Abstract
Recently, relations were established between the coefficients of free and forced amplitude detuning polynomial expansions. The forced oscillations were considered only in a single plane. In this paper we extend and generalize previous results by developing analytical equations that transform the free amplitude detuning function into the amplitude detuning involving forced oscillations in both transverse planes. These are used to obtain closed approximated formulas for the beam-beam amplitude detuning with forced oscillations. Formulas are compared to single and multiparticle simulations.
Highlights
Forced oscillations play a very important role in modern accelerators
Forced oscillations have been purposely used in accelerators to avoid spin resonances with AC dipoles [2]
In [5,7,12] it is studied how the dynamics of forced oscillations differs from free oscillations
Summary
Forced oscillations play a very important role in modern accelerators. They may be induced by magnets with imperfect power supplies or by radio frequency noise in deflecting devices, like crab cavities [1], possibly leading to instabilities. Beam-beam effects in HL-LHC will possibly induce β-beating above the tolerances from machine protection [20] and forced oscillations with AC dipoles are promising instruments to measure the beam-beam β-beating. In [5,7,12] it is studied how the dynamics of forced oscillations differs from free oscillations. II to the beam-beam amplitude detuning and compares analytical formulas to single and multiparticle simulations
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