Flat Bunches for the LHC Luminosity Upgrade towards 10 35 cm -2 sec -1

1. Flat Bunchesfor the LHC Luminosity Upgrade towards 1035 cm-2sec-1 Chandra Bhat Fermilab LARP CM13 Collaboration Meeting November 4-6, 2009 Port Jefferson (Hosted by BNL)

2. Acknowledgements • Frank Zimmermann, • Oliver Brüning, • Elena Shaposhnikova • HeikoDamerau • GianluigiArduini Inputs on beam instability • in LHC upstream accelerators • Elias Metral, Giovanni Rumolo •  LHC Operation Group •  J. MacLachlan (ESME simulations) LARP CM13 Meeting, Nov. 4-6, 2009, Chandra Bhat

3. LHC upgrade paths with L1035 cm-2sec-1 (F. Zimmermann, CARE-HHH Workshop, 2008) Early Separation (ES) Full Crab Crossing (FCC) L. Evans, W. Scandale, F. Zimmermann J.-P. Koutchouk I=1.7E11ppb # of Bunch=2808 Bunch Spacing=25ns *~10 cm I=1.7E11ppb # of Bunch=2808 Bunch Spacing=25ns *~10 cm Small-Angle Crab Cavity Small-Angle Crab Cavity • early-separation dipoles inside detectors • → hardware inside ATLAS & CMS detectors, • first hadron crab cavities; off-d b , =3.75m • crab cavities with 60% higher voltage • → first hadron crab cavities, off-d b-beat =3.75m Large Piwinski Angle (LPA) Low Emittance (LE) R. Garoby F. Ruggiero, W. Scandale. F. Zimmermann I=1.7E11ppb # of Bunch=2808 Bunch Spacing=25ns *~10 cm I~6E11ppb # of Bunch=1404 Bunch Spacing=50ns *~25 cm Wire Compensator • long-range beam-beam wire compensation • → novel operating regime for hadron colliders, beam generation • =3.75 m • smaller transverse emittance • → constraint on new injectors, off-d b-beat • =1 radian LARP CM13 Meeting, Nov. 4-6, 2009, Chandra Bhat

4. ECLOUD Simulationsfor Gaussian and Flat bunches Average Heat Load 2nd Batch Humberto Maury Cuna, CINVESTAV, Mexico Frank Zimmermann (CERN) and Humberto Maury Cuna, (CINVESTAV, Mexico) Nominal LHC Beam Ultimate LHC Beam Conclusions: The estimated heat load from the e-cloud effects on LHC cryogenics with flat bunches is about two times smaller than that with Gaussian bunches at the same bunch int.. Without satellite Without satellite  50 nsec LARP CM13 Meeting, Nov. 4-6, 2009, Chandra Bhat

5. “Flat Bunches” Types and Generation Larger E Smaller E E t t • There are two distinct methods to create flat bunches • Barrier rf • Resonant rf systems • Double, triple or multiple harmonic rf system • Longitudinal hollow bunches, Carli’s technique t and E t Flat Bunches come in two forms LARP CM13 Meeting, Nov. 4-6, 2009, Chandra Bhat

6. Flat Bunches in the Fermilab Recycler(2000 - Present) Broad-band RF Cavities #of Cavities=4, Vrf=2kV, 10kHz-100MHz, Rs~50, Two Flat Bunches of unequal Int. Single Flat Bunch V RF t Multiple Flat Bunches of unequal Int. 9.3 sec RF Waveforms Line-charge Distribution • Measurements • 35% drop in peak int. • 25% drop in E for • flat bunches LARP CM13 Meeting, Nov. 4-6, 2009, Chandra Bhat Beam

7. SPS Studies: Single Bunch, Local Loss of Landau Damping E. Shaposhnikova, T. Bohl, T. Linnecar, C. Bhat, T.Argyropoulos*, J.Tuckmantel Range of Vrf in the Experiment h2/h1=4 November 2008 BSM V4/V1=0.25, Beam Energy = 270 GeV # of Bunches = 1-4, Intensity1E11 (L=0.4 eVs) Bucket Length=5 nsec 0.9nsec 1.22nsec • Conclusions (for h4/h1=4) : • BLM is unstable under almost all time & • BSM is more stable almost all time. Experiment with a single harmonic rf wave also showed the signs of instability(?!?). More studies are being carried out LARP CM13 Meeting, Nov. 4-6, 2009, Chandra Bhat What is going on here?

