1. E-Cloud Effects in the Proposed CERN PS2 Synchrotron M. Venturini, M. Furman, and J-L Vay (LBNL) ECLOUD10 Workshshop, Oct. 8-12 Cornell University Work supported by the US DOE and LHC Acceleration Research Program (LARP)

2. 2 Motivations & Outline One of the upgrade options considered for future LHC injector complex upgrades entails replacing PS with PS2. One of the upgrade options considered for future LHC injector complex upgrades entails replacing PS with PS2. Larger (1.34km circumference) Larger (1.34km circumference) Higher energy (in@4GeV, extr@ 50GeV) Higher energy (in@4GeV, extr@ 50GeV) E-cloud identified as a possible factor limiting machine performance. E-cloud identified as a possible factor limiting machine performance. We present results of recent studies of We present results of recent studies of E-cloud build-up (POSINST) E-cloud build-up (POSINST) Simulation of effect of e-cloud on single-bunch instability (WARP) Simulation of effect of e-cloud on single-bunch instability (WARP)

3. 3 Parameters for E-Cloud Build-up Simulations (POSINST)

4. 4 Note roll-over of e-density with increasing bunch- population Note roll-over of e-density with increasing bunch- population BUILD-UP IN FIELD-FREE REGION BUILD-UP IN DIPOLE REGION E-density vs. bunch population for various vacuum chamber sizes E-density vs. bunch population for various choices of max energy of yield curve

5. 5 E-density vs. peak secondary yield for various regions, train structures (extraction) E-density vs. peak secondary yield for various regions, train structures (injection)

6. 6 Summary of E-cloud Build-up Studies Results obtained for 6D gaussian beams. Alternate bunch shape (parabolic transverse, flat longitudinal) yields build-up results 5-10% lower Results obtained for 6D gaussian beams. Alternate bunch shape (parabolic transverse, flat longitudinal) yields build-up results 5-10% lower

7. 7 Effects of Ecloud on Beam Focus on single-bunch e-cloud driven instability Focus on single-bunch e-cloud driven instability Simulations carried out with WARP Simulations carried out with WARP Quasi-static approximation Quasi-static approximation Transversly uniform ecloud localized at finite no. of stations distributed along the ring (refreshed after each bunch passage) Transversly uniform ecloud localized at finite no. of stations distributed along the ring (refreshed after each bunch passage) Smooth approx. for lattice Smooth approx. for lattice 6D gaussian beam 6D gaussian beam Selected parameters used in WARP simulations

8. 8 An fast head-tail like instability develops for sufficiently high e-cloud density An fast head-tail like instability develops for sufficiently high e-cloud density Detect instability by monitoring evolution of transverse emittances and amplitude of transverse centroid offset Detect instability by monitoring evolution of transverse emittances and amplitude of transverse centroid offset Vertical dipole moment a long the beam as the instability develops. Snapshots are taken for 5 successive bunch passage starting from turn no. 200 and 600 Evolution of vertical and horizontal emittances for three values of the e-cloud density

9. 9 Identify instability threshold by recording max. values of bunch emittances, & amplitude of centroid oscillations over 1000 turns (4.5ms). Start simulations with small initial transverse offset x 0, y 0. Bunch population: 5.9*10 11. Negative chromaticities stabilize the motion (PS2 lattice has negative mom. compaction).

10. 10 To model electrons dynamics in dipoles use Warp option to pin electrons to vertical lines. To model electrons dynamics in dipoles use Warp option to pin electrons to vertical lines. This suppresses instability in horizontal plane This suppresses instability in horizontal plane Instability threshold in vertical plane somewhat higher (left Fig.) Instability threshold in vertical plane somewhat higher (left Fig.) Reducing bunch population is found to affect instability in vertical plane minimally while increasing stability in horizontal plane (middle Fig.) Reducing bunch population is found to affect instability in vertical plane minimally while increasing stability in horizontal plane (middle Fig.) At injection instability occurs at higher e-cloud densities (right Fig.) At injection instability occurs at higher e-cloud densities (right Fig.)

11. 11 Conclusions For vanishing chromaticities instability thresholds in terms of e-density are found to be about 0.4 in the vertical and 0.5 in the horizontal plane (units of 10 12 m -3 ) For vanishing chromaticities instability thresholds in terms of e-density are found to be about 0.4 in the vertical and 0.5 in the horizontal plane (units of 10 12 m -3 ) Chromaticities=-3 increase threshold by about 50% Chromaticities=-3 increase threshold by about 50% Pinning electrons to vertical lines (dipoles) suppresses instability in the horizontal plane. Instability threshold in the vertical plane at  e =0.8*10 12 m -3 Pinning electrons to vertical lines (dipoles) suppresses instability in the horizontal plane. Instability threshold in the vertical plane at  e =0.8*10 12 m -3 Above values lie in the mid-range of POSINST estimates of e-cloud build-up, suggesting that mitigation measures would have to be taken to decrease effective peak secondary to below 1.3 Above values lie in the mid-range of POSINST estimates of e-cloud build-up, suggesting that mitigation measures would have to be taken to decrease effective peak secondary to below 1.3