A method for calculating the effective charge of ions decelerated in a hot dense plasma
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A Method for Calculating the Effective Charge of Ions Decelerated in a Hot Dense Plasma S. Yu. Gus’kova, N. V. Zmitrenkob, D. V. Il’inc, A. A. Levkovskiic†, V. B. Rozanova, and V. E. Shermanc aLebedev
b
Physical Institute, Russian Academy of Sciences, Leninskiі pr. 53, Moscow, 119991 Russia Institute for Mathematical Modeling, Russian Academy of Sciences, Miusskaya pl. 4a, Moscow, 125047 Russia cSt. Petersburg Machinery Institute, Polyustrovskiі pr. 14, St. Petersburg, 195197 Russia Received February 3, 2009
Abstract—A method for calculating the effective charge of fast ions decelerated in a hot dense plasma is pro posed. The method is based on the known experimental dependence of the effective charge of an ion decel erated in cold matter on its velocity. The ion velocity in this dependence is replaced with the velocity of an ion relative to plasma electrons, averaged over the Fermi−Dirac distribution. Using results of numerical calcula tions performed in a wide range of plasma parameters (from a Maxwellian plasma to a fully degenerate one), a scaleinvariant representation of the effective charge of a decelerating ion as a function of its initial velocity and the plasma temperature and density is obtained. An analytical formula fitting the calculated results to within 5% is derived. The obtained dependences of the effective charge are incorporated in the model describ ing deceleration of fast ions in plasma. Using this model, the stopping powers of krypton and lead ions in a relatively cold rarefied gasdischarge plasma and hot ICF plasma are calculated. The results of calculations are shown to agree satisfactorily with available experimental data. PACS numbers: 52.40.Mj, 52.57.Kk DOI: 10.1134/S1063780X09090013 †
1. INTRODUCTION
the relationship between the plasma density and tem perature.
Progress in heavy ion fusion research and the development of methods for fast ignition of ICF tar gets by means of short pulses of highenergy ions stim ulate interest in the problem of deceleration of fast multicharged ions in plasma (see, e.g., [1, 2]). Unlike protons, multicharged ions possess a rather compli cated structure. Being decelerated to velocities com parable with the velocities of electrons in their electron shells, they capture electrons from the ambient matter. As a result, for a given ion velocity u, an equilibrium effective charge Zeff(u) is established, which deter mines deceleration of ions in plasma. In contrast to deceleration of ions in cold matter, the effective charge of ions decelerated in a hot dense ICF plasma may depend significantly on the plasma state, because the velocities of plasma electrons may be comparable with both the ion velocity and the velocities of electrons in their shells. Mathematical modeling of the dynamics of ICF targets under these conditions is a rather difficult task, because, in the course of beam−target interaction, the plasma state varies in a wide range, from a relatively cold, fully degenerate plasma to a hot plasma, in which the degree of degeneracy of
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