Gennady Stupakov 2006 New J. Phys. 8 280 doi:10.1088/1367-2630/8/11/280
Using the parabolic equation for calculation of beam impedance
Focus on Accelerator and Beam PhysicsGennady Stupakov
Show affiliationsPart of Focus on Accelerator and Beam Physics
In this paper we develop a new method, using the parabolic equation (PE), for the calculation of both high-frequency and small-angle taper (or collimator) impedances. The applicability of the PE in the high-frequency limit is based on the observation that in this case the contribution to impedance comes from the electromagnetic 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 the PE is that it eliminates the spatial scale of the small wavelength from the problem. As a result, the numerical solution of the PE requires coarser spatial meshes. In this paper we focus on the longitudinal impedance for an axisymmetric geometry and assume a perfect conductivity of the walls. We show how the known analytical results which include a small-angle collimator, step-in and step-out transitions, and a pillbox cavity, can be derived within the framework of the PE.
- PACS
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29.27.Bd Beam dynamics; collective effects and instabilities
- Subjects
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Accelerators, beams and electromagnetism
- Dates
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Issue 11 (November 2006)
Received 10 April 2006
Published 28 November 2006
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Using the parabolic equation for calculation of beam impedance
Gennady Stupakov 2006 New J. Phys. 8 280
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