Generalized impedances and wakes in asymmetric structures

Technical Report · Thu Jan 01 04:00:00 EST 1998

DOI:https://doi.org/10.2172/663316· OSTI ID:663316

Heifets, S; Wagner, A; Zotter, B

In rotationally structures, the dominant m = 0 longitudinal impedance does not depend on the offsets of either the leading or the trailing particles, while the dominant m = 1 transverse impedance is proportional to the offset of the leading particles, while it is still independent of the offsets of the trailing ones. This behavior is no longer true in rotationally non-symmetric structures, where in general all impedances depend on the offsets of both the leading and the trailing particles. The same behavior is shown by wake functions and wake potentials. The concept of generalized impedances or generalized wake functions must be used to calculate the effect of leading particles on trailing ones with different offsets, each described by two transverse coordinates. This dependence of wake potentials on four additional parameters (two for each offset) would make their use very cumbersome. Fortunately, it was found that the transverse wake potentials can be separated into superpositions of dipolar components, which are proportional to the offset of the leading bunch, and quadrupolar components, which are proportional to the offset of the trailing particles. Higher multipole components are much smaller, and can be neglected for most structures without rotational symmetry. In this report, the authors derive analytical expressions for these multipolar components, which permits estimates of the size of the neglected terms. In particular, when structures have one or two transverse symmetry planes, the expressions simplify and explain the behavior of wake potentials which had been computed for rotationally non-symmetric structures.

• Research Organization: Stanford Univ., Stanford Linear Accelerator Center, CA (US)
• Sponsoring Organization: USDOE Office of Energy Research, Washington, DC (US)
• DOE Contract Number: AC03-76SF00515
• OSTI ID: 663316
• Report Number(s): SLAC/AP--110; ON: DE98059089
• Country of Publication: United States
• Language: English

Related Subjects

43 PARTICLE ACCELERATORS
ASYMMETRY
IMPEDANCE
LEADING PARTICLES
MULTIPOLES
SYMMETRY