8. PS Studies at 26 GeV: Stable Flat Bunches using Double-harmonic rf System C. Bhat, H. Damerau, S. Hancock, E.Mahner, F.Caspers using LHC25 10 MHz RF system only, 32 kV at h = 21 Vrf(h=21)=31kV and Vrf(h=42)=16 kV Std. Bunches Flat Bunches h2/h1=2 V2/V1=0.5 LE(4)= 1.45 eVs I=840E10/batch Bunches in Double harmonic RF Bunches in single harmonic RF Last two bunches h = 21 h = 21+42 • Conclusions • Beam in h=21 showed coupled bunch oscillations • Beam in DOUBLE HARMONIC rf became stable (~for 120 ms) C. M. Bhat, et. al., PAC2009 LARP CM13 Meeting, Nov. 4-6, 2009, Chandra Bhat

9. Beam Stability Criterion November 2008 Study • Large synchrotron frequency spread improves the stability. • If • inside the bucket, particles in the vicinity of this region can become unstable against collective instabilities. • As the slope of the rf wave is reduced to zero at the bunch center, the bunch becomes longer and synchrotron frequency spread is greatly increased. This increases Landau damping against coupled bunch instabilities. No Landau Damping V. I. Balbekov (1987) July 09 Study fsyn/fsyn(h=1@bunch length=0) Stable Beam A. Hofmann & S. Myers, Proc. Of 11th Int. Conf. on HEA, ISR-Th-RF/80-26 (1980) LARP CM13 Meeting, Nov. 4-6, 2009, Chandra Bhat

10. Flat Bunch Prospects for LHC(Simulation Studies with ESME) • Two scenarios for creating flat bunches at LHC have been investigated • Flat Bunches at 7 TeV using • 400 MHz + 800 MHz RF • 200 MHz + 400 MHz RF systems in the Ring • Flat Bunches creation at 450 GeV and acceleration LARP CM13 Meeting, Nov. 4-6, 2009, Chandra Bhat

11. Flat Bunches in the LHC at 7 TeV with 200 MHz and 400MHz rf Preliminary ESME Simulations Mountain Range Vrf(400MHz)=8MV Time for flattening 10s Normal Bunch E vs t • Conclusions: • The flat bunches are stable for l 2.5 eVs • lb 75 cm in the case of 200MHz+400MHz rf. • lb38 cm in the case of with 400MHz +800MHz rf. • Calculated drop in • Peak int. 25% • E 15% 2.5 eVs Vrf(200MHz)=3MV Vrf(400MHz)=1.5MV Flattened Bunch E vs t 2.5 eVs Remark: Required 200 MHz rf cavities exist. R. Losito et. al., EPAC2004 LARP CM13 Meeting, Nov. 4-6, 2009, Chandra Bhat

12. LPA Scheme – Some Options  (Normalized) = 3.75 m, Allowed Qsum<0.015 (LHC Design Rept. III) LPA Scheme Bunches with Harmonic RF Long. Profile Gaussian MHz 400+800 400 200+400 RF Combination 200+400 11.5 cm 7.55 Bunch Length (RMS) 22 17 LARP CM13 Meeting, Nov. 4-6, 2009, Chandra Bhat

13. ProposalTheoretical Investigations of Flat Bunch Scenarios for the LHC Luminosity Upgrade(November 4, 2009 )C. Bhat, H-J. Kim, F.-J. Ostiguy, T. Sen

14. Issues for Theoretical Investigations Proposing to do theoretical investigations on the following issues --   • For creation of flat bunches, investigate the use of • multiple harmonic cavities (perhaps 2 to 3 harmonics) and • barrier bucket system Specify • Optimal RF parameters • Beam intensity limits • Reevaluate impedance budget and constraints • If flat bunches are to be produced in one of the LHC upstream machines, explore beam instability issues for acceleration up to 7 TeV. • Single-bunch and multi-bunch instability issues.  LARP CM13 Meeting, Nov. 4-6, 2009, Chandra Bhat

