Eur. Phys. J. C 27, 609-621 (2003)
DOI: 10.1140/epjc/s2002-01126-x

On the coupling impedance for particles with opposite velocities

D. Davino¹, G. Dôme² and L. Verolino<sup>3

1</sup>  Università degli Studi del Sannio, Dipartimento di Ingegneria, Piazza Roma, 82100 Benevento, Italy
²  Retired from CERN, 1211 Geneva 23, Switzerland
³  Università Federico II di Napoli, Dipartimento di Ingegneria Elettrica, via Claudio 21, 80125 Napoli, Italy

(Received: 27 March 2002 / Revised version: 5 December 2002 / Published online: 26 February 2003 )

Abstract
As already shown by several authors, the reciprocity theorem can be rewritten as a simple formula connecting the longitudinal coupling impedances of a particle travelling in the positive and negative directions of an infinitely long vacuum chamber crossing a scattering structure (cavity, step junction, iris, etc.) of general shape. The formula is valid for any particle velocity. As an example, we consider the case of two semi-infinite circular vacuum chambers with different radii; for this case we give the explicit difference between the coupling impedances and the wake potentials.

© Società Italiana di Fisica, Springer-Verlag 2003