Ya. Derbenev JLEIC R&D meeting 12.01.16 CASA Jefferson Laboratory Magnetized Electron Cooling at a non-magnetized e-gun     Ya. Derbenev JLEIC R&D meeting 12.01.16 CASA Jefferson Laboratory

Outline Why magnetized beam in cooling section ? Constraints of a magnetized injector for ERL Emittance Exchange idea and suitability Cooler with EmEx layout EmEx RF and transport evaluation Non-Magnetized Injector: rehabilitation and requests EmEx pros & cons Summary

Why the e-beam in cooling section must be magnetized? Reason #1: Space charge kick to angle spread is reduced by a big factor: (𝛿𝜃 ) 0 (𝛿𝜃 ) 𝐵 =2𝜋 𝐿 𝑐 𝜆 𝐿 =300 ! , 𝑎𝑡 𝐿 𝑐 =60 𝑀; 𝐵=1𝑇 ; 𝛾=100 ; (𝜆=2𝜋 𝛾𝑚 𝑐 2 𝑒𝐵 =1.25 𝑀) Reason # 2: Cooling rate in a strong solenoid has low sensitivity to electron transverse temperature 𝑇 𝑒⟘ Concerning the solenoid field misalignments: Short-wave beam velocity misalignments are equivalent to increase of the 𝑇 𝑒⟘ Long-wave misalignments can be controlled by BPMs

Constraints of a magnetized injector for ERL Classical solution for magnetized beam: put the and whole the RF injector to ERL in a continuous (warm 1-2 KGs) solenoid Technical problems: - High charge (2-4 nC) e-bunches must be long (up to 1ns) - Low frequency (large diameter) bunching/pre-accelerating cavities require large solenoid size - Difficulties with operation and access the cavities (cooling etc.)

“Innovations for potential use in EC” /Proposal for Research on Electron Beam for HEEC/ /JLEIC R&D meeting, CASA JLab, June 09, 2016/ Counter energy recovery beam (ERB) Annular beams for EC Magnetized high-average current low emittance thermionic electron source ERL-based magnetized EC using non-magnetized electron gun and longitudinal-to-transverse (LT) emittance exchange Non-magnetized flat beams low emittance thermionic e-guns (but still magnetized EC by use of EmEx and cooling solenoid) HEEC using electron storage ring A. Dual energy SR with ERL and EmEx B. High energy SR with EmEx

Magnetized EC using non-magnetized electron gun and longitudinal-to-transverse emittance exchange High charge/bunch current source of a non-magnetized electron beam Buncher, preaccelerator, ERL Emittance exchanger (EmEx) for the phase space manipulations. Flat to round beam transformer (FBR) Matching the rotating beam with solenoid ion beam 1T cooling solenoid 1T cooling solenoid helicity exchange chirper de-chirper FK septum Circulator ring septum FK FRB 50 MeV Linac EmEx Non-magnetized gun MnM cooler 5 MeV Booster dump The idea: Transfer a large longitudinal emittance after ERL into the horizontal transverse phase space, after that to the drift mode of the cooling solenoid - while the initial x-emittance becomes transferred into the longitudinal degree of freedom ! The initial y-emittance of a non-magnetized gun will then be automatically transformed to the Larmor emittance in solenoid

Fitting the EC requirements with EmEx Magnetized Bunched Beam Electron Cooling at a non-magnetized gun Y. Derbenev, D. Douglas, J. Grames, C. Hernandez, V. Morozov, M. Poelker, R. Rimmer, R. Suleiman, H. Wang, and Y. Zhang Abstract for IPAC 2017 We consider concept of an ERL-based high energy electron cooling (HEEC) facility for cooling ion beams in the future polarized Electron-Ion Collider of Jefferson Laboratory (JLEIC) which includes the following succession of the matched principal elements: 1) a non-magnetized pulse current electron gun (average current up to 200 mA) delivering 2 nC, 1 ns bunches of normalized transverse emittance about 1 micron; 2) RF compressor/pre-accelerator delivering short (1-2 cm) bunches; 3) 50 MeV energy recovery SRF linac delivering electron bunches of normalized longitudinal emittance about 500 microns; 4) longitudinal-to-transverse (horizontal) emittance exchanger (EmEx); 5) flat-to-round beam transformer (FRBT); 6) 1-2 T superconducting solenoid of cooling section. In result, e-beam arrives in cooling section essentially magnetized (typical Larmor radii of electrons about 30-50 microns at beam radii about 1mm). Another very important improvement thank to implementation of EmEx is very small resulting energy spread (< 𝟏𝟎 −𝟓 ) of the cooling beam. In this way organized e-beam transport allows one use of the well-known critical special features of the magnetized electron beam while avoiding difficult technical constraints of building a magnetized RF injector for ERL. This beam transport scheme can also be combined with the multi-turn recirculated cooling scheme based on implementation of the super-fast harmonic RF kickers which currently under development at JLab.