15. Issues for Theoretical Investigations (cont.) • What are the optimal bunch and beam parameters for the LPA scheme with due consideration of the following • Integrated luminosity (i.e. luminosity and lifetime) • Emittance growth from beam-beam interactions, IBS • Instability growth rates • Beam loading compensation • Event pile-up: number, space and time resolution of events per bunch crossing • Beam losses • Investigate possible locations and effects due the cavities in the machine lattices.  • A hybrid scheme that would allow the FCC scheme to benefit from some of the advantages of flat bunches. This would be worth exploring. • Lower peak intensity decreases the e-cloud effect and space-charge effects • Lower momentum spread • Possibly better event resolution (spatial and time) in the detectors LARP CM13 Meeting, Nov. 4-6, 2009, Chandra Bhat

16. Existing Simulation Tools I have already shown some ESME simulation results. More to come • ESME • This is a 2D code to study longitudinal beam dynamics in (E, t)-phase space in synchrotrons. We will use it to address • Flat bunch creation and acceleration with single and multiple harmonic rf systems, • Beam in barrier buckets, • Longitudinal single and multi-bunch instability • Beam loading issues. • Beam-beam code BBSIM • This code will be used to study the impact of beam-beam interactions on the emittance growth. Comparisons between a longitudinal Gaussian profile and a flat profile will be made for the LPA and for the FCC schemes. •  Vlasov solver • This will be used to investigate long term beam stability and particle losses. Also, 1) extract spectral information and 2) help establish the optimal ratio of harmonic amplitudes and bunch length, in the presence of realistic impedances. LARP CM13 Meeting, Nov. 4-6, 2009, Chandra Bhat

17. Summary • The flat bunch scheme is a viable path for the LHC luminosity towards 1035 cm-2sec-1. But, there are a number of issues, may be unique to the LHC, that need to be investigated. • The results from studies in the PS and SPS are very encouraging and more experimental work is being carried out. • It will be useful to have a test 400MHz rf cavity (Vmin~2MV) in the SPS to conduct dedicated studies on beam instability in flat bunches. • I have discussed viable schemes for • flat bunch creation at 7TeV with 200MHz+400MHz /400MHz+800MHz systems • creation at 450GeV and acceleration to 7TeV Some problems need to be addressed. • A group is formed at Fermilab to perform in-depth “Theoretical Investigations of Flat Bunch Scenarios for the LHC Luminosity Upgrade” under LARP (0.8FTE/YEAR, for two years) LARP CM13 Meeting, Nov. 4-6, 2009, Chandra Bhat

18. Flat Bunches with Double Harmonic RF during the Recent MDs at CERN • HeikoDamerau • Steven Hancock • Edgar Mahner • Fritz Caspers • Frank Zimmermann • Chandra Bhat • Elena Shaposhnikova • Thomas Bohl • Trevor Linnecar • TheodorosArgyropoulos • Joachim Tuckman • Chandra Bhat • Studies in PS • November 2008 • LHC-25 cycle, Flat Bunch at 26 GeV • Beam Intensity: ~8.42E12  Equivalent LHC nominal Intensity • Bunch Emittance:~1.4 eVs  Nominal emittance to LHC beam • RF with V(h=21)=31kV and V(h=42)=16kV  V42/V21~0.5, 0.0 • July 2009 • PS Cycle and Emittance same as above, Intensity about 15% larger • RF with V(h=21)=10kV and V42/V21=0.0 to 1.0 in steps of 0.1 • Studies in SPS • November 2008: Study on BLM and BSM • Coasting beam at 270 GeV • # Bunches =4, with bunch separation of 520 nsec • Bunch intensity and emittances similar to Nominal LHC beam • RF with V(800MHz/200MHz) = 0.25, with varieties of V(200MHz) • July 2009: Study on BLM and BSM • Studies at 26 GeV • # Bunch= 1, Varying Bunch Intensity and emittance (max. comparable to LHC beam) • RF with V(800MHz)/V(200MHz) = 0.25 and .1 , with V(200MHz)=1.7MV LARP CM3 Meeting, Nov. 4-6, 2009, Chandra Bhat

19. SPS Beam Studies(cont.): BSM and BLM(Preliminary) BLM BSM Bunch 1 Bunch 2 Bunch 1 Bunch 2 4 Bunch Length(nsec) Bunch 4 Bunch 4 Bunch 3 Bunch 3 Time(sec) Both BSM and BLM scenarios showed beam blowup The instability kicked in between 0-350 sec. The order in which a bunch becomes unstable was quite random Even though initial bunch parameters are nearly the same, they stabilized at different bunch properties LARP CM3 Meeting, Nov. 4-6, 2009, Chandra Bhat

