Abstract
Weak-strong tracking simulations for the Large Hadron Collider have shown that long-range beam-beam collisions give rise to a well-defined diffusive aperture beyond which particles are lost quickly. In order to derive analytical estimates of this stability boundary, we use leading order perturbation theory and the Chirikov resonance overlap criterion applied to a simplified model with a 2-dimensional transverse phase space. In addition, a Fokker-Plank\char21{}type diffusion coefficient is calculated through the nonlinear action kicks imparted by the long-range beam-beam force. The analytical results are compared with the tracking data.
Highlights
In a colliding-beam storage ring, one of the largest perturbations affecting the motion of beam particles is the collision with the opposing beam
In the case of the Large Hadron Collider (LHC), a 7-TeV double-ring proton collider presently under construction at CERN, the long-range collisions occur in the vicinity of each main head-on interaction points (IPs), before the beams are fully separated into two disjunct beam pipes
In the LHC the effective strength of the long-range collisions depends on the ratio of the beam crossing angle to the rms beam divergence at the main IPs
Summary
In a colliding-beam storage ring, one of the largest perturbations affecting the motion of beam particles is the collision with the opposing beam. In the LHC the effective strength of the long-range collisions depends on the ratio of the beam crossing angle to the rms beam divergence at the main IPs. On either side of the two LHC main collision points, a beam encounters about 15 parasitic collisions with an approximate average separation between the closed orbits of the two beams of 9.5 rms beam sizes (see Table I). Beam energy Particle species Full crossing angle rms beam divergence rms beam size Normalized transv To this end, we apply the Chirikov overlap criterion to a simplified model describing the long-range interactions encountered at one IP of a circular machine. Throughout this article, we assume LHC-like parameters As a simplification, both in the simulation and in the analytical treatment we consider particle motion in one transverse plane only (1 transverse degree of freedom). Results, and figures presented in the remainder of this article refer to a 2-dimensional transverse phase space
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