Effect of nonlinear radiofrequency electromagnetic fields on the emittance of bunched beams

Gap transformations are frequently used in ion Linac codes, to efficiently describe the particle dynamics. Using similar approach, we analyze the uniformly bunched beam passing through an axis-symmetric radiofrequency (RF) cavity. The method can be used for other distributions as well using a similar six dimensional analysis. The effect of non-linear RF field in radial and axial directions in an RF cavity and the finite phase width of the bunch, on the transverse and longitudinal emittance growth have been studied. The expressions obtained have been verified for the two types of cavity cells namely the zero mode DTL and pi mode CCL type used frequently in ion linacs. The results are seen to be valid for the entire maximum phase acceptance up to 360 degrees. Simulations with the equivalent beams of non-uniform distributions namely Waterbag and Gaussian show that at synchronous phases closer to the wave crest, the results give a good approximation of emittance growth in both planes for non-uniform beams