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

2. 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

3. Strong Cooler Specifications (Electrons)
Energy 20–55 MeV 1
Charge 2.0 (3.2) nC
CCR pulse frequency MHz
Gun frequency 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

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

5. 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

6. 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

7. 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 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

8. 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

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

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

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

12. Longitudinal Phase Space: 0.20 MV
after 20 turns
initial

13. 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

14. 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

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

16. 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: v1 “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 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