10.23732/CYRCP-2018-001.11
Berrig, O. E.
Paciolla, F.
New Longitudinal Beam Impedance Formula with 8 Terms
CERN
2018
Beam coupling impedance; new formula; 8 terms; Lorentz; reciprocity; principle; multipolar; decomposition; second order.
2018-04-26
2018-04-26
2018-11-07
2018-11-08
en
Article
11-58-738
10.23732/CYRCP-2018-001
11 Pages
This work is licensed under a Creative Commons Attribution 4.0 International License.
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.
CERN Yellow Reports: Conference Proceedings, Vol 1 (2018): Proceedings of the ICFA Mini-Workshop "Impedances and Beam Instabilities in Particle Accelerators"