EmEx by use of a gradient RF mode 2 V V RF RF 1 3 𝐻 𝑖𝑛𝑡 =−𝐾𝑞𝑥− 𝑒 𝐸 𝐴 𝑠 𝑧,𝑥,𝑡 ; 𝐴 𝑠 ⟹𝐴 𝑠0 𝑧,𝑥 𝑠𝑖𝑛𝜑 ⟹ 𝜕 𝐸 𝑠0 𝜕𝑥 𝑥𝑠⟹ 2𝜋𝑒 𝜆 𝐵 𝑦0 (𝑧)𝑥𝑠 𝑞 ′ =− 1 𝐸 𝜕 𝜕𝑠 𝐻 𝑖𝑛𝑡 = 2𝜋𝑒 𝜆𝐸 𝐵 𝑦0 (𝑧)𝑥 𝑥 ′′ + 𝐾 2 −𝑛 𝑥=𝐾𝑞+ 2𝜋𝑒 𝜆𝐸 𝐵 𝑦0 𝑧 𝑠 𝑠 ′ = 𝛾 −2 𝑞−𝐾𝑥 1. D. Xiang “Overview of phase space manipulations of relativistic electron beams” AIP Conference Proceedings 1507, 120 (2012); 2. V. Balandin, W. Decking, N. Golubeva “Mirror Symmetric Chicane-type Emittance Exchange beamline with two deflecting cavities” IPAC 2015, Richmond, VA (2015).

EmEx by use of a bunching mode 2 V V RF RF 1 3 𝐻= 1 2 [ 𝑥 ′2 +( 𝐾 2 −𝑛) 𝑥 2 + 𝑦 ′2 +𝑛 𝑦 2 + 𝛾 −2 𝑞 2 + 2𝜋𝑒 𝐸𝜆 𝐸 𝑠0 𝑧 𝑠 2 ]−𝐾𝑥𝑞; 𝐻 𝑖𝑛𝑡 =−𝐾𝑥𝑞 𝑞 ′ =− 2𝜋𝑒 𝐸𝜆 𝐸 𝑠0 𝑠 𝑠 ′ =𝑞 𝛾 −2 −𝐾𝑥 𝑥 ′′ + 𝐾 2 −𝑛 𝑥=𝐾𝑞 𝑦 ′′ +𝑛𝑦=0

Rehabilitation of a non-magnetized injector DC or RF (SRF) gun Voltage 300 KV Impulse duration 1.4 ns Bunch charge 4 nC Peak current 2.8 A Repetition rate MHz 238 Beam radii 1 mm Average current mA SpCh energy gradient 0.2 KV Tr. emittance, norm. 1 𝝁𝑴 cathode anode 300 kV chirper dechirper preaccelerator solenoid ERL compression drift Bunch compressor Initial bunch length 42 cm Chirper frequency 238 MHz Voltage 400 KV Velocity chirp ± 0.25 Drift length 4 m Post bunch length 2 cm Sp.Ch. tr.energy gradient 18 KV Dechirper frequency 238 MHz Voltage 1.6 MV Preaccelerator (NC RF) Frequency 238 MHz Voltage 4.2 MV RF energy gradient 𝟏𝟎 −𝟑 SRF energy corrector

Pros & Cons of EmEx Pros: 1. Solenoid-free source and injector, small beam radii in ERL etc. 2. Allows for subtracting long bunches (large charge) 3. Easing the requirement to the post-acceleration energy spread 4. Low the resulting energy spread Cons: Insertion of LT EmEx ( SRF cavities and bends) after ERL

Requests for nM source DC Photo-gun: 200 mA; 10 cm long, 2nC bunches (?) Thermionic RF (SRF?) low frequency gun (10 cM or longer, 2-4 nC bunches; 1-2 A average current) Other RF operated thermionic guns Flat cathode gun (small vertical emittance at relatively large the horizontal one

HEEC using storage ring with EmEx Storage ring formed by two CCRs: Cooling Ring (CR) and Emittance Reduction Ring (ER), coupled through SRF ERL. CR is largely CS with the circulating 8-50 MeV CB. ER is essentially an undulator (wiggler) for the enhanced synchrotron radiation dumping/cooling. ER with wiggler only (no reduction in the energy spread; the IPAC 2016 paper by F. Lin et al. “Storage-ring electron cooler for relativistic ion beams”) ER with wiggler (short period, low dispersion) and emittance exchanger (EEX) for reducing the longitudinal emittance (energy spread) while retaining the low cyclotron emittance of the CB. Storage ring as the next stage for cooling hadron beams of the higher energy. In this case, the Storage ring is the CR, in addition to the CS with circulating CB includes EmEx (two) and the Radiated Energy Compensating Linac (ECL, few MeV, ~1A). Studies to determine the desirable Storage Rings energy ranges and to include into considerations, in particular, the IBS (inter and intra beam scattering) effects on the emittance and cooling efficiency among other important phenomena.