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 2017October 10-12, 2017

Brookhaven National Lab, Upton NY

EIC Collaboration Meeting, October 10-12, 2017 1

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 2

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

ion beamion beam magnetization flip

top ring: CCR

bottom ring: ERL

injectorbeam dump linacfast extraction kicker fast injection kicker

De-chirper Re-chirper

circulating bunchesseptum

vertical bend

magnetization flipB < 0 B < 0B > 0B > 0

septum

EIC Collaboration Meeting, October 10-12, 2017 3

Strong Cooler Specifications (Electrons)• Energy 20–55 MeV • Charge 3.2 nC• CCR pulse frequency 476.3 MHz• Gun frequency 43.3 MHz• Bunch length (tophat) 2 cm (23°)• Thermal (Larmor) emittance <19 mm-mrad • Cathode spot radius 2.2 mm• Cathode field 0.1 T 3• Gun voltage 400 kV• Normalized hor. drift emittance 36 mm-mrad• rms Energy spread (uncorr.)* 3x10-4

• Energy spread (p-p corr.)* <6x10-4

• Solenoid field 1 T• Electron beta in cooler 37.6 cm• Solenoid length 4x15 m• Bunch shape beer can

EIC Collaboration Meeting, October 10-12, 2017 4

Cooler Specifications (protons)Case 1 – 63.3 GeV center of mass energy• Energy 100 GeV• Particles/bunch 2.0x1010

• 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 GeV center of mass energy• Energy 100 GeV• Particles/bunch 6.6x109

• 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 5

Need to Match Cooling Rate with IBSProton beam (CM energy 63.5 GeV)

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

Electron beam 3.2 nC

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 6

Consequence of Mismatch

o Proton beam (CM energy 63.5 GeV): Energy: 100 GeV Proton number: 0.804x1010 (82%) Normalized emit. (rms):

0.50/0.15 μm Beta function in cooler: 60/200 m

Electron beam 3.2 nC

Longitudinal overcooling reducesthe bunch length, which increasesthe charge density and thus theIBS rate. Transverse equilibrium isbroken.Could decrease RF to keep bunchlong.

EIC Collaboration Meeting, October 10-12, 2017 7

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 8

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 9

Weak Cooler Specifications (Electrons)• Energy 20–55 MeV • Charge 420 pC• Gun frequency 476.3 MHz• Bunch length (tophat) 2 cm (23°)• Thermal emittance <19 mm-mrad • Cathode spot radius 2.2 mm• Cathode field 0.1 T 3• Gun voltage 400 kV• Normalized hor. drift emittance 36 mm-mrad• rms Energy spread (uncorr.)* 3x10-4

• Energy spread (p-p corr.)* <6x10-4

• Solenoid field 1 T• Electron beta in cooler 37.6 cm• Solenoid length 4x15 m• Bunch shape beer can

EIC Collaboration Meeting, October 10-12, 2017 10

ERL (Weak cooling) Design Status

• Injector output is 420 pC at 476.3 MHz• All transport is locally symmetric• Have completed S2E and I2E 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.• I2E looks good but we have not been able to produce the initial distribution

from injector simulations.

Start of Injector-to-End (I2E) simulations

EIC Collaboration Meeting, October 10-12, 2017 11

Transverse behavior in ERL (I2E)

• 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 12

Larmor emittance vs. Distance

Location I2E420 pC

I2E420 pC + CSR

S2E420 pC

Ideal2 nC

Initial Distribution 2.0 2.0 2.0 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

Big challenge: preserving the emittance in the injector merger.

EIC Collaboration Meeting, October 10-12, 2017 13

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 injectionEach of these has advantages and disadvantages. We are exploring both to find the best solution.

EIC Collaboration Meeting, October 10-12, 2017 14

Longitudinal Distribution at Cooling Solenoid

420 pC I2E

420 pCS2E

420 pC I2Ew/CSR

2 nCI2E

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S2E beam after Booster

EIC Collaboration Meeting, October 10-12, 2017 16

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 17

Challenges in the Strong Cooling Design

• Increased charge enhances space charge and CSR forces, but long pulse raises the possibility of shielding.

