Abstract
In colliders with asymmetric rigidity such as the proposed Large Hadron electron Collider, jitter in the weaker beam can cause emittance growth via coherent beam-beam interactions. The LHeC in this case would collide 7 TeV protons on 60 GeV electrons, which can be modeled using a weak-strong model. In this work we estimate the proton beam emittance growth by separating out the longitudinal angular kicks from an off-center bunch interaction and produce an analytic expression for the emittance growth per turn in systems like the LHeC.
Highlights
The beam-beam effect is the term given to the mutual lensing action that each beam in a collider causes on the other
Due to the asymmetric rigidities in these beams, the beam-beam tune shift is 9.6x10-5 for the proton beam and 0.75 for the electron beam, it is the coherent effects that will drive emittance growth
Using the definition of a change in emittance for a given transverse dimension, 〈x 〉〈 p ∆p 〉 〈xp 〉, we find that we can isolate the Δpx term as ε 1 〈∆p 〉〈x 〉/ε
Summary
The beam-beam effect is the term given to the mutual lensing action that each beam in a collider causes on the other. Due to the asymmetric rigidities in these beams, the beam-beam tune shift is 9.6x10-5 for the proton beam and 0.75 for the electron beam, it is the coherent effects that will drive emittance growth. These coherent effects will add different transverse momentum changes to different parts of the beam, increasing emittance. Since this is a linac-ring system, the offset jitter that drives this increase will not reach an equilibrium, since the linac will continuously add a new beam with new jitter [2]
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