Transient beam response in synchrotrons with a digital transverse feedback system

Abstract

The transient beam response to an externally applied impulse force in synchrotrons with a digital transverse feedback system is studied. Experimental data from the LHC on damping of coherent transverse oscillations excited by the discrete-time unit impulse are analysed. Good agreement on the measured and theoretically predicted decrements has been obtained. A method of feedback fine tuning, based on measurements of the bunch response to the harmonic excitation impulse, is discussed.

Damping of coherent betatron oscillations of a charged particle beam in synchrotrons with a feedback system

“…The characteristic equation in this case is equivalent to the set of equations (6) It is easy to see that the reduced set of equations in the linear approximation to g has solution (4). The parameters α and ΔQ are proportional to g according to Eq.…”

“…(5). Therefore, we can write the following for the second equation of set (6) in the second approxi mation to g:…”

“…Thus, equations for the decrement α and the shift in the number of betatron oscillations ΔQ coincide with similar approximate equations that have been derived in the original discrete model of the damping system where the local character of measure ments of the beam deviation and the action of the cor recting force are considered [6]. We should note that the decrement is maximal at which answers the well known criterion of optimal phase conditions for transverse damping.…”