The beam quadrupole moment of stored beams can be measured with a four-plate quadrupole pick-up. The frequency spectrum of the quadrupole moment contains not only the usual first-order dipole modes (the betatron tunes) but also the second-order coherent modes, comprising of (1.) (even) normal envelope modes, (2.) odd (skew) envelope modes and (3.) dispersion modes. As a novel diagnostic tool, the measured frequencies and amplitudes provide direct access to transverse space charge strength through the tune shift as well as linear coupling (and mismatch thereof), along with the benefit of a non-invasive beam-based measurement. Technically, quadrupole moment measurements require a pick-up with non-linear position sensitivity function. We discuss recent developments and depict measurements at the GSI SIS18 heavy-ion synchrotron.
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J.P. Edelen, N.M. Cook, J.A. Einstein-Curtis
RadiaSoft LLC, Boulder, Colorado, USA
K.A. Brown, V. Schoefer
BNL, Upton, New York, USA
Funding:This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics under Award Number DE-SC0019682 One of the fundamental challenges of using machine-learning-based inverse models for optics tuning in accelerators, particularly transfer lines, is the degenerate nature of the magnet settings and beam envelope functions. Moreover, it is challenging, if not impossible, to train a neural network to compute correct quadrupole settings from a given set of measurements due to the limited number of diagnostics available in operational beamlines. However, models that relate BPM readings to corrector settings are more forgiving, and have seen significant success as a benchmark for machine learning inverse models. We recently demonstrated that when comparing predicted corrector settings to actual corrector settings from a BPM inverse model, the model error can be related to errors in quadrupole settings. In this paper, we expand on that effort by incorporating inverse model errors as an optimization tool to correct for optics errors in a beamline. We present a toy model using a FODO lattice and then demonstrate the use of this technique for optics corrections in the AGS to RHIC transfer line at BNL.
