Magnetized Bunched Beam ERL Cooler Stephen Benson Slava

Magnetized Bunched Beam ERL Cooler Stephen Benson, Slava Derbenev, David Douglas, Fay Hannon, Andrew Hutton, Rui Li, Bob Rimmer, Yves Roblin, Chris Tennant, Haipeng Wang, He Zhang, Yuhong Zhang EIC Accelerator Collaboration Meeting 2017 October 10 -12, 2017 Brookhaven National Lab, Upton NY EIC Collaboration Meeting October 10 -12, 2017

Outline • Bunched beam Cooler design specifications • Cooling partition issue • ERL (weak cooling) simulations • CCR (strong cooling) design issues. • Injection/extraction scheme • Injector design • Summary (future work) EIC Collaboration Meeting October 10 -12, 2017

Baseline Design is Cooling Ring Fed by ERL • Same-cell energy recovery in 952. 6 MHz SRF cavities • Uses harmonic kicker to inject and extract from CCR (divide by 11) • Assumes high charge, low rep-rate injector (w/ subharmonic acceleration and bunching) • Use magnetization flips to compensate ion spin effects top ring: CCR magnetization flip ion beam B>0 B<0 septum B<0 injector circulating bunches extracted De-chirper B>0 linac beam dump fast extraction kicker ion beam magnetization flip septum fast injection kicker injected vertical bend Re-chirper bottom ring: ERL EIC Collaboration Meeting October 10 -12, 2017

Strong Cooler Specifications (Electrons) • • • • Energy Charge CCR pulse frequency Gun frequency Bunch length (tophat) Thermal (Larmor) emittance Cathode spot radius Cathode field Gun voltage Normalized hor. drift emittance rms Energy spread (uncorr. )* Energy spread (p-p corr. )* Solenoid field Electron beta in cooler Solenoid length Bunch shape 20– 55 Me. V 3. 2 n. C 476. 3 MHz 43. 3 MHz 2 cm (23°) <19 mm-mrad 2. 2 mm 0. 1 T 3 400 k. V 36 mm-mrad 3 x 10 -4 <6 x 10 -4 1 T 37. 6 cm 4 x 15 m beer can EIC Collaboration Meeting October 10 -12, 2017

Cooler Specifications (protons) Case 1 – 63. 3 Ge. V center of mass energy • Energy 100 Ge. V • Particles/bunch 2. 0 x 1010 • Repetition rate 158. 77 MHz • Bunch length (rms) 2. 5 cm • Normalized emittance (x/y) 1. 2/0. 6 mm-mrad • Betatron function in cooler 100 m (at point between solenoids) Case 2 – 44. 7 Ge. V center of mass energy • Energy 100 Ge. V • Particles/bunch 6. 6 x 109 • Repetition rate 476. 3 MHz • Bunch length (rms) 1. 0 cm • Normalized emittance (x/y) 1. 0/0. 5 mm-mrad • Betatron function in cooler 100 m (at point between solenoids) Ion ring lattice may be coupled or dispersed in solenoid. Ion beam may be partially offset from the electron beam. EIC Collaboration Meeting October 10 -12, 2017

Need to Match Cooling Rate with IBS Proton beam (CM energy 63. 5 Ge. V) Electron beam 3. 2 n. C Units x y z Cooling rate 10 -3 1/s -0. 431 -1. 434 -1. 605 IBS rate 10 -3 1/s 3. 192 0. 102 0. 618 Total rate 10 -3 1/s 2. 761 -1. 332 -0. 987 In horizontal direction, cooling is about one order weaker than IBS. To find equilibrium: Apply dispersion at cooler to transfer longitudinal cooling to transverse directions Apply transverse coupling to transverse horizontal IBS to vertical direction Increase proton beam emittance Decrease proton bunch charge • • EIC Collaboration Meeting October 10 -12, 2017

