Beam-beam simulations with large synchrotron tune for strong RF focusing scheme D.Shatilov (BINP), M.Zobov (LNF) SBSR Workshop LNF, Frascati, 7-8 November 2005

Noise and damping in tracking (simplified variant) Initial (unperturbed) emittances and the energy spread are the input parameters. The noise correlations (6D) are unknown, so the noises are assumed to be without correlations, completely independent. Very simple method. If the details of the machine’s structure are unknown, this is the most adequate and the only possible way to implement noise and damping. Linear perturbation in the lattice (e.g. linear part of beam-beam kick) results in incorrect emittances. Sometimes even the sign of change is wrong! Nonlinear perturbations can give even more “interesting” results. For example, in the presence of strong beam-beam effects, the way the synchrotron noise is generated can essentially affect the transverse emittance (e.g. vertical beam size). Main featuresSide effects

Noise and damping in tracking (advanced variant) Actually, the same tracking speed as in the simplified variant. Emittances and the energy spread are the output parameters. Any perturbations in the lattice, both linear and nonlinear, result in correct emittances and the energy spread. For example, we checked by tracking how the energy spread depends on the synchrotron tune, and got a good agreement with the analytical formula. The noise and damping 6  6 matrixes for all beam-lines are calculated using the already known lattice of the machine. These matrixes are used as the input parameters for tracking. During the tracking, the noises and damping are applied only at the end of each beam-line, once per turn. Only 6 calls to RNG are needed, as well as in the simplified variant, but the noises for different degrees of freedom are correlated, according to the noise matrix. Main featuresMethod

Betatron resonances up to 6th order (red) and their first synchro-betatron satellites (blue). The synchrotron tune is 0.01 (left) and 0.40 (right). Qs=0.01Qs=0.40

Luminosity contour plots versus betatron tunes. Current DAFNE parameters, but without crossing angle,  =0.04. In some units, red corresponds to 1.0 (left) and 0.7 (right), yellow corresponds to 0.2 (left) and 0.15 (right). Qs=0.01 Qs=0.40

Betatron resonances up to 6th order (red) and their first synchro-betatron satellites (blue). The synchrotron tune is 0.01 (left) and 0.40 (right). Qs=0.01Qs=0.40

Qs=0.01 Qs=0.40 Luminosity contour plots versus betatron tunes. Current DAFNE parameters, but without crossing angle,  =0.04. In same units, red corresponds to 0.95 (left) and 0.9 (right), yellow corresponds to 0.2 (both left and right).

Luminosity contour plot versus betatron tunes, “good” area from the previous slide, Qs=0.40. In same units, maximum is 0.95 (red), minimum is 0.45 (looks like red again, right-bottom corner).

Beam tails versus betatron tunes, the same area as in the previous slide.

Dynamic aperture (4D) versus betatron tunes, calculated by P.Piminov. XY

Dynamic aperture (6D) versus betatron tunes, calculated by P.Piminov. XYZ

Conclusions High synchrotron tune increases the distance between betatron resonances and their synchrotron satellites. As a result, they cross the standard “good” working areas of betatron tunes, reducing them essentially. Luminosity, beam tails, and dynamic aperture are strongly affected by these resonances. In these conditions, choice of the working point may cause troubles. Additional investigations are required to find working parameters which allow to operate a collider with high synchrotron tune.