The conditions for validity and the limitations of experiments intended to simulate astrophysical hydrodynamics are discussed, with application to some ongoing experiments. For systems adequately described by the Euler equations, similarity criteria required for properly scaled experiments are identiÐed. The conditions for the applicability of the Euler equations are formulated, based on the analysis of localization, heat conduction, viscosity, and radiation. Other considerations involved in such a scaling, including its limitations at small spatial scales, are discussed. The results are applied to experiments aimed at simulating three-dimensional hydrodynamics during supernova explosions and hydrodynamic instabilities in young supernova remnants. In addition, hydrodynamic situations with signiÐcant radiative e †ects are discussed.

The quotation is from the summary lecture presented by Lev Artsimovich at the 1961 IAEA Conference in Salzburg. Here then is our continuing Report from Purgatory, Issue number 7, Chapter 1, Magnetic Confinement Experiments.

When one deals with a plasma column whose radius a is much smaller than its length L, one can think of it as of a thin filament whose kink instability can be adequately described simply by a 2D displacement vector, ξ x =ξ x (z,t); ξ y =ξ y (z,t). Details of the internal structure of the column such as the current, density, and axial flow velocity distribution would be lumped into some phenomenological parameters. This approach is particularly efficient in the problems with non-ideal (sheath) boundary conditions (BC) at the end electrodes, with the finite plasma resistivity, and with a substantial axial flow. With the sheath BC imposed at one of the end-plates, we find instability in the domain well below the classical Kruskal-Shafranov limit. The presence of an axial flow causes the onset of rotation of the kink and strong axial "skewness" of the eigenfunction, with the perturbation amplitude increasing in the flow direction. We consider the limitations of the phenomenological approach and find that they are related to the steepness with which the plasma resistivity increases at the plasma boundary with vacuum.

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The currently accepted value for the upper bound for the photon mass m ph is 22 orders of magnitude less than the electron mass. As the mass m ph is so incredibly small, it has essentially no effect on the atomic and nuclear physics, and it is very difficult to improve this estimate by laboratory experiments. However, even a very small mass may have significant effect on astrophysical phenomena occurring at the scale exceeding the photon Compton length ! D (where ! D~ 3 million kilometers for the currently accepted mass). Based on the set of MHD equations (written with the account for the finite photon mass), the author analyzes properties of the Solar wind at the Pluto orbit and comes up with an improved (reduced) by a factor of 70 estimate of the photon mass. Possible opportunities and challenges for the further reduction of the upper limit for m ph based on the properties of larger-scale astrophysical objects, are discussed.