Abstract
A six-dimensional symplectic beam-beam interaction map using finite discrete slices of a strong beam is extended to infinitesimal slices. The new map is calculated under the assumption of a longitudinal Gaussian distribution with approximations. A round Gaussian beam is simulated to demonstrate accuracies of the approximations.
Highlights
In early beam-beam simulations the dependence on longitudinal position has been ignored in calculating the beam-beam force exerted on a particle
For today’s high luminosity storage ring, where b can be very small at the interaction point (IP), this simplified approach must be replaced by a method which includes longitudinal effects [1]
Such longitudinal effects can be divided into two parts: the transverse kick should be influenced by the longitudinal position of the particle and there should be a longitudinal kick appearing as an energy change
Summary
In early beam-beam simulations the dependence on longitudinal position has been ignored in calculating the beam-beam force exerted on a particle. We will apply the map to infinitesimal strong slices of a longitudinally Gaussian distributed strong beam. Comparisons with discrete slice methods using the synchro-beam map suggested by Hirata et al are made with various levels of approximations developed in this paper. Hirata et al proposed a synchro-beam mapping for a particle-slice interaction, which is generated by. To reflect the change in the strong beam due to translation of CP, Q ءis a function of the displacement S Using this map, we can apply the beam-beam interaction based on the coordinate at the CP, Xnew exp: 2nءUX, Y ; Q͑ءSZ, z ͔͒͒ء:͒X . The same calculation is performed slice after slice to obtain the total effect due to the strong bunch
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