On the directional symmetry of the impedance
The independence of the impedance on the beam direction is an important feature of an accelerator structure, in particular, for the electron-positron storage rings where bunches of opposite charges travel through the same vacuum chamber in opposite directions. Recently Gluckstern and Zotter considered a cylindrically symmetric but longitudinally asymmetric cavity with side pipes of equal radii. They were able to prove that for a relativistic particle the longitudinal impedance of the cavity with an arbitrary shape is independent of the direction in which the beam travels through it. Their result corroborates numerical observations of the independence of the wakefield obtained with the code TBCI. Bisognano gave an elegant proof of the same statement. His approach is based on a reciprocity relation applied to the tensor Green's function. I follow here his idea in a somewhat simpler way to obtain more general and physically transparent proof of this property for both longitudinal and transverse impedances. The result is valid for a cavity with no azimuthal symmetry and for arbitrary particle velocity, as soon as it may be considered constant. At the same time the limits of its validity are shown.
- Research Organization:
- SLAC National Accelerator Lab., Menlo Park, CA (United States)
- Sponsoring Organization:
- DOE/ER
- DOE Contract Number:
- AC03-76SF00515; AC05-84ER40150
- OSTI ID:
- 6960992
- Report Number(s):
- SLAC/AP-79; ON: DE90010685; TRN: 90-026902
- Country of Publication:
- United States
- Language:
- English
Similar Records
Transverse mode coupling in a bunched beam
Stability of the higher order longitudinal modes for PEP