Coherent synchrobetatron beam-beam modes: Experiment and simulation

Analytic calculation and numerical simulations reveal a multiline structure in the spectrum of coherent dipole oscillations in the colliding beam system due to coupled synchrobetatron beam-beam modes. The model employed in the analysis involves linearization of the beam-beam kick and takes into account the fact that the length of the colliding bunches is finite. In the present paper, we discuss the behavior of the synchrobetatron beam-beam modes, obtained both analytically and numerically, and compare it with the experimental results for the VEPP-2M collider. A particular case of the betatron tune close to the half-integer resonance is considered on the basis of the presented models.