• Locally symmetric arcs are difficult at 55 MeV 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.

B < 0 B < 0B > 0B > 0

EIC Collaboration Meeting, October 10-12, 2017 18

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 19

after 20 turnsinitial

Correct Slew with RF cavity

Use RF cavity to remove chirp and reaccelerate the beam.

EIC Collaboration Meeting, October 10-12, 2017 20

Microbunching Gain using C.Y. Tsai Code• µBI gain is ≤ unity• needs to be less than unity for multiple passes (gain grows

exponentially)

EIC Collaboration Meeting, October 10-12, 2017 21

Exchange Region Layout

• CCR back leg

• ERL to CCR

EIC Collaboration Meeting, October 10-12, 2017 22

DIMAD Simulations After 11 Passes Through Exchange

• No CSR• No Space

charge

• All 6D 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 23

Magnetized Source (see Mamun’s talk)

• Magnetized Source for e-cooler at 32 mA: A high charge (420 pC) magnetized source is funded by the Jefferson Lab LDRD program that should operate up to 32 mA average current. This project concludes in 2018.

Magnetized beam parameters:• 𝑎𝑎0 = 1 – 5 mm, Bz = 0 – 2 kG • Bunch charge: 1 – 500 pC• Frequency: 15 Hz – 476.3 MHz• Bunch length: 10 – 100 ps• Average beam currents up to 32

mA• Gun high voltage: 200 – 350 kV

EIC Collaboration Meeting, October 10-12, 2017 24

Injector Design

EIC Collaboration Meeting, October 10-12, 2017 25

Start to Merge Simulation

EIC Collaboration Meeting, October 10-12, 2017 26

Where are We, and Where Do We Go?ERL Design

Add doglegs and update injector design. Calculate collective effects (BBU, ion trapping, halo formation)

Beam exchange designLinac design

Optimize HOM damping. Consider 3rd harmonic cavity for CCR operation.

Cooling Insertion Balance cooling partition Specify solenoid tolerances

CCR Design Microbunching gain is low. Explore shielding Calculate collective effects (ion trapping, wakes, resonances)

o Injector design Magnetization is preserved up to end of booster Need to try lower frequency

o Merger Design Many options to explore Might be able to just go straight in (straight merger).EIC Collaboration Meeting, October 10-12, 2017 27

Thank you!

EIC Collaboration Meeting, October 10-12, 2017 28

Bunched Beam Electron Cooling Observed !

Institute of Modern Physics (IMP), China

A collaboration of Jlab and IMP (China)

thermionic gun

cathode

anode pulsing grid

• 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)

• May 2016, 1st experiment: bunched beam electron cooling was observed for the 1st time

• Nov. 2016, machine development (improving beam diagnostics) • April 2017, 3rd experiment: more measurements (data under analyses)

4/26, Log 1.2, e pulse = 1 us, Vrf = 1.43/1.2 kV (W/R), Ie = 66.35/9.5 mA, run 1, 2579-2593

ion 12C+6 intensity signal from i-BPM

Electron current signal from e-BPM

Total 200 turns=885.4uselectron cooling pulses uncooled ion bunch position

cooled bunch position

EIC Collaboration Meeting, October 10-12, 2017 29

Multi-Step Cooling for High Luminosity• Cooling of JLEIC proton/ion beams

• Achieving very small emittance (~10x reduction) & very short bunch length ~1 cm (with SRF)• Suppressing IBS induced emittance degradation

• high cooling efficiency at low energy & small emittance

dzcool 42~ εσγγγτ ∆

Ring FunctionsProton

kinetic E (GeV)

Lead ionkinetic E (GeV/u)

Electron kinetic E

(MeV)

Cooler type

booster ring

Accumulation of positive ions

0.1(injection) 0.054 DC

collider ring

Maintain emitt. during stacking

2 (injection)

1.1 DC

Pre-cooling for emitt. reduction

7.9 (injection)

