12,000

We have over 12,000 students, from over 100 countries, within one of the safest campuses in the UK

93%

93% of Lancaster students go into work or further study within six months of graduating

Home > Research > Publications & Outputs > Electromagnetic fields produced by moving sourc...
View graph of relations

« Back

Electromagnetic fields produced by moving sources in a curved beam pipe

Research output: Contribution to journalJournal article

Published

???articleNumber???063510
Journal publication date2009
JournalJournal of Mathematical Physics
Journal number1
Volume50
Number of pages45
Original languageEnglish

Abstract

A new geometrical perturbation scheme is developed in order to calculate the electromagnetic fields produced by charged sources in prescribed motion moving in a nonstraight perfectly conducting beam pipe. The pipe is regarded as a perturbed infinitely long hollow right-circular cylinder. The perturbation maintains the pipe’s circular cross section while deforming its axis into a planar space curve with, in general, nonconstant curvature. Various charged source models are considered including a charged bunch and an off-axis point particle. In the ultrarelativistic limit this permits a calculation of the longitudinal wake potential in terms of powers of the product of the pipe radius and the arbitrarily varying curvature of the axial space curve. Analytic expressions to leading order are presented for beam pipes with piecewise defined constant curvature modeling pipes with straight segments linked by circular arcs of finite length. The language of differential forms is used throughout, and to illustrate the power of this formalism, a pedagogical introduction is developed by deriving the theory ab initio from Maxwell’s equations expressed intrinsically as a differential system on (Minkowski) space-time.