Beam Dynamics in Proton Linear Accelerators

The uncoupled equations of motion of charged particles in the longitudinal and transverse directions in a linear accelerator in the absence of space charge forces are reviewed. The effect of coupling on the dynamics is introduced and results are obtained for the apparent increase of the projected phase space areas. Questions of non-linearities and fringing field couplings are discussed. In the presence of space charge forces, oscillation frequencies are decreased, admittances are changed, and additional couplings and non-linearities are introduced. These cause further deterioration in beam quality. An effort has been made to identify those particular effects which play the major role in increasing phase space areas. Comparisons are made with detailed three dimensional orbit computations in an effort to sort out the various effects.