7.9 (ramp to) 4.3 DC

Maintain emitt. during collision Up to 100 Up to 40 Up to 54.5 ERL

Pre-cool when energy is low

Cool when emittance is small(after pre-cool at low energy)

ion sources

ion linac

booster (0.285 to 8 GeV)

collider(8 to 100 GeV)

DC/ERL cooler

DC cooler

Can’t reduce emittance due to space charge limit

ERL cooler can’t reach energy below 20 MeV

Pre-cooling both protons and lead ions

EIC Collaboration Meeting, October 10-12, 2017 30

Possible Merger Option

Septum Magnet

RF Separator with Superposed Magnetic Field

ERL Cryomodule

Injected Beam

Injector 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 31

Waveforms

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

RFDCRF+DC

Injected Bunch Recirculated Bunch

EIC Collaboration Meeting, October 10-12, 2017 32

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 µBI

• Requires transfer of long bunch• Must be observant of kicker (non)linearity…

EIC Collaboration Meeting, October 10-12, 2017 33

Kicker Dynamics• Kick generated by superposition of waveforms

• e.g. “fewest modes” configuration: kicker fundamental + 4 harmonics

• Kick angle as function of time:

∆𝑦𝑦′ = Δ𝜃𝜃𝐷𝐷𝐷𝐷 + �𝑛𝑛=1

𝑁𝑁

𝑔𝑔𝑛𝑛 cos𝑛𝑛

𝑁𝑁𝑏𝑏𝑏𝑏𝑛𝑛𝑏𝑏𝑏(𝜔𝜔𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑡𝑡 − 𝜑𝜑𝐵𝐵)

• 𝜑𝜑𝐵𝐵 = 2𝜋𝜋𝜋𝜋 = phase of bunch train B centroid at beam fundamental, B=0,1,2,...,Nbunch-1

• Δ𝜃𝜃𝐷𝐷𝐷𝐷 = DC offset (to null “unkicked” bunches)• 𝜔𝜔𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 = angular frequency of beam fundamental• Nbunch = number of bunches in full waveform period• t = temporal offset of test ray from centroid of bunch B

normalized kick v. beam RF fundamental phase (degrees) (Nbunch=11)

EIC Collaboration Meeting, October 10-12, 2017 34

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 35

Optics Requirements/Constraints

• ¼-wave EK to S, S to IK; ½-wave EK to IK𝑀𝑀𝐸𝐸𝐸𝐸→𝑆𝑆 = 𝑀𝑀𝑆𝑆→𝐼𝐼𝐸𝐸~ 0 𝛽𝛽

−1/𝛽𝛽 0 ; 𝑀𝑀𝐸𝐸𝐸𝐸→𝐼𝐼𝐸𝐸 = 𝑀𝑀𝑆𝑆→𝐼𝐼𝐸𝐸𝑀𝑀𝐸𝐸𝐸𝐸→𝑆𝑆~ −1 00 −1

• ¼-wave PREK to S; ½-wave PREK to IK (same matrices)• ¼-wave S to PSTK; ½-wave EK to PSTK (same matrices)• dispersion management ⇒ full wave VDD to S, S to VRD

𝑀𝑀𝐸𝐸𝐸𝐸→𝑆𝑆 = 𝑀𝑀𝑆𝑆→𝐼𝐼𝐸𝐸~ 1 00 1

• Matching of ERL to/from exchange (up & downstream telescopes)• Matching of CCR to/from exchange (up & downstream telescopes)• Axially symmetric transport ERL to CCR, CCR to ERL• “Soft” constraints:

• Axially symmetric transport CCR to S, S to CCR• Axially symmetric transport ERL to S, S to ERL• Avoid excessively large or small beam envelope functions

• Aberration control, error sensitivity• Halo (no 100s of m); space charge (no pinches at few cm)

• Provision for phase space exchange in transport from ERL linac back to ERL linac• Can be provided in recovery arc-to-linac transport

CCR

ERL

extraction kicker (EK) injection kicker (IK)

septum

vertical delivery dipole (VDD) vertical return dipole (VRD)

post-kicker (PSTK)pre-kicker (PREK)

EIC Collaboration Meeting, October 10-12, 2017 36