Requirements and Results for Quadrupole Mode Measurements

Direct space charge may be quantified, and hence the beam brightness observed, by measuring the quadrupolar beam modes in the CERN Proton Synchrotron (PS). The spectrum of the transverse beam size oscillations (i.e. the quadrupolar beam moment) contains valuable information: the betatron envelope modes and the coherent dispersive mode indicate optics mismatch, while their frequency shifts due to space charge allow a direct measurement thereof. To measure the quadrupolar beam moment we use the Base-Band Q-meter system of the PS which is based on a four electrode stripline pick-up. Past experiments with quadrupolar pick-ups often investigated coasting beams, where the coherent betatron and dispersion modes correspond to single peaks in the tune spectrum. In contrast, long bunched beams feature bands of betatron modes: the mode frequencies shift depending on the transverse space charge strength which varies with the local line charge density. By using the new transverse feedback in the PS as a quadrupolar RF exciter, we measured the quadrupolar beam transfer function. The beam response reveals the distinct band structure of the envelope modes as well as the coherent dispersive mode.