Abstract
At the interaction point of a storage ring collider each beam is subject to perturbations due to the electromagnetic field of the counterrotating beam. For flat beams, a well-known approximation models the beam by a current sheet which is uniform in the horizontal plane, restricting the particle motion to the vertical direction. In this classical model a water-bag beam distribution has been used to find working points and beam-beam tune shift parameters which lead to a stable beam distribution. We investigate the stability of a more realistic Gaussian equilibrium distribution. A linearized Vlasov equation written in action-angle variables is used to compute the radial and angular modes of a perturbation in two-dimensional phase space to first order in the displacement from the design trajectory. We find that the radial modes, which are often neglected, can have a stabilizing effect on the beam motion.
Highlights
Colliding particle bunches in a storage ring exert an electromagnetic force on each other
In e e colliders, where the action of radiation excitation and damping produce a flat beam, the observed vertical beam-beam parameter limit is in the approximate range 0:02 y 0:1 [1,2]. At present it is not known whether the emittance increase is due to an incoherent, single-particle effect or to a coherent, collective instability of the colliding beams
The DCI storage rings at LAL, Orsay, France, used a pair of e and e beams to collide with another pair, in an attempt to cancel the beam-beam force [3]
Summary
Colliding particle bunches in a storage ring exert an electromagnetic force on each other. In e e colliders, where the action of radiation excitation and damping produce a flat beam, the observed vertical beam-beam parameter limit is in the approximate range 0:02 y 0:1 [1,2]. At present it is not known whether the emittance increase is due to an incoherent, single-particle effect or to a coherent, collective instability of the colliding beams. III we solve the equations of motion for radial and angular modes up to first order in the displacement from the design trajectory and discuss the implications of our results
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