Effective charge and collision logarithm for slow ions in fusion plasmas

Abstract

We find a general expression for the effective charge ${Z}_{\mathrm{eff}}$ of slow ions in dilute plasmas at temperature $T$, which applies for atomic numbers $5<~{Z}_{1}<~92$. The ratio $\frac{{Z}_{\mathrm{eff}}}{{Z}_{1}}$ becomes a function of $\frac{T}{{Z}_{1}^{2}}$. The effective-charge dependence of the collision logarithm for slow ions in the plasma is analyzed. A transition from classical to quantum regimes occurs with increasing $T$, for $\frac{T}{{Z}_{1}^{2}}\ensuremath{\approx}{10}^{6}$ K. The effective ion charge is relevant in the classical domain. For temperatures across and over the transition the ions are fully stripped of electrons.