Magnet strength measurement in circular accelerators from beam position monitor data

Abstract

Recent measurements of resonance terms suggested the extension of the existing technique to measure magnet strengths from turn-by-turn beam position monitor data. This article describes the algorithm to infer the magnet strength from the variation along the ring of the resonance terms and reports on the first measurement. Both the algorithm and the software written for the analysis of the data can be particularly useful in the commissioning period of an accelerator in order to find magnets with wrong strengths or polarities as well as magnets with large magnetic errors.

First simultaneous measurement of sextupolar and octupolar resonance driving terms in a circular accelerator from turn-by-turn beam position monitor data

“…A last interesting figure to evaluate the quality of the TbT BPM data and of its harmonic analysis is represented by a cancellation condition that shall be satisfied by some measured CRDTs. According to the definitions of the normal sextupole terms of Table I it is straightforward to prove that F 0 = 2ℜ{F N S2 } − ℜ{F N S1 } + ℜ{F N S0 } ≡ 0 (7) anywhere in the ring: the closer F 0 is to zero, the more reliable is the harmonic analysis described here. Note that the measured F 0 along the ring depends only on: (i) the linear lattice model (β functions used to normalize the BPM TbT data); (ii) the BPM calibration factors, spatial and spectral resolution, electronic noise and the like; (iii) initial beam excitation, i.e.…”

“…By looking at Table IV of Ref. [7] and Fig. 24 it is clear that secondary spectral lines of the complex signal h r and excited by either coupling or sextupoles, become indistinguishable.…”

“…The fundamental ingredient to establish this correlation is provided by the resonance driving terms (RDTs) of Refs. [4][5][6][7]. These may be evaluated both from analytic formulas (rather simple in most cases) and from the harmonic analysis of the phase space curves, i.e.…”

“…For a reliable analysis of the ESRF nonlinear lattice model, the normal form and RDT description of Refs. [4][5][6][7] needs to be extended to the second order. The theoretical background has been already developed in previous works, among which the fundamental Ref.…”

“…The method was successfully applied to the CERN Super Proton Synchrotron [7], as well as to the Relativistic Heavy Ion Collider [24]. On the other hand, the applicability of the 3-BPM signal is hampered whenever the phase advance between the monitors is close to either zero or π, which is unfortunately the case of many BPMs in the ESRF storage ring.…”