Update on ERL Cooler Design Studies S.V. Benson, March 9, 2017

Big Change: Baseline is now the CCR Same-cell energy recovery in SRF cavities Uses Yulu’s kicker design to inject and extract from CCR Assumes high charge injector (can be lower frequency) ion beam cooling solenoid (B>0) magnetization flip cooling solenoid (B<0) top ring: CCR bottom ring: ERL injector beam dump linac fast extraction kicker fast injection kicker dechirper rechirper circulating bunches extracted bunches injected bunches exchange septum vertical bend into ERL to CCR MEIC Collaboration Mtg. Oct. 6, 2015

Strong Cooler Specifications (Electrons) Energy 20–55 MeV 1 Charge 2.0 (3.2) nC CCR pulse frequency 476.3 MHz Gun frequency 23.82 MHz Bunch length (tophat) 2 cm (23°) Thermal emittance <19 mm-mrad 2 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 2x30 m 4 Bunch shape beer can MEIC Collaboration Mtg. Oct. 6, 2015

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 Particles/bunch 6.6x109 Repetition rage 476.3 MHz Bunch length (rms) 1.0 cm Normalized emttance (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. LERF Readiness Review 9/30/15

Electron Cooling (CM Energy 63.5 GeV) Proton beam (CM energy 63.5 GeV) Electron beam 2 nC Cooling rate 10-3 1/s -0.279 -0.914 -1.062 IBS rate 3.192 0.102 0.618 Total rate 2.913 -0.813 -0.443 Electron beam 3.2 nC Cooling rate 10-3 1/s -0.431 -1.434 -1.605 IBS rate 3.192 0.102 0.618 Total rate 2.761 -1.332 -0.987 In horizontal direction, cooling is about one order weaker than IBS. In the other two directions, cooling is stronger 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 beam current He Zhang

Electron Cooling (CM Energy 44.7 GeV) Proton beam (CM energy 44.7 GeV): Energy: 100 GeV Proton number: 0.804x1010 (82%) Normalized emit. (rms): 0.50/0.15 μm Beta function in cooler: 60/200 m Bunch size (rms): 0.528/0.528 mm Momentum spread: 8x10-4 Bunch length (rms): 1.5 cm Dispersion at cooler: 2.0/0.6 m Transverse coupling: 40% Longitudinal overcooling reduces the bunch length, which increases the charge density and thus the IBS rate. Transverse equilibrium is broken. Assume the longitudinal overcooling is compensated, for example, by choosing a specific RF phase (?). Electron beam 3.2 nC Electron beam 3.2 nC He Zhang

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

Round-to-Flat Beam Transform arc entrance arc exit 73.6 mm-mrad 73.7 mm-mrad 2.0 mm-mrad 2.1 mm-mrad

Round-to-Flat Beam Transform 74.7 mm-mrad 4.4 mm-mrad

(t,p) Evolution half-turn 1-turn 2-turns

(t,p) Evolution – Zoomed View 5-turns 10-turns 20-turns

Longitudinal Phase Space: 0.20 MV after 20 turns initial

MEIC Collaboration Mtg. Oct. 6, 2015 Critical Design Tasks Verify cooling model with Derbenev thesis formulas Is it really good to have an electron beam smaller than the proton beam? Should we scan the position and time? Can we use x/y coupling and dispersion in the proton ring to balance cooling? Can we recirculate the beam (CCR design)? How do we match into and out of the CCR? How do we make a 3.2 nC bunch and accelerate to 55 MeV? Solenoid non-uniformities (tools?) Need Merger Design for traditional ERL layout. MEIC Collaboration Mtg. Oct. 6, 2015

LERF Readiness Review 9/30/15 Conclusions Really starting over from scratch. Do not assume anything from the ERL. Emittance exchange is possible with longitudinal cavities Still have to figure out proper way to partition cooling to match IBS. Do not want to lose what we came up with for the ERL so we are documenting this. May be able to use globally symmetric arcs. Maintaining beam brightness in CCR with high charge is a real challenge! Need better tools. Still no solution for an injector. LERF Readiness Review 9/30/15

LERF Readiness Review 9/30/15 Backups LERF Readiness Review 9/30/15

Notes on Specifications 1 This assumes that the maximum proton energy is 100 GeV. If the maximum energy changes to 200 GeV, this must increase to 110 MeV. All the specifications below assume a beam energy of 55 MeV. 2 The measured thermal energy is 0.16 eV for CsKSb. This means that the thermal emittance is 0.56 mm-mrad/mm (rms) (see Bazarov et al. arXiv:1105.2221v1 “Thermal emittance measurements of cesium potassium antimonide photocathode”). Due to space charge we presume that there will be some effective growth in the emittance up to >1 mm-mrad. For a 1.1 mm radius spot size (rms spot size is 0.78 mm) the calculated thermal emittance should be 0.44 mm-mrad. We have to keep the emittance growth less than factor of 40. 3 We think the cathode field is limited by technical reasons to 0.2 T. We have chosen 0.1T to keep the beam large and reduce space charge forces. 4 The ion ring lattice is being designed with ~70 meters of space available for the cooling channel. The baseline assumes that we use all of this space with an angular momentum reverser in between. The second space has a solenoid of opposite polarity. 5 It is assumed that the proton beam emittance and energy spread are in equilibrium such that the IBS growth is matched by the cooling rate. The calculated horizontal spot size in the cooler is ~1 mm for these parameters. We will assume that the proton beam is uncoupled so that the vertical emittance is eventually much smaller than the horizontal emittance. LERF Readiness Review 9/30/15