Next nearest neighbor coupling in side-coupled linacs based on analytical expressions

This manuscript corrects and supplements results of a previous paper which first appeared at the 1999 Particle Accelerator Conference. Since then, substantial data have been gathered in the design of the Accelerator Production of Tritium Linac and corrections have been made to the original formula. In order to design any accelerator one should know three values related to the coupling slots: Δf, k, and kk. The Δf determines the no-slot cavity frequency, i.e., the cavity frequency will drop with the introduction of coupling slots. The value of k represents the coupling between an on-axis (accelerating) cavity and its adjoining coupling cavity. The value of kk represents the next nearest neighbor coupling, between two on-axis cavities that are separated by an intervening coupling cavity. Recent work at Los Alamos National Laboratory has employed a perturbation technique developed by Gao. Accurate values of k are obtained from analytical expressions. It is the purpose of this paper to extend this type of analysis to include kk in a side-coupled linac. The approach will be to calculate the dipole induced in the slot by the field in the accelerating cavities, calculate an interaction energy between the two dipoles, and finally employ the Slater perturbation technique. The calculated value of kk is typically a little less than 1%, which will be verified with the measured data.