Transformation of time-of-flight spectra into energy spectra for extended targets

Abstract

If in a time-of-flight (TOF) experiment the target extends over a large part of the flight path, two identical energy loss processes at different positions contribute differently to the projectile's TOF. So, the energy spectrum cannot be obtained directly from the measured TOF spectrum. For keV-ions in gas targets we have solved the corresponding transport equation numerically. We show that the TOF variance at the end of the flight path is a sum of energy loss straggling and what might be called “position straggling”. To a good approximation, the TOF to energy transformation can be based upon the continuous slowing down approximation (CSDA), if only the first moment of both distributions is considered. In the CSDA, energy loss is assumed to be distributed continuously, so energy loss straggling is zero and projectile velocity gets a unique function of penetrated path length.