Bunch length effects in the beam-beam compensation with an electron lens

Abstract

Electron lenses for the head-on beam-beam compensation are under construction at the Relativistic Heavy Ion Collider. The bunch length is of the same order as the β-function at the interaction point, and a proton passing through another proton bunch experiences a substantial phase shift which modifies the beam-beam interaction. We review the effect of the bunch length in the single pass beam-beam interaction, apply the same analysis to a proton passing through a long electron lens, and study the single pass beam-beam compensation with long bunches.

Head-on beam-beam compensation in RHIC

“…In this configuration, a proton, after receiving a beam-beam kick at IP8, passes a triplet with nonlinear magnetic fields from field errors, an arc with chromaticity sextupoles and dodecapoles in the quadrupoles as dominating nonlinear field errors, and another triplet in IR10. To avoid bunch length effects, the parameter β * cannot be too small [47,48]. In simulations, a value as low as β * = 0.5 m was found to be acceptable [70].…”

“…[70], and bunch length effects have been investigated in Refs. [47,48]. The Tevatron experience also provides tolerances for positioning errors, transverse shape and size mismatches, and electron current variations.…”

Compensation of head-on beam-beam induced resonance driving terms and tune spread in the Relativistic Heavy Ion Collider

“…With a proton bunch length σ z comparable to or larger than β Ã , σ z ⪆β Ã , the phase advance during the passage of a proton through the other beam changes, and the phase advance condition kπ between the p þ p and p þ e interactions is only approximately fulfilled [21]. (Table II).…”

“…The figures show that the largest deviations are reached for r i ≈ 1σ and large r 0 i . Deviations from complete compensation are also created by particles arriving early or late relative to the bunch center of the opposing beam, mismatches of the electron beam size to the proton beam size, or mismatches of the electron beam current to the proton bunch intensity [21]. The full effect of these deviations can only be assessed with long-term simulations (Sec.…”

“…The more general case is presented, e.g., in Refs. [9,21]. The beam-beam parameters from the protonproton and proton-electron collisions with ξ p ¼ −ξ e are then…”