Correction of beam-steering effects in low-velocity superconducting quarter-wave cavities

Abstract

Superconducting cavities presently used for acceleration of ions in velocity range ϳ0.01c to 0.3c (where c is the speed of light) are based on quarter-wave resonators. Currently there are several design proposals in nuclear physics laboratories for application of this type of cavity for acceleration of light and heavy ions. The operating frequencies of the cavities range from ϳ50 to 360 MHz to satisfy various specifications. Electrodynamics studies of the field distributions in the beam-cavity interaction area indicate appreciable dipole components of both electric and magnetic fields, especially for higher-frequency cavities. The dipole fields induce beam steering, which is a strong function of rf phase and which couples the longitudinal and transverse motion. This can result in growth in the transverse emittance of the beam. In this paper, we propose two possible methods for the correction of such dynamic beam-steering effects in quarter-wave resonators. We analyze and discuss the correction methods for the particular examples of two quarter-wave resonators operating at 57.5 and 115 MHz designed for the driver linac of the Rare Isotope Accelerator facility.

Beam steering in superconducting quarter-wave resonators: An analytical approach

“…due to the beam port tilting, see below), every single peak should be used independently (nulling all points out of the peak) to calculate G Eyj , d Eyj , and g Eyj in order to be consistent with the used approximation. This is not difficult, however, since the contributions of the wall tilting are very well defined in space [2].…”

“…By means of a proper vertical offset of the beam, rf defocusing (13) can be used to counteract the transverse electric and magnetic steering [2]. The net effect of all steering components results just in the displacement of the optimum electromagnetic axis of the cavity (one of the reasons why QWRs steering was not observed for a long time in heavy ion linacs is probably that it was mistaken for rf steering caused by misalignment).…”

“…A smart correction method developed at ANL [2], which can be applied also in high-QWRs [10], is based on the creation of artificial E y components able to counteract the steering; this can be done by properly shaping the cavity walls at the beam ports positions, both at the outer and inner conductors. By tilting the surface with respect to the plane perpendicular to the beam axis it is possible to create new E y ðzÞ components, of either positive or negative sign (see an example in Fig.…”

“…Along the beam axis, in addition to the usual accelerating field, QWRs have always additional transverse field components, in the vertical direction y parallel to the main resonator axis (electric, E y ) and in the horizontal one x (magnetic, B x ), which both deflect the beam in the vertical direction y. This steering effect strongly depends on synchronous phase, beam velocity, accelerating gradient, and resonator geometry [1][2][3][4][5][6]. This is usually not critical in normal conducting resonators; in superconducting ones, due to the very high gradient and to special constraints in the cavity design, the magnetic component can be very strong and steering could become intolerable, especially for acceleration of high q=A beams [7].…”

Track: The New Beam Dynamics Code

“…The new code should be used for the statistical analysis of beam parameters obtained by tracking large numbers of particles through hundreds of accelerators each with randomly seeded errors. We have started developing the code TRACK [1] due to the lack of any code capable of simulating multiple-charge-state heavy-ion beam dynamics through such a wide range of 3D elements.…”