Stability of Single Particle Motion with Head-On Beam-Beam Compensation in the RHIC

To compensate the large tune shift and tune spread generated by the head-on beam-beam interactions in the polarized proton run in the Relativistic Heavy Ion Collider (RHIC), we proposed a low energy electron beam with a Gaussian transverse profiles to collide head-on with the proton beam. In this article, with a weak-strong beam-beam interaction model, we investigate the stability of single particle motion in the presence of head-on beam-beam compensation. Tune footprints, tune diffusion, Lyapunov exponents, and 10⁶ turn dynamic apertures are calculated and compared between the cases without and with beam-beam compensation. A tune scan is performed and the possibility of increasing the bunch intensity is studied. The cause of tune footprint foldings is discussed, and the tune diffusion and Lyapunov exponent analysis are compared.