Compensation of the “Pacman” tune spread by tailoring the beam current

“Factory”-like e⁺-e^--colliders presently under design or construction achieve high luminosity by resorting to large numbers of closely-spaced bunches. The short bunch spacing implies that there are unavoidable parasitic collisions (PCs) in the neighborhood of the interaction point (IP). Since the bunch population of the beam is not uniform due to an intentional ion-clearing gap, the bunches at the head or tail of the train (“pacman bunches”) experience different beam-beam tune shifts than those away from the edges (“typical bunches”). We present here a method to minimize the vertical tune spread at the expense of increasing the horizontal tune spread (we assume that there is only one IP). Since the beam-beam dynamics for flat beams typically tolerates a significantly higher horizontal tune spread than a vertical tune spread, this method implies a net advantage. We present our discussion in the context of the PEP-II collider