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

Abstract

a b s t r a c tBoth 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 lg/cm 2 and this remained unchanged until a maximum target thickness of 98 lg/cm 2 . 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 C 2+ , C 3+ , and C 4+ incident ions merged into quasi-equilibrium values at a target thickness of 5.7 lg/cm 2 in the pre-equilibrium region and evolved simultaneously to the 'real equilibrium' values for all of the initial charge states, including C 5+ and C 6+ 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.

Disentangling the bulk and exit surface contribution on projectile-charge-state evolution

“…The CSDs are normally measured by the standard electromagnetic techniques [21][22][23][24] and in order to understand the measured equilibrium charge state data, many empirical formulas such as Thomas-Fermi model, Bohr model, Betz model, Nikolaev-Dmitriev model, To-Drouin model, Shima-Ishihara-Mikumo model, Itoh model, Ziegler-Biersack-Littmark model, Schiwietz model, etc., have been developed in tune with the experimental results from electromagnetic measurements [25 and references therein]. Interestingly, in some distinct cases, like, calculation of non-equilibrium charge state distribution [26,27], estimation of equilibrium target thickness [28], etc., the empirical predictions readily fail to estimate desired parameters. The contribution of the charge-changing processes in the bulk is further modified by the charge-exchange phenomena from the exit surface of the foil.…”

Neutralization Dynamics of Slow Highly Charged Ions in 2D Materials

“…While the charge transfer above a surface is well described by the classical-over-barrier (COB) model, the mechanisms at work inside the solid after ion impact, i.e., electron capture, deexcitation processes, and stopping, are still not fully understood. The challenge arises from the fact that ions travelling in a 3D solid will rapidly reach their equilibrium charge state, which is independent of the original charge state and just determined by the ion velocity, limiting the access to the pre-equilibrium regime of the interaction [11][12][13][14].…”