The Effect of High Spatial Harmonics in RF Linac

The effect of high spatial harmonics on beam dynamics in a axisymmetric radio frequency linear accelerator (RF linac) is examined. The high spatial harmonics forms the second order ponderomotive focusing for the relativistical particle beam when the transverse motion is averaged over the period of RF structure, the beam transverse envelop equation is obtained including the ponderomotive focusing force which is useful for the design of RF gun and linac. Under a certain of high spatial harmonics coefficients, the high spatial harmonics increase the energy spread due to the stochasitical beam energy diffusion.