Analytic method for determining the parameters of the fission chain reaction for a cylindrical uranium bar and estimates of the energy release for hybrid targets in heavy-ion fusion

Abstract

Under conditions of heavy-ion fusion (HIF), there arises the possibility of obtaining a fission chain reaction for a HIF cylindrical target (Koshkarev, Sharkov, 2002). The Akhiezer-Pomeranchuk method (1952), which was developed for spherically symmetric configurations of fissile matter, is generalized here. This method does not reduce to the simple diffuse approximation, which is inapplicable, in particular, to the case of ²³⁵U. For a uranium bar, an analytic solution to the Peierls integral equation is obtained in the kinetic limit, which is opposite to the diffusion limit. This solution is interpolated to that in the diffusion approximation in order to derive a general approximate formula both for the critical radius of the bar and for the exponent characterizing the chain reaction in the supercritical state. The resulting critical parameters, generalized to the case of a uranium envelope, are applied to evaluate roughly the energy release in HIF hybrid targets (in hydrodynamic processes of fission and fusion) within the quasistationary approximation for the Peierls equation. A simple approximate description is given for the contribution to the energy release from nuclear reactions accompanying uranium fission induced by thermonuclear neutrons, this description being of particular importance if the conditions of the chain reaction are not satisfied.