Computation and Consequences of High Order Amplitude- and Parameter-Dependent Tune Shifts in Storage Rings for High Precision Measurements
AbstractNonlinear effects of the various electric field and magnetic field components of storage
rings to confine the particles and bend their trajectory can cause substantial amplitude-dependent
tune shifts within the beam. Furthermore, tune shifts are often sensitive to
variations of system parameters, e.g. total particle momentum offsets δp. Such
amplitude- and parameter-dependent tune shifts influence the dynamics and stability of
a beam in particle storage rings. Thus, it is critical for high precision measurements to
analyze and understand these influences. On this basis, we present normal form
methods for the calculation of high order amplitude and system parameter
dependencies of the horizontal and vertical tunes in storage rings using the differential
algebra (DA) framework within COSY INFINITY. A storage ring is simulated using
COSY INFINITY to generate a DA Poincaré return map describing the transverse
phase space behavior after each revolution in the storage ring. The map is expanded
around the parameter-dependent closed orbit of the system before transforming the
resulting map into normal form coordinates to extract the high order tune dependencies
on the phase space amplitude and variation in the system parameters. As a specific
example, a storage ring similar to the Storage Ring of the Muon g−2 Experiment at
Fermilab (E989) is investigated.
A. Weisskopf, D. Tarazona, M. Berz,
Int. Journal of Modern Physics A, 34, 36 (2019) 1942011.
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