Calculation of ion transport beam lines with stepwise change in beam parameters

Diaphragms or slits (to limit the size of the ion beam) and degraders (to reduce the kinetic energy of ions) are often used in beam lines for ion transport. When an ion beam travels through these elements, parameters such as rms sizes, angle, and momentum spread change abruptly. This fact should be taken into account in calculating the subsequent sections of the beam line. Formulas are derived for determining new parameters of the ion beam immediately after its passage through those elements. The results of calculations are given regarding the transport of different kinds of heavy ions in the beam lines of the U400M cyclotron of the Joint Institute for Nuclear Research (JINR) Flerov Laboratory of Nuclear Reactions intended for testing electronic microchips.