J.-C. Gauthier, et al.
J. Phys. IV France 133 (2006) 329-334
Self-similar plasma expansion of a limited mass into vacuumM. Murakami and M.M. Basko
Institute of Laser Engineering, Suita, Osaka 565-0871, Japan
A new self-similar solution is presented which describes non-relativistic expansion of a finite plasma mass into vacuum with a full account of charge separation effects. The solution exists only when the ratio R/ of the plasma scale length R to the Debye length is invariant, i.e. under the condition T [ n(t)] , where , 2, and 3 corresponds, respectively, to the planar, cylindrical, and spherical geometries. For the position of the ion front and the maximum energy E of accelerated ions are calculated analytically: in particular, for one finds E 2ZTW( /2), where T is the initial electron temperature, Z is the ion charge, and W is the Lambert W-function. It is argued that, when properly formulated, the results for E can be applied more generally than the self-similar solution itself.
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