J. Phys. IV France
Volume 133, June 2006
Page(s) 329 - 334
Publié en ligne 16 juin 2006
Inertial Fusion Sciences and Applications 2005
J.-C. Gauthier, et al.
J. Phys. IV France 133 (2006) 329-334

DOI: 10.1051/jp4:2006133066

Self-similar plasma expansion of a limited mass into vacuum

M. 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 ${\rm\Lambda} =$ R/ ${\lambda}_{\rm D}$ of the plasma scale length R to the Debye length ${\lambda}_{\rm D}$ is invariant, i.e. under the condition T$_{\rm e}$ $ \propto $ [ n$_{\rm e}$(t)] $^{1 - 2 /\nu}$, where ${\rm\nu} = 1$, 2, and 3 corresponds, respectively, to the planar, cylindrical, and spherical geometries. For ${\rm\Lambda} \gg 1$ the position of the ion front and the maximum energy E $_{\rm i,max }$ of accelerated ions are calculated analytically: in particular, for ${\rm\nu} =3$ one finds E $_{\rm i,max}=$ 2ZT$_{\rm e0}$W( ${\rm\Lambda}
^{2}$/2), where T$_{\rm e0}$ 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 $_{\rm i,max }$ can be applied more generally than the self-similar solution itself.

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