20. Beam Studies in the PS at 26 GeV C. Bhat, H. Damerau S. Hancock, E.Mahner, F.Caspers ESME simulations • Simulations predicted • 20% increase in RMSW from beginning of rf manipulation to the flattened bunch • Bunches in these double harmonic rf buckets should be stable with LHC beam parameters. Previously, the studies with double harmonic rf at PSB at CERN (A. Blas et. al., PS/ RF/ Note 97-23 (MD)) have shown beam becoming unstable, in contrast to these simulations. Hence, more studies were undertaken in the PS LARP CM3 Meeting, Nov. 4-6, 2009, Chandra Bhat

21. Bunch Flattening of the LHC Beam at 7 TeVwith 400 MHz and 800MHz rf Vrf(400MHz)=16MV + Vrf(800MHz)=8.5MV Vrf(400MHz)=16MV Mountain Range Normal Bunch Flattened Bunch E vs t E vs t 2.5 eVs Preliminary Synchrotron Tune vs ½ Bunch Length Line charge Distribution Line charge Distribution lb=41cm z=7.5cm Energy Distribution Energy Distribution E=3.2GeV rms=0.72GeV E=2.6GeV rms=0.6GeV Conclusions: The 41 cm long flat bunches (2.5 eVs) with 400MHz+800MHz rf systems may be susceptible to beam instability. LARP CM3 Meeting, Nov. 4-6, 2009, Chandra Bhat

22. Luminosity and Beam-beam Tune-shifts for Colliding Beams cCrossing angle c/2 c/2 Luminosity for single crossing is given by, Incoherent beam-beam tune shift due to additional focusing and defocusing EM force caused by one beam on the other beam is given by, Ref: 1. F. Ruggiero and F. Zimmermann PRST-AB-Vol. 5, 061001 (2002)) and 2. Heiko Damerau, Ph. D. Thesis 2005 LARP CM3 Meeting, Nov. 4-6, 2009, Chandra Bhat

23. Luminosity ExpressionsGaussian and Rectangular Colliding Beams Luminosity for two colliding beams with Gaussian (RMS bunch length=“z“) line-charge distributions is, Luminosity for two colliding beams with Rectangular line-charge distributions of bunch length “lb” is, where, frev, Np, nb, and  are revolution frequency, Number of protons/bunch, number of bunches/beam and RMS transverse size of the colliding beam, respectively. LARP CM3 Meeting, Nov. 4-6, 2009, Chandra Bhat

24. Beam-beam Tune-shiftsGaussian and Rectangular Colliding Beams The total beam-beam spread for colliding beams with two interaction points in the ring – one crossing horizontally and another crossing vertically but with similar values of crossing angles c. Assuming no shielding inside the detector of lengthldet The beam-beam spread for colliding rectangular beams is , with, rp= classical radius of the proton. LARP CM3 Meeting, Nov. 4-6, 2009, Chandra Bhat

25. Special Cases of Beam-beam Tune-shifts For Gaussian bunches with small cwith sin(c) c& cos(c ) 1and  *<<z<< * at the interaction points, and then one can show that, Similarly, for the rectangular bunches with small cand  *<<z<< * also with *c / *>>1 Difficult Now, by taking the ratio of these two expressions one can show that, the Luminosity of rectangular bunch crossing is a factor of 2 larger than that of a Gaussian bunch crossing if QFTotal= QGTotaland lb = 2 z . Advantageous Easy However, LARP CM3 Meeting, Nov. 4-6, 2009, Chandra Bhat

26. Examples from the July 09 Studies A first look Beam (4) Emittance = 1.45 eVs, Batch intensity=924E10 2009-07-14_LHC25_FlatTop_10kVh21_0kVh42_cb_18b_c Std. Bunches BL=65nsec 2009-07-14_LHC25_FlatTop_10kVh21_5kVh42_cb_18b_b Flat Bunches BL=65nsec Beam became unstable near the end of the cycle LARP CM3 Meeting, Nov. 4-6, 2009, Chandra Bhat