Detuning Properties of RF Phase Modulation in an Electron Storage Ring

In electron storage rings, it is possible to increase the bunch length by applying phase modulation to the radio frequency accelerating field by choosing appropriate parameters for the modulation. Such a bunch lengthening effect improves beam parameters such as beam lifetime, which can help us achieve better beam stability. It is well known that the modulation frequency around the double synchrotron frequency is effective in lengthening the bunch. The dependence of bunch lengthening on modulation frequency, the so-called detuning property, has a peak around the double synchrotron frequency with a frequency width that depends on the modulation amplitude. Nonlinear effects due to phase modulation lead to a peak frequency shift in a negative direction from the double synchrotron frequency, accompanied by an asymmetric peak shape. Beam current also affects the properties of the detuning condition of such bunch lengthening. We investigated the detuning property using a theoretical model and systematic measurements at the electron storage ring KARA, and we verified the qualitative agreement between the experiments and the theoretical model. The macro-particle simulations have confirmed the agreement.