Next nearest coupling from analytical expressions for the APT linac

In order to design any accelerator one should know three constants, 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. Constant k determines the coupling between on-axis cavity to cavity. Constant kk determines the next nearest coupling from on-axis cavity to cavity. In a Coupled Cavity Drift Tube Linac the quantity kk is minuscule. However in a Coupled Cavity Linac because of the close proximity of the coupling cavity slots the qantity kk or next nearest becomes significant. Recent work at Los Alamos National Laboratory has employed a perturbation technique by J. Gao (1992). Good values of k are obtained from analytical expressions. With less success the quantity Δf can be calculated. It is the purpose of this paper to extend this type of analysis to include kk in a CCL. The approach is to calculate the dipole induced in the slot by the field in the accelerating cavities. Next calculate an interaction energy between the two dipoles and finally employ Slater perturbation. The calculated value of kk is approximately 0.002, a reasonable number compared to experimental data from the LAMPF accelerator at LANL