1. Moriond 2003M. Benedikt, S. Hancock Injection and Accumulation in a High Energy Ion Storage Ring Michael Benedikt, Steven Hancock AB Division, CERN

2. Moriond 2003M. Benedikt, S. Hancock Beta Beam Accelerator Complex Neutrino Source Decay Ring Ion production ISOL target & Ion source Proton Driver SPL Decay ring B  = 1500 Tm B = 5 T C = 7000 m L ss = 2500 m 6 He:  = 150 18 Ne:  = 60 SPS Bunching and acceleration to medium energy Cyclotrons Storage ring and RCS PS Acceleration to final energy PS & SPS Experiment

3. Moriond 2003M. Benedikt, S. Hancock Desired beam parameters in the decay ring 6 Helium 2+ –Intensity: 1.0x10 14 ions –Energy: 139 GeV/u –Rel. gamma: 150 –Rigidity: 1500 Tm 18 Neon 10+ –Intensity: 4.5x10 12 ions –Energy: 55 GeV/u –Rel. gamma: 60 –Rigidity: 335 Tm The neutrino beam at the experiment will have the “time stamp” of the circulating beam in the decay ring. We need to concentrate the beam in as few and as short bunches as possible to maximize the number of ions/nanosecond. (background suppression) Clearly 6 He is the more demanding ion and considered further on.

4. Moriond 2003M. Benedikt, S. Hancock What can we get from the injector chain Overall cycling time of the injector chain is determined by the SPS to about 8 seconds. Number of ions per bunch at SPS injection is limited by space charge effects (we should have many bunches….). Baseline scenario foresees 8 bunches arranged in 2 trains of 4 bunches on opposite sides in the SPS. 6 Helium 2+ at SPS ejection energy –Intensity: 8 bunches of 1.2x10 12 ions –Tr. emit: 0.6  m (geometrical) –Longit. emit: ~1 eVs –Bunch length: ~1 ns Though optimistic, the number of ions per batch (8 bunches) is a factor 10 below what is needed in the decay ring!

5. Moriond 2003M. Benedikt, S. Hancock SPS SPS as injector 2 x 4 bunches injected from the PS. Transverse blow-up before transfer and additional 40 MHz rf system to increase bunch length to reduce space charge effects. PS SPS PS Bunch spacing: 0.25  s Train distance: 10.50  s

6. Moriond 2003M. Benedikt, S. Hancock Stacking in the decay ring There is an absolute need for stacking in the decay ring. –Not enough flux from source and injection chain. –Life time is an order of magnitude larger than injector cycling (120 s as compared to 8s). –We need to stack at least over 10 to 15 injector cycles. Cooling is not an option for the stacking process: –Electron cooling is excluded because of the high electron beam energy and in any case far too long cooling times. –Stochastic cooling is excluded by the high bunch intensities. Stacking without cooling creates “conflicts” with Liouville.

7. Moriond 2003M. Benedikt, S. Hancock Asymmetric bunch pair merging Try to cheat Liouville macroscopically by: –Stacking longitudinally in the centre of the existing beam. –Using the fact that “older” parts of the stack are naturally loosing density because of beta decay. Asymmetric bunch pair merging moves the fresh bunch into the centre of the stack and pushes less dense phase space areas to larger amplitudes until these are cut by the momentum collimation system. The maximum density is always in the centre of the stack as required by the experiment.

8. Moriond 2003M. Benedikt, S. Hancock Requirements for asymmetric merging Dual harmonic RF systems: –Decay ring will be equipped with 40 and 80 MHz system. –Gives required bunch lengths of < 10 ns for physics. Stack and fresh bunch need to be positioned in adjacent “buckets” of the dual harmonic system (12.5 ns distance!) Adjustment of phase and voltage ratios allows merging.

9. Moriond 2003M. Benedikt, S. Hancock Asymmetric bunch merging (SPS model)

10. Moriond 2003M. Benedikt, S. Hancock Full scale simulation with SPS as model Simulation conditions: –Single bunch after injection and ¼ turn rotation. –Stacking again and again until steady state is reached. –Each repetition, a part of the stack (corresponding to  -decay) is removed. Results: –Steady state intensity was ~85 % of theoretical value (for 100% effective merging). –Final stack intensity is ~10 times the bunch intensity (~15 effective mergings). –Moderate voltage of 10 MV is sufficient for 40 and 80 MHz systems for an incoming bunch of < 1 eVs.

11. Moriond 2003M. Benedikt, S. Hancock Injection into the decay ring Bunch merging requires fresh bunch to be injected at ~10 ns from stack! –Conventional injection with fast elements is excluded. Off-momentum injection on a matched dispersion trajectory. Rotate the fresh bunch in longitudinal phase space by ¼ turn into starting configuration for bunch merging. –Relaxed time requirements on injection elements: fast bump brings the orbit close to injection septum, after injection the bump has to collapse within 1 turn in the decay ring (~20  s). –Maximum flexibility for adjusting the relative distance bunch to stack on ns time scale.

12. Moriond 2003M. Benedikt, S. Hancock Injection into the decay ring

13. Moriond 2003M. Benedikt, S. Hancock Horizontal aperture layout Assumed machine and beam parameters: –Dispersion:D hor = 10 m –Beta-function:  hor = 20 √m –Moment. spread stack:  p/p = ±1.0x10 -3 (full) –Moment. spread bunch:  p/p = ± 2.0x10 -4 (full) –Emit. (stack, bunch):  geom = 0.6  m Septum & alignment 10 mm Stack: ± 10mm momentum ± 4 mm emittance Beam: ± 2 mm momentum ± 4 mm emittance Required separation: 30 mm, corresponds to 3x10 -3 off-momentum. Required bump: 22 mm Central orbit undisplaced

14. Moriond 2003M. Benedikt, S. Hancock SPS Decay ring operation SPS Stack: four bunches, concentrated in ~1/20 of the circumference. Full bunch length for physics: < 10ns. Every 8s four fresh bunches injected off-momentum, phase rotated and merged to stack. Immediately after first merging, the procedure is repeated with second batch of 4 bunches. Total injection and merging time for 2x4 fresh bunches ~1s. Afterwards 7s in physics mode and again injection.

15. Moriond 2003M. Benedikt, S. Hancock Decay ring design issues Main design issues: –Superconducting for high bending field (~5T) to have large useful straight section. –Low transition gamma for high synchrotron frequency and fast merging. –Special insertion for off-momentum injection (large normalized dispersion D/√  ). –Sophisticated collimation system for loss protection and momentum collimation.

16. Moriond 2003M. Benedikt, S. Hancock Acknowledgements We would like to especially thank all our colleagues in the “beta beam study group” for their support and helpful discussion. Conclusions Asymmetric bunch merging is a promising method for stacking beams of radioactive ions. Simulations give excellent results, an experimental proof of principle is under way. For a beta beam decay ring, an off-momentum injection with bunch merging seems at present the favorable injection an stacking scenario.