Applications of cavity transverse modes in accelerators

Abstract

Different applications of TE modes in accelerator physics are discussed. In this discussion, the Fourier transform of the squared axial component of magnetic field, B z 2 z, plays an important role. If it turns out to be zero, the rf field-particle energy transfer is negligible and the focal length of the TE mode lens is phase independent. Such rf lens focuses continuous beams just as a solenoid. In order to compensate spherical aberrations and emittance growth caused by field nonlinearities of a focusing solenoid, the rf focusing is used also even if the beam space charge is taken into account. If the transform has its maximum, excitations of TE mode resonances and electron beam self-focusing are possible. Furthermore, the rf field of the TE mode can be used to expand the radial acceptance of a FEL for the THz region.

Beam breakup instability suppression in multicell superconducting rf guns

“…[11]). Because the dipole HOM frequencies are large, the BBU instability is affected, and hence, the voltages calculated with Eq.…”

“…[10]). We recall that the focusing effect distribution along the axis depends on the field amplitude distribution B TE ðzÞ 2 [11]. In such a scenario, the trajectories depicted in Fig.…”

“…One of them isolates the fundamental rf power mode from the HOM load while the second isolates the TE focusing mode (see Figs. [10][11][12]. The field of the TE mode is axiasymmetric due to the TE couplers, and a dipolelike component of the field appears [13].…”

Prediction and suppression of beam breakup instability in multicell superconducting cavities

“…The only difference is that the rf lens has a small variable component of the focusing force with the double the frequency (2! TE ), whose amplitude decreases exponentially with TE-mode frequency [15,17]. If we take a TE mode with sufficiently high frequency, this variable part of the focusing force may be neglected.…”

“…In order to take into account the influence of the focusing force of the magnetic mode, it is sufficient to add to Eq. (4) the term of TE focusing mode force [17] in the form of À½eB TE ðzÞ=2m 2 y, where only the constant component is taken into account. New differential equation for trajectories Y 1 ðzÞ and Y 2 ðzÞ will differ from the previous equation (13) only by a larger coefficient at YðzÞ or by larger ''betatron'' frequency:…”