Beam dynamics in transverse deflecting rf structures

Abstract

The beam dynamics in transverse deflecting structures, operating in streaking mode, is discussed concentrating on slightly nonrelativistic particle energies. Transverse offsets of the average trajectory, bunch lengthening, and defocusing as well as emittance growth due to nonlinearities of the cavity field are considered. The analysis of the deflecting field reveals the origin of nonlinearities and leads to proposals for their suppression. An optimized cavity design which combines minimal aberrations with a high rf efficiency is proposed.

Electron Pulses Made Faster Than Atomic Motions

“…In the simulation of the σ t;uv ¼ 100 fs case, the bunch reaches a longitudinal minimum of 5.0 fs at the center of the deflector when it is off. With the cavity on, the induced energy spread causes the bunch length to grow to 6.0 fs at the center of the cavity, corresponding to ∼3 fs added in quadrature, in agreement with analytical predictions [26]. The synthetic measurement produces σ t ¼ 6.7 fs, which is additionally inflated by both transverse field nonlinearities and rf-induced defocusing, and is in close agreement with the measurement in Fig 4. Note that any focusing imparted by the deflector can lead to a systematic error in the PSF of the measurement which is otherwise given by I off ðtÞ.…”

“…As a consequence of the Panofsky-Wenzel theorem [37], any deflecting structure will induce a nonzero energy spread for a finite vertical beam size in the cavity [26,38]. This induced energy spread can, in turn, induce bunch lengthening and defocusing, which will affect the measurement.…”

“…The resulting smaller emittance not only benefits the beam transverse quality, it also enables the production of shorter bunch lengths by reducing the timeof-flight differences of radially separated particles in bunching schemes [25], along with alleviating bunch length measurement-corrupting transverse effects in deflecting cavities [26], as discussed below.…”

Aberration corrected emittance exchange

“…Under a thin lens approximation the deflector cavity does not produce a transverse offset for the reference particle at zero crossing. However, due to the finite length of the cavity the reference particle would traverse the deflector cavity with a nonzero mean transverse momentum [17], resulting in a transverse offset. In order to mitigate this, each of the cavity end cells provides half the kick of a full cell.…”

“…Therefore, fluctuations should be held below the ratio of emittances which are exchanged as shown in Eq. (17).…”