1. Preservation of Magnetized Beam Quality in a Non-Isochronous Bend
Chris Tennant
Jefferson Laboratory
JLEIC Collaboration Meeting | March 29-30, 2016

2. Outline Longitudinal Match 180° Recirculation Arc “S2E” Results
iterative process with front end (injector, merger)
180° Recirculation Arc
“S2E” Results
Linac Scan
Lattice Functions
Tracking Results
Emittance
Summary

3. Match from dechirper to solenoid
Parameters
pinj = 5 MeV/c
pmax = 55 MeV/c
fRF = 952 MHz
Qbunch = 420 pC
sz = 2 cm (full) (at cooling channel)
sdp/p = 3×10-4 (rms) (at cooling channel)
sx=y = 1 mm (at cooling channel)
Bsolenoid = 1 T
Beam: magnetized
 bx=y = 0.37 m  en,drift = 289 mm-mrad
dechirper
linac
180° arc
solenoid
Match from linac to arc
Match from dechirper to solenoid

4. Match from dechirper to solenoid
Longitudinal Match
Required: electron beam parameters at cooler
defines linac phase set points
defines compaction requirements (R56, T566)
linac
solenoid
Match from linac to arc
Match from dechirper to solenoid
180° arc
dechirper
Iterative process with the front end development
Linac: -15 degrees
Arc: R56 = m, T566 = m
Dechirper: zero-crossing

5. Arc Architecture
Utilize indexed dipoles to provide azimuthally symmetric focusing  preserve magnetization
Avoid envelope modulation  avoid space charge driven degradation
With uniform bending the dispersion is large and it is difficult to achieve desired R56
introduce reverse bending
Three bend achromats (TBA) with reversed center bend
2 four-period achromats
TBA period, ¼-integer tunes
angles chosen to set compaction (q1= o, q2= o)
(courtesy D. Douglas)

6. Arc Momentum Compactions

7. Arc Lattice Functions

8. 1 Tesla Cooling Solenoid
Cooler ERL Layout
Magnetized Gun
Booster
50 MeV Linac Cryomodule
De-chirper
Chirper
Ion Beam
1 Tesla Cooling Solenoid
Beam dump
start
end

9. Initial Beam: Linac Entrance
st = 21 ps (6.3 mm) full
sdp/p = 2.1% full (sdp = 105 keV full)
bx,y = 2.00 m
ax,y = -0.50
Create flat beam (i.e. ex = 586 mm-mrad, ey = 4.0 mm-mrad) and apply flat-to-round-beam transform
Transverse: Gaussian distribution
Longitudinal: Hard-edge distribution

10. Round Beam

11. Beam Envelopes

12. Flat-to-Round-Beam Transform
Flat to round beam transform for arbitrary b and a (JLAB-TN )
= 𝛼 𝛽 −𝛾 1−𝛼 1−𝛼 −𝛽 𝛾 1+𝛼 1−𝛼 −𝛽 𝛾 1+𝛼 1+𝛼 𝛽 −𝛾 1−𝛼
Flat Beam
Round Beam

13. Linac Entrance
Inject at 5 MeV/c
21 ps
105 keV

14. Linac Exit: elegant
Six 5-cell 952 MHz cavities
Operate at -15°

15. Arc Exit: elegant R56 = +0.55 m, T566 = -1.5 m
2 cm bunch length (full)

16. De-chirper Exit: elegant
Single 5-cell 952 MHz cavity with 3.65 MV gain
Operate at zero crossing
25 keV
(4.5×10-4)

17. Lattice Functions

18. Lattice Functions

19. Transverse Emittance: 0 pC

20. RMS Beam Sizes: TStep (420 pC)

21. (x,y) Phase Space: TStep (420 pC)
linac entrance
linac exit
arc entrance
arc exit
de-chirper exit
solenoid entrance

22. Solenoid Entrance: Transverse
sx = sy = 1 mm

23. (t,p) Phase Space: TStep (420 pC)
linac entrance
linac exit
arc entrance
arc exit
de-chirper exit
solenoid entrance

24. Solenoid Entrance: Longitudinal
100 keV (full)
can be further optimized to remove slope/curvature
no gross distortion from space charge wake
2 cm (full)

25. How are We Doing?!
An inverse flat-beam-transform (FBT) segregates the basis: magnetized modes go to one plane, Larmor modes go to the other
magnetized modes: defines beam size in cooling channel
drift emittance  “x plane” emittance after inverse FBT
Larmor modes: control the cooling rate
cyclotron emittance  “y plane” emittance after inverse FBT
(courtesy D. Douglas)

26. Round-to-Flat-Beam Transform: 420 pC
307 mm-mrad
581 mm-mrad
313 mm-mrad
25 mm-mrad

27. Cooler Design: An Iterative Process
COOLING RATE
IBS RATE
Aperture Constraints
Beam Size
Linac Re-design
Longitudinal Match
Bunch Charge
Not included: linac scan required for changes in bunch charge, beam size
Bunch Length
Collective Effects
Arc Re-design
B-Field
Transverse Match

28. Adding the “Start” to S2E
Next iteration of S2E must include the beam formation process
gun (400 keV), booster (400 keV  5 MeV), merger (5 MeV)
Space charge will induce unwanted correlations
need to assess impact on transverse matching and cooling rate

29. Summary We are converging on beam parameters for the cooler
Have a complete longitudinal match
Reducing the bunch length eases constraints on momentum compactions, de-chirper system and potential longitudinal phase space distortion
Results of particle tracking through the recirculation arc – with space charge – are encouraging
Need to take care in matching the beam from the linac
Still to investigate:
How does the system perform after we integrate front end?
Collective effects (mBI gain, CSR, BBU)
Cooling efficiency with degraded beam? Sensitivities?

31. 1 Tesla Cooling Solenoid
Emittance Evolution
Magnetized Gun
Booster
50 MeV Linac Cryomodule
De-chirper
Chirper
Ion Beam
1 Tesla Cooling Solenoid
Beam dump

32. Describing A Round Beam
Ideally, a round beam can be described via the sigma matrix in the following way (TN ):
We note that at the exit of the linac, the distribution from TStep contains many coupling terms that are not strictly zero 𝛽𝜖
−𝛼/ 1+ 𝛼 2
1/ 1+ 𝛼 2 𝛾𝜖
−1/ 1+ 𝛼 2
𝜎 55
𝜎 56
𝜎 66
2.16E-03
9.73E-01
0.00E+00
2.33E-01
5.51E-04
-2.33E-01
3.00E-03
1.00E-03
2.16E-03
9.73E-01
-8.93E-05
2.30E-01
-1.07E-02
-1.11E-02
5.51E-04
-2.30E-01
-2.37E-04
4.87E-03
4.80E-03
2.43E-03
2.29E-03
4.95E-12
9.98E-01
9.42E-03
Description of an ideal beam at linac exit
Actual description of beam at linac exit