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

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

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

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 = +0.55 m, T566 = -1.65 m Dechirper: zero-crossing

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= 20.4031o, q2=18.1531o) (courtesy D. Douglas)

Arc Momentum Compactions

Arc Lattice Functions

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

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

Round Beam

Beam Envelopes

Flat-to-Round-Beam Transform Flat to round beam transform for arbitrary b and a (JLAB-TN-15-026) = 1 2 1+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

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

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

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

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)

Lattice Functions

Lattice Functions

Transverse Emittance: 0 pC

RMS Beam Sizes: TStep (420 pC)

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

Solenoid Entrance: Transverse sx = sy = 1 mm

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

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

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)

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

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

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

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?

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

Describing A Round Beam Ideally, a round beam can be described via the sigma matrix in the following way (TN-15-026): 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