1. Beam-beam studies for eRHIC Y. Hao, V.N.Litvinenko, C.Montag, E.Pozdeyev, V.Ptitsyn

2. Features of beam-beam interaction of linac-ring scheme Compared with “usual” beam-beam interactions in collider rings, the linac-ring collision scheme brings on very specific effects:  Electron beam disruption.  Fluctuation of electron beam parameters.  Kink instability of the proton beam.  Effect of electron beam pinch on the incoherent proton beam emittance growth. All those effect are studied in details using a dedicated simulation code written by Y.Hao.

3. Electron beam disruption Two effects:  Linear mismatch caused by the beam-beam interaction increases the effective emittance in design lattice (without beam-beam). Lower  * -> less mismatch. Also, the design lattice can include into the account the beam-beam lens. Techniques for fast (bunch-by-bunch) mismatch compensation are under consideration (fast quadrupoles, electron beam lens).  The geometric emittance increases due to non-linear beam-beam force. ~ 2 times. Not the big problem.

4. Kink instabiity Proton emittance growth caused by transverse instability. The head of the proton bunch affects the tail through the interactions with the electron beam. Includes synchrotron oscillations. Without tune spread (zero chromaticity) the instability threshold is at 1.6e10 proton per bunch. The tune spread stabilizes the instability. Required chromaticity: >3 units. Nonlinearity character of the beam-beam Interactions also helps.

5. Effect of the Electron Pinch on Protons Source – The electron beam is focused by strong beam- beam force. – Electron beam distribution has a dense core. Enhanced beam-beam parameter value. Main Factors under Consideration – Working Points (avoid nonlinear resonance ) – Electron optics and initial emittance (reduce synchrotron-betatron oscillation)

6. Pinch Effect versus Electron  * Design β * = 1m at IP Initial emittance 1nm The maximum beam-beam parameter of protons is as large as 0.19 The average beam-beam parameter of protons is 0.067. Design β * = 0.25m at IP Initial emittance 4nm The maximum beam-beam parameter of protons is 0.054 The average beam-beam parameter of proton is 0.031 e-beam

7. Change the waist position to minimize pinch The maximum beam-beam parameter for proton is as large as 0.022 The average beam-beam parameter for proton is 0.014, while design is 0.015 e-beam

8. Not only electron rms beam size counts The nonlinear force will form a dense core in electron beam distribution. The field is different from Gaussian beam field which only depends on rms beam size of opposite beam.

9. L=1.72 ×10 33 cm-2-s-1 L= 2.46 ×10 33 cm-2-s-1 This shows the dense core of electron beam plays a very important role in proton beam emittance growth. Large emittance and small design beta* is preferred for electron beam.

10. Summary Several features of the beam-beam interactions are under consideration. The kink instability is stabilized for design beam intensities by proper choice of the chromaticity. Techniques for compensation of the mismatch caused by the beam-beam are under consideration. Both electron beam disruption and proton beam-beam parameter benefit from lower  * of electrons. More investigations are underway for incoherent proton beam emittance growth in the presence of electron pinch, including the optimal choice of the working point.