Abstract
The Napoly integral is the very useful method for calculations of wake potentials in structures where parts of the boundary extend below the beam pipe radius or the radii of the two beam pipes at both ends are unequal. It reduces CPU time a lot by deforming the integration path so that the integration contour is confined to the finite length over the gap of the structures. However, the original Napoly method cannot be applied to the transverse wake potentials in a structure where the two beam tubes on both sides have unequal radii . In this case, the integration path needed to be a straight line and the integration is stretched out to an infinite, in principle. We generalize the Napoly integrals so that integrals are always confined in a finite length even when the two beam tubes have unequal radii, for both longitudinal and transverse wake potential calculations. The extended method has been successfully implemented to the ABCI code.
Highlights
Calculation of wake potentials in accelerators is done mostly using simulation codes such as ABCI [1] which solve the Maxwell equations for given structures
Fig. 1) is defined in such a way that it consists of a straight line Lr and Napoly-Zotter contour C and the two radial lines connecting between them at z 1
A closed loop G is defined in such a way that it consists of a straight line Lr and Napoly-Zotter contour C and the two radial lines connecting between them at z 1
Summary
Calculation of wake potentials in accelerators is done mostly using simulation codes such as ABCI [1] which solve the Maxwell equations for given structures. For the monopole wake potential case, this method permits a structure with unequal beam pipe radii at both ends by adding the contribution from the source fields (this was already done by themselves, see Appendix A), because the contribution of the radiated fields from z 1 is still zero in this monopole mode. This method is very useful for the numerical calculations, where the electromagnetic (EM) fields satisfying all the boundary conditions are known.
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