Simulation of Beam-Beam Effects in $e^+e^-$ Storage Rings

Source: arXiv


The beam-beam effects of the PEP-II as an asymmetric collider are studied with strong-strong simulations using a newly developed particle-in-cell (PIC) code. The simulated luminosity agrees with the measured one within 10% in a large range of the beam currents. The spectra of coherent dipole oscillation are simulated with and without the transparency symmetry. The simulated tune shift of the coherent $\pi$ mode agrees with the linearized Vlasov theory even at large beam-beam parameters. The Poicare map of coherent dipole is used to identify the beam-beam resonances.

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    ABSTRACT: A simple consideration is given of the eigenmodes of the coherent betatron oscillation excited by a series of sinusoidal kicks and influenced by the beam-beam interaction in e+e− colliding storage rings. The differences between tunes corresponding to the eigenmodes are just half of what is expected from rigid point like bunches. The discussion is mainly limited to the case where the beam-beam force is not so strong so that the bunches remain Gaussian and the linear approximation of the force is valid. The nonlinear effect is also discussed briefly.
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    ABSTRACT: The coherent normal modes of the nonlinear colliding beam system are calculated using averaging methods to find an equivalent infinite system of linear coupled oscillators. The condition of a consistent, stationary state leads to an eigenvalue equation for the characteristic frequencies and transverse exitation distributions of the modes. Results are presented for modes along the narrow axis of a Gaussian ribbon beam. The tune split is related to L/¿(I+I-) for different values of I+/I- and of ¿+/¿- .
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    ABSTRACT: We have modified the beam-beam simulation code CBI to handle asymmetric beams and used it to look at energy transparency and symmetries in the beam-beam interaction. We find that even a small violation of energy transparency, or of the symmetry between the two beams, changes the character of the collective (coherent) motion; in particular, period-n oscillations are no longer seen. We speculate that the one-time observation of these oscillations at LEP, and the more ubiquitous observation of the flip-flop instability in colliders around the world, may be a consequence of breaking the symmetry between the electron and positron beams. We also apply this code to the asymmetric collider PEP-II, and find that for the nominal parameters of PEP-II, in particular, the nominal tune-shift parameter of xi0=0.03, there are no collective beam-beam issues. Collective quadrupole motion sets in only at xi0=0.06 and above, consistent with earlier observations for symmetric beams.
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