Low Frequency Impedance of Tapered Transitions with Arbitrary Cross Sections
We study the impedance of a tapered transition at small frequencies for an arbitrary shape of the transition cross section. Our approach does not require a symmetry axis in the system (unlike round geometry). We show that the calculation of the impedance reduces to finding a few auxiliary potential functions that satisfy two-dimensional Poisson equations with Dirichlet boundary conditions. In simple cases such solutions can be obtained analytically; for more complicated geometries they can easily be found numerically. We apply our method to axisymmetric geometry and reproduce results known from the literature. We then calculate the impedance of a taper with rectangular cross section in which the vertical dimension of the cross section is a slowly changing function of the longitudinal coordinate. Finally, we find a transverse kick experienced by a beam passing near a conducting wall with a variable distance from the beam to the wall.
- Research Organization:
- Stanford Linear Accelerator Center (SLAC)
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- AC02-76SF00515
- OSTI ID:
- 910291
- Report Number(s):
- SLAC-PUB-12648
- Journal Information:
- Physical Review Special Topics - Accelerators and Beams, Journal Name: Physical Review Special Topics - Accelerators and Beams; ISSN 1098-4402
- Country of Publication:
- United States
- Language:
- English
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