Comment on wake field computation in time domain

Abstract

A bunch of charged particles passing an accelerating cavity -or any other structure of varying shape-excites electromagnetic fields that act back on the particles. These wake fields are functions of space and time coordinates. The net change in momentum due to such fields is obtained by an integration over all times during that the fields interact with the particles, i.e. normally from t = *-oo to t -+ oo > For ultrarelativistic particles passing structures of cylindrical symmetry this infinte range for the inte gration -which is very inconvinient for all practical computations-can be replaced by a finite range over the section where the scattered fields originate from.

Beam Instabilities in Hadron Synchrotrons

“…For rotationally symmetric structures, it is sufficient to integrate the wake at an arbitrary radial coordinate, as the radial dependence is known a priori. This radial coordinate can be chosen right at the perfectly conducting beam pipe surface, reducing the integration to the cavity gap length [75]. In rotational symmetric structures it is also possible to choose a curved contour, the Napoly integral [76,77].…”

Origin and reduction of wakefields in photonic crystal accelerator cavities

“…where X m ðsÞ and Y m ðsÞ become the quantities of interest, independent of transverse coordinates [30,33]. The value of ϕ 0 has been set to zero in the above since only the difference in azimuth (ϕ − ϕ 0 ) appears in the above expressions.…”

Time domain wake field computation with boundary element method

“…Thus, for this case it is not necessary to calculate the fields inside the structure. On the other hand, we can also use an indirect integration path across the region inside the structure, e.g., a straight path over a gap of the structure along the beam tubes [21], as shown in Fig. 8.…”