New Longitudinal Beam Impedance Formula with 8 Terms
DOI:
https://doi.org/10.23732/CYRCP-2018-001.11Keywords:
Beam coupling impedance, new formula, 8 terms, Lorentz, reciprocity, principle, multipolar, decomposition, second order.Abstract
A previous formula for longitudinal beam impedance was developed by H. Tsutsui and consists of 13 terms. The formula by H. Tsutsui is developed up to terms of second order in the transverse offsets. In this report we develop a new formula, which use symmetries from the Lorentz reciprocity principle and the multipolar decomposition of transverse fields to reduce the number of terms from 13 to 8. This new formula is also developed up to second order, but could of course be developed up to any higher order. The transverse beam impedances (for horizontal and vertical planes) can be by obtained by differentiation of this new formula.
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Published
2018-11-07
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Section
Submission to the proc. of the ICFA Mini-Workshop Workshop "Impedances and Beam Instabilities in Particle Accelerators"
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