The use of flows with uniform velocity gradient in modelling free expansion of a polytropic gas

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Abstract
The free expansion of a heated mass of uniform gas (e.g. a laser produced plasma) can be modelled by self-similar motion with a linear velocity gradient. Using a series of numerical solutions we have shown that a reasonable representation is obtained by the use of a matching parameter relating the scale lengths in the prototype and its model, and that the representation improves as the ratio of the heating and disassembly times increases. In this paper we re-examine these two inferred results, and re-derive them on an analytic basis. The extension of the theory to multi-structured bodies shows that such systems of symmetric form allow self-similar motion, as does the particular case of an asymmetric one-dimensional foil. The case of isothermal foils is examined in detail to illustrate the derivation of the matching conditions.