Abstract
This paper deals with the determination of the wake-function, impedance and energy loss due to surrounding accelerator components of two countermoving beams, i.e., two beams moving in opposite directions. Differently from the classical case, the distance between source and test charges cannot be considered constant. The paper defines a generalized wake-function, independent of the source and test particle's direction of motion. From this generalized wake-function a wake-potential is derived. The paper focuses in particular on the longitudinal direction. The expression of the energy dissipated by two beams transiting in the same vacuum chamber is obtained. This expression is valid both in the comoving and countermoving beam scenario. Subsequently, the proposed model is benchmarked by calculating the longitudinal co and countermoving wake-functions, the corresponding impedances and wake-potentials for two simple geometries (a circular pipe and a pillbox cavity) traversed by two countermoving beams, and by comparing the results with the ones of the electromagnetic code CST Studio Suite. Finally, for the pillbox geometry, the energy loss of the two countermoving beams and their rf-heating are investigated.
Highlights
The particles of a beam traversing a vacuum chamber interact electromagnetically with it generating the so-called wakefields
This paper deals with the determination of the wake-function, impedance and energy loss due to surrounding accelerator components of two countermoving beams, i.e., two beams moving in opposite directions
This is done for two example geometries: a resistive wall pipe and a pillbox cavity
Summary
The particles of a beam traversing a vacuum chamber interact electromagnetically with it generating the so-called wakefields. These wakefields dissipate heat on the vacuum chamber materials (rf-heating) and act back on the beam particles potentially triggering instabilities. In the case of a single beam traversing the vacuum chamber all the particles move in the same direction. Using the nomenclature proposed by Wang [1], this paper names this scenario comoving wakefield or wakefield (in Fig. 1(a) two comoving particles are reported, most of the quantities used in the paper are presented).
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