Equilibrium and non-equilibrium charge-state distributions of 2.0Â MeV/u carbon ions passing through carbon foils

Both equilibrium and non-equilibrium charge-state distributions were studied experimentally for 2.0 MeV/u carbon ions after passing through carbon foils. Measured charge-state distribution established the equilibrium at a target thickness of 10 μg/cm2 and this remained unchanged until a maximum target thickness of 98 μg/cm2. The equilibrium charge-state distribution, the equilibrium mean charge-state, and the width and skewness of the equilibrium distribution were compared with predictions using existing semi-empirical formulae as well as simulation results, including the ETACHA code. It was found that charge-state distributions, mean charge states, and distribution widths for C2+, C3+, and C4+ incident ions merged into quasi-equilibrium values at a target thickness of 5.7 μg/cm2 in the pre-equilibrium region and evolved simultaneously to the 'real equilibrium' values for all of the initial charge states, including C5+ and C6+ ions, as previously demonstrated for sulfur projectile ions at the same velocity (Imai et al., 2009). Two kinds of simulation, ETACHA and solution of rate equations taking only single electron transfers into account, were used, and both of them reproduced the measured charge evolution qualitatively. The quasi-equilibrium behavior could be reproduced with the ETACHA code, but not with solution of elementary rate equations.