Consequence of Mismatch o Proton beam (CM energy 63. 5 Ge. V): § Energy: 100 Ge. V § Proton number: 0. 804 x 1010 (82%) § Normalized emit. (rms): 0. 50/0. 15 μm § Beta function in cooler: 60/200 m Longitudinal overcooling reduces the bunch length, which increases the charge density and thus the IBS rate. Transverse equilibrium is broken. Could decrease RF to keep bunch long. EIC Collaboration Meeting October 10 -12, 2017 Electron beam 3. 2 n. C

Cooling Simulations (See He Zhang’s talk) A few main issues: • Working in a new parameter regime. Can we trust Betacool? • Fixing the partition problem. • Benchmarking the code. Some progress with IMP measurements. EIC Collaboration Meeting October 10 -12, 2017

Cooler Development History Develop Figure 8 cooler CCR concept Fall 2013 CCR option de-scoped due to µBI issues Spring 2014 Magnetized cooler solution chosen Spring 2015 µBI suppression developed 2014 -16 Harmonic Kicker Prototype developed Summer 2016 ERL solution (weak cooling) developed Fall 2016 Change back to CCR solution Fall 2016 EIC Collaboration Meeting October 10 -12, 2017

Weak Cooler Specifications (Electrons) • • • • Energy Charge Gun frequency Bunch length (tophat) Thermal emittance Cathode spot radius Cathode field Gun voltage Normalized hor. drift emittance rms Energy spread (uncorr. )* Energy spread (p-p corr. )* Solenoid field Electron beta in cooler Solenoid length Bunch shape 20– 55 Me. V 420 p. C 476. 3 MHz 2 cm (23°) <19 mm-mrad 2. 2 mm 0. 1 T 3 400 k. V 36 mm-mrad 3 x 10 -4 <6 x 10 -4 1 T 37. 6 cm 4 x 15 m beer can EIC Collaboration Meeting October 10 -12, 2017

ERL (Weak cooling) Design Status • • Injector output is 420 p. C at 476. 3 MHz All transport is locally symmetric Have completed S 2 E and I 2 E simulations for ERL design Would eventually want to use two helicity exchanges and four solenoids. • Have not yet included the cooling leg merger and demerger. • I 2 E looks good but we have not been able to produce the initial distribution from injector simulations. Start of Injector-to-End (I 2 E) simulations EIC Collaboration Meeting October 10 -12, 2017

Transverse behavior in ERL (I 2 E) • Start with ideal distribution at booster exit (above). • Find rms beam size vs. distance without (top) and with (bottom) CSR • No re-optimization performed with CSR. EIC Collaboration Meeting October 10 -12, 2017

Larmor emittance vs. Distance Location I 2 E 420 p. C + CSR S 2 E 420 p. C Ideal 2 n. C 2. 0 Merger Exit 3. 01 7. 24 2. 72 15. 96 Linac Exit 2. 87 7. 09 2. 79 23. 59 Arc 1 Exit 3. 03 7. 32 2. 80 22. 42 Solenoid Entrance 3. 02 7. 26 2. 76 22. 45 Arc 2 Exit 3. 46 6. 60 3. 98 22. 19 Linac Exit 4. 44 7. 79 4. 06 22. 92 Initial Distribution Big challenge: preserving the emittance in the injector merger. EIC Collaboration Meeting October 10 -12, 2017

Merger Options We are looking at several ideas for mergers: • Penner Bend • Double bend achromat • W-bend • Chicane • Double barrel linac cavities • RF separator based merger • Off axis injection Each of these has advantages and disadvantages. We are exploring both to find the best solution. EIC Collaboration Meeting October 10 -12, 2017

Longitudinal Distribution at Cooling Solenoid 420 p. C I 2 E w/CSR 420 p. C S 2 E 2 n. C I 2 E EIC Collaboration Meeting October 10 -12, 2017

