What sets the beam-beam tune-shift limit in electron-positron colliders
In plain words
Colliding beams focus each other; above a certain strength they blow up, and that ceiling is known from experience rather than derived.
Precise statement
In $e+e-$ ring colliders the vertical beam-beam parameter $\xi_y$ has saturated in operation at approximately 0.03-0.09 (highest values at LEP and KEKB), with simulations suggesting higher limits at stronger damping; with crab-waist collisions and beamstrahlung, coherent X-Z instabilities intervene. Derive the maximal $\xi_y$ as a function of radiation damping time per turn, synchrotron tune, Piwinski angle and beamstrahlung parameters, and compare with SuperKEKB, DAFNE and LEP data.
What would settle it
A theory or strong-strong simulation predicting xi_y,max for the three colliders within 20 percent with one set of assumptions.
Related problems
- More general than Beam-beam instabilities in large Piwinski angle crab-waist collisions