Charge evolution of swift-heavy-ion beams explored by matrix method

The approach to charge equilibrium of a beam of swift ions can be expressed by a matrix with rows and columns expressing the initial and instantaneous charge state, respectively. We have explored the capability of this matrix formalism in comparison with the standard method, i.e., numerical solution of linear rate equations as implemented in the ETACHA code. The matrix method is computationally more efficient, and the acceptable numerical error can be pre-defined. The agreement with predictions based on ETACHA is generally good. Significant discrepancies are primarily due to differences in the applied cross sections for electron capture and loss. Comparisons have been made also with experimental results for sulphur in carbon.