S 2 E beam after Booster EIC Collaboration Meeting October 10 -12, 2017

Harmonic Kicker (H. Wang) • Harmonic Beam Kicker. A first 952. 6 MHz copper cavity has been prototyped, bench measured, and satisfies beam dynamic requirements for a Circular Cooler Ring design for the bunched electron cooler. EIC Collaboration Meeting October 10 -12, 2017

Challenges in the Strong Cooling Design B<0 B>0 B<0 • Increased charge enhances space charge and CSR forces, but long pulse raises the possibility of shielding. • Locally symmetric arcs are difficult at 55 Me. V Globally symmetric arcs can work but must be tested one-by-one. • Need tools for simulating the system. Want CSR, LSC, and shielding. • Beams are big and halo creation and loss will be a problem. EIC Collaboration Meeting October 10 -12, 2017

CSR Induces Slew in Energy 5 -turns 10 -turns 20 -turns Initial bunch assumed to be super-Gaussian profile EIC Collaboration Meeting October 10 -12, 2017

Correct Slew with RF cavity after 20 turns initial Use RF cavity to remove chirp and reaccelerate the beam. EIC Collaboration Meeting October 10 -12, 2017

Microbunching Gain using C. Y. Tsai Code • m. BI gain is ≤ unity • needs to be less than unity for multiple passes (gain grows exponentially) EIC Collaboration Meeting October 10 -12, 2017

Exchange Region Layout • CCR back leg • ERL to CCR EIC Collaboration Meeting October 10 -12, 2017

DIMAD Simulations After 11 Passes Through Exchange • No CSR • No Space charge • All 6 D Phase space projections shown • Hourglass shape due to Chromaticity • No large deformations in phase space after 11 passes. EIC Collaboration Meeting October 10 -12, 2017

Magnetized Source (see Mamun’s talk) • Magnetized Source for e-cooler at 32 m. A: A high charge (420 p. C) magnetized source is funded by the Jefferson Lab LDRD program that should operate up to 32 m. A average current. This project concludes in 2018. EIC Collaboration Meeting October 10 -12, 2017

Injector Design EIC Collaboration Meeting October 10 -12, 2017

Start to Merge Simulation EIC Collaboration Meeting October 10 -12, 2017

Summary: Where are We, and Where Do We Go? ü ERL Design Ø Add doglegs and update injector design. Ø Calculate collective effects (BBU, ion trapping, halo formation) ü Beam exchange design ü Linac design Ø Optimize HOM damping. Ø Consider 3 rd harmonic cavity for CCR operation. ü Cooling Insertion Ø Balance cooling partition Ø Specify solenoid tolerances ü CCR Design Ø Microbunching gain is low. Ø Explore shielding Ø Calculate collective effects (ion trapping, wakes, resonances) o Injector design Ø Magnetization is preserved up to end of booster Ø Need to try lower frequency o Merger Design Ø Many options to explore Ø Might be able to just go straight in (straight merger). EIC Collaboration Meeting October 10 -12, 2017

BACKUPS EIC Collaboration Meeting October 10 -12, 2017

Bunched Beam Electron Cooling Observed ! • All electron cooling to this day were performed using a DC electron beam • Cooling by a bunched electron beam is one critical R&D for JLEIC • Proof-of-Principle Experiment: using a DC cooler, modulating grid voltage of a thermionic gun to generate a pulsed beam (as short as ~100 ns) A collaboration of Jlab and IMP (China) • May 2016, 1 st experiment: bunched beam electron cooling was observed for the 1 st time • Nov. 2016, machine development (improving beam diagnostics) • April 2017, 3 rd experiment: more measurements (data under analyses) ion 12 C+6 intensity signal from i-BPM Institute of Modern Physics (IMP), China Electron current signal from e-BPM cooled bunch position thermionic gun electron cooling pulses uncooled ion bunch position Ti me pulsing grid ber um nn tur anode Total 200 turns=885. 4 us (us ) cathode Time (us) 4/26, Log 1. 2, e pulse = 1 us, Vrf = 1. 43/1. 2 k. V (W/R), Ie = 66. 35/9. 5 m. A, run 1, 2579 -2593 EIC Collaboration Meeting October 10 -12, 2017

