Numerical Calculation of Coupling Impedances in Kicker Modules for Non-Relativistic Particle Beams

Open boundary conditions. Since the source current, Eq. 1, extends from z = −∞ to +∞ whereas our computational domain is finite, one has to apply suitable boundary conditions (see also [2]). Consider some accelerator component, residing in a vacuum cavity with attached beam pipe of smaller cross section than the cavity. Generally, the transitions from the pipe to the module have to be included into the computation, since steps of pipe cross sections contribute to the coupling impedance. For frequencies below beam-pipe cutoff, the fields excited within the cavity decay exponentially along the beam pipe. Thus, at some distance along the beam pipe, the perturbation resulting from the cavity can be neglected and fields can be considered stationary in the sense that (E,B)pipe ∝ exp(−ikz). Using this property, one can set up boundary conditions for the full 3D problem by solving for (E,B)pipe in a 2D cross section of the beam pipe.