Ionization by Fission Fragments Escaping from a Source Medium

The space-dependent ion production rate by fission fragments escaping from a fuel plate is studied using: 1) the Bohr stopping equation with the Thomas-Fermi approximation of the effective charge Z_eff; 2) the Alexander-Gazdik (A-G) semiempirical velocity-distance relationship for fission fragments. The assumptions are: a) no scattering during slowing down; b) the nonionizing energy loss in nuclear recoils can be taken into account by increasing the w value for fission fragments over that for α particles; c) a delta-function mass distribution for the light and heavy group; and d) a monoenergetic source. The energy current carried by the fragments at a point in the outer medium is first derived, and the energy deposition per unit volume per second is obtained by taking the gradient of the energy current. Dividing the energy deposition by the w value for the medium yields the ion production rate by fission fragments in that medium. The results show that the semiempirical velocity-distance relationship gives a higher ion production rate than that given by the velocity-distance relationship derived from the Bohr stopping equation with the Thomas-Fermi approximation of the effective charge Z_eff. The volumetric, spatial average ion production rate is also obtained. For a fuel plate containing 20% ²³⁵U and 80% Pt and for a flux of 6 × 10¹⁰ n/(cm² sec), the velocity-distance relationship based on the Bohr stopping equation gives an average ion production rate of 2.0 × 10¹³ ion pairs/(cm³ sec) in a mixture Ne + 0.1% Ag. Using the same values for the fragment ranges, the semiempirical velocity-distance relationship yields an average volumetric ion production rate in neon higher by about 18% for the light fragment and by about 20% for the heavy fragment. According to existing experimental results on plasmas induced by fission fragments, an ion source of 2.0 × 10¹³ ion pairs/(cm³ sec) would yield a conductivity of about 1 × 10⁻³ (Ωm)⁻¹ in the gas mixture Ne + 0.1% Ag, at 200-mm Hg and 400 °K and at an electric field of 560V/m.