Multi-Step Cooling for High Luminosity • Cooling of JLEIC proton/ion beams • Achieving very small emittance (~10 x reduction) & very short bunch length ~1 cm (with SRF) • Suppressing IBS induced emittance degradation Pre-cool when energy is low • high cooling efficiency at low energy & small emittance ion sources Ring ion linac DC cooler Functions booster (0. 285 to 8 Ge. V) DC/ERL cooler Proton kinetic E (Ge. V) Cool when emittance is small (after pre-cool at low energy) Lead ion kinetic E (Ge. V/u) 0. 1 (injection) Electron kinetic E (Me. V) Cooler type 0. 054 DC 1. 1 DC Can’t reduce emittance due to space charge limit 7. 9 (injection) 2 (injection) 7. 9 (ramp to) 4. 3 DC Pre-cooling both protons and lead ions Up to 100 Up to 40 Up to 54. 5 ERL booster Accumulation of ring positive ions Maintain emitt. during stacking collider Pre-cooling for ring emitt. reduction Maintain emitt. during collision collider (8 to 100 Ge. V) EIC Collaboration Meeting October 10 -12, 2017 ERL cooler can’t reach energy below 20 Me. V

Possible Merger Option Recir culate d Bea m Injected Beam Injector Cryomodule • • • Septum Magnet RF Separator with Superposed Magnetic Field ERL Cryomodule Use an RF Separator to separate the injected beam from the recirculating beam Immerse the RF Separator in a DC magnetic field Arrange timing and relative amplitudes so that the injected beam is not deflected – Bunches are at maximum of RF deflection – bunch center has zero slope This means that the kick seen by the recirculated beam is doubled Needs to be sufficient to provide adequate separation at the septum EIC Collaboration Meeting October 10 -12, 2017

Waveforms 2, 5 RF 2, 0 DC RF+DC 1, 5 1, 0 0, 5 0, 0 0 100 200 300 400 500 600 700 800 900 -0, 5 -1, 0 -1, 5 Injected Bunch Recirculated Bunch EIC Collaboration Meeting October 10 -12, 2017 1000 1100

Longitudinal Match • Use longitudinal match developed for ERL-based cooler (C. Tennant et al. , JLAB-TN in preparation) – off-crest acceleration bunch of modest length • induce chirp for downstream bunching • bunch long enough to mitigate space charge, short enough to stay within linac phase acceptance – debunch, dechirp during transport to cooling system – rechirp, compress during return transport for energy recovery – recover bunch of modest length with energy compression of chirp – Simply replace “ERL cooling system” with CCR – Invokes isochronous transport, avoids bunch length modulation in CCR • Mitigate m. BI – Requires transfer of long bunch • Must be observant of kicker (non)linearity… EIC Collaboration Meeting October 10 -12, 2017

Kicker Dynamics • normalized kick v. beam RF fundamental phase (degrees) (Nbunch=11) EIC Collaboration Meeting October 10 -12, 2017

From Schematic To Design • • • “Match” 8 quad telescope There is are 2 additional matches in the ERL – Present optimization adds a wavelength here and there… – between PREK and vertical step up • gives ½-wave transform PREK to IK (~¼ wave PREK to S) – between vertical step down and PSTK • gives ½-wave transform EK to PSTK (~¼ wave S to PSTK) Layout: Use figures from tech note. EIC Collaboration Meeting October 10 -12, 2017

Optics Requirements/Constraints injection kicker (IK) CCR extraction kicker (EK) septum pre-kicker (PREK) vertical delivery dipole (VDD) • EIC Collaboration Meeting October 10 -12, 2017 post-kicker (PSTK) ERL vertical return dipole (VRD)