Determining the radiofrequency dipole and quadrupole effects in quarter wave resonators

Abstract

The asymmetry of a quarter wave resonator (QWR) around the beam axis z causes deflection and additional (de)focusing of the beam: these effects are immediately related to the first terms, the dipole and the quadrupole, in a Fourier-Bessel multipole expansion of the quasistatic potential φ; the non-relativistic impulse approximation for heavy ion acceleration is given. General features of multipole dependencies from beam phase and velocities are shown. Since the electric field square modules | E| 2 is measurable with the bead technique, an iterative determination of E x and E y from E z and the potential φ is proposed here; the noise contribution is not amplified at the shortest wavelength Fourier components, and it can be filtered. Field errors are reduced by imposing the fit to the correct analytic form inside the drift tubes, where the fields exponentially decrease. The preliminary set of data relative to a QWR with an ogiva central rod is treated as an example, showing that dipole effects have a zero near the beam velocities optimal for acceleration.