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Cockcroft Colloquium
Calculation of beam impedance for long tapers
and short bunches
Gennady StupakovStanford Linear Accelerator
Center Cockcroft Institute Seminar Room,
1030am, Monday 3rd July 2006
We develop a new method of parabolic equation
(PE) for calculation of both high-frequency
and/or small-angle taper (or collimator)
impedances. The applicability of PE in the
high-frequency limit is based on the observation
that in this case the contribution to impedance
comes from the waves that catch up with the beam
far from the obstacle and propagate at
small-angles to the axis of the pipe. One of the
most important advantages of PE is that it
eliminates the spatial scale of the small
wavelength from the problem. As a result, a
numerical solution of PE can be found with a much
coarser spatial mesh.