Energy straggling of heavy ions in thin foils

2014 The energy straggling of heavy ion beams at tandem energies, passing through thin foils, has been studied with ions of mass up to A = 35. Charge exchange in the foils has been found to have a considerable effect on the energy spread. Thickness non-uniformities in the foils can also make significant contributions. Extrapolation of the observations to the case of a uniform carbon stripper foil in a tandem accelerator suggests energy straggling of the order a few tenths per cent of the beam energy. However, large non-uniformities in the foil could appreciably worsen the beam resolution. REVUE DE PHYSIQUE APPLIQUÉE TOME 12, OCTOBRE 1977, PAGE This paper is concerned with some of the effects produced on heavy ion beams at Tandem energies on their passage through a thin solid foil. Because of the statistical nature of the collisions and charge-changing processes which take place inside the solid, an initially monoenergetic, parallel beam of ions emerges from a foil with a distribution in angular direction, a distribution of charges (except for very light ions which may be fully stripped) and a distribution in energy about a mean corresponding to the average energy lost in the foil. Experimental information on this energy straggling is sparse, sometimes contradictory and showing large discrepencies with established theory. We distinguish three distinct ways in which experimentally observed energy straggling may arise : 1. a FLUCTUATIONS IN COLLISIONAL EXCITATION OF TARGET ATOMS. For ions of a given velocity and constant charge Z (equal to the atomic number for a fully stripped ion), the average energy loss in a given thin foil of uniform thickness Ax is, according to basic theory : (*) Present address : Physics Department, University of Melbourne, Vic. Australia. and the standard deviation 6 of the energy distribution about the average value is given by : where K and K’ are constants in the given conditions. For partially stripped ions with a charge-state distribution F (q) in the solid, the ions on average have a charge q for a total distance F (q) Ax in the foil, so that their energy loss in this mode is with corresponding (a2),. Summing over q, the total energy loss and straggling are then predicted to be as in equation (1) and (2) above with Z2 = q2, the mean square charge, or effective charge squared, in the solid. 1. b CHARGE-EXCHANGE STRAGGLING. The calculation above assumes that all the ions behave the same as regards the time they spend in their respective charge states in the foil. In fact, as Vollmer [1 ] has pointed out, there are fluctuations in these times, since the charge-exchange is also a statistical process. For example, following an individual ion which enters the foil with a charge state q, its passage through the foil might be as indicated in figure 1. For another ion the distribution amongst the various charge states would Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/rphysap:0197700120100153900