scaling vffag erhic design progress report june 24, 2013stephen brooks, erhic ffag meeting1
TRANSCRIPT
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Scaling VFFAG eRHIC Design
Progress Report
June 24, 2013 Stephen Brooks, eRHIC FFAG meeting 1
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June 24, 2013 Stephen Brooks, eRHIC FFAG meeting 2
I. Beam Distribution Model
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Input from Beam-Beam Simulation
• To check dynamic aperture, want a “worst case” beam with tails
• Received a distribution from Yue Hao– Electrons immediately after interaction at 10GeV
• Loss required <1e-6 so long tails are important– Define model distribution not discrete particles
• Fit model to Yue’s beam distribution
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y-y’ with Linear Histograms
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y-y’ with Log Histograms
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Distribution Model
• y’ (and x’) tails on log plots look like e^-x• Turns out in a 4D (x,x’,y,y’) distribution that’s
not a very natural tail to have• Cumulative F(Z) = (1-e^-Z)^4 mostly works
– Z is normalised amplitude (expressed in sigmas)– Needed to scale to 0.85Z to get good fit in tails
• Idea is phase-independent distribution that is “at least as bad” as real one in all projections
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Distribution Model Comparison
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Comparison Without 0.85 Scaling
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Beam Size in Real Phase Space
• sigma_x = 13.6um, sigma_x’ = 72.9mrad– At IR! So beta_RMS = 18.6cm
• em_geom_RMS = 0.99 nm.rad (at 10GeV)– em_norm_RMS = 19.4 um.rad
• Scaling to beta = 5m and 1.2GeV gives– sigma_x = 203um– Tails were approaching 10 sigma
• So [dynamic] aperture needs to be +/- 2mm: large!
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x-y Example VFFAG Beam @1.2GeV
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Zoom 20x to see Beam at IR
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II. Dynamic Aperture k Scaling
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Scaling VFFAG Design from April• k=100m^-1 (reminder: B_y = B_0 e^ky)
– 21.2mm orbit offset, B_0=0.0529T, B10GeV=0.441T
• Used triplet “2nd stability region” lattice• Tracking indicated dynamic aperture too small• F=1.23m, D=1.3m (2cm fringe), O=2.507m– FDFO lattice cell = 6.267m– 60% packing factor– Circumference factor = 3.241
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2nd Stability Region Optics
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April 2013 Stephen Brooks, PASI 2013 & BNL seminar 15
2nd stability region parameter spaceNB: old values, diagram indicative only!
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How to Scale k?
• Orbit spacing scales with 1/k• Magnet/drift lengths with 1/sqrt(k)
– 2k with same magnet L gives focal L/2– But 2k with magnet L/sqrt(2) gives focal L/sqrt(2)
• Beta is focal length so also 1/sqrt(k)• Fringe field length with 1/k
– Because magnet height scales with 1/k
• Dipole fields remain the same
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Dynamic Aperture Simulation
• Most difficult turn is 1.2GeV: largest beam– Higher order poles smaller for smaller beams
• Disrupted beam is harder than original• Do 2 turns of disrupted beam at 1.2GeV as
proxy for whole 1.2->10->1.2 cycle– C_eRHIC = 3843.16m, 2 turns ~ 7.7km– 10000 particles for now
• 1.2-10GeV orbit excursion = 2.12/k
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Transmission as k is Decreased
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k=100m^-1
k=50
k=30
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Better but Not Good Enough!
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III. Stability Diagrams
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Necktie FDF Triplet Stability Plot
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Lattice Variables & Constraints
• FDFO triplet has 3 lengths and 2 magnet strengths (the B_0 for F and D; k is fixed)
• Packing factor 60% fixes Length_O• Tunnel bending radius 378.26m fixes overall
field magnitude– The previous “necktie” plots didn’t enforce this!
• Leaves 5-2=3 free parameters: L_F, L_D and F/D strength ratio
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L_F vs. L_D plot from 0 to 2mCurvature constant, 60% packing, strength F/D=1
FDF 1st stability regionMax beta ~ 5m, 6-7GeV
FDF 2nd stability regionMax beta ~ 20-50m, 10-11GeV
DFD 1st stability regionSimilar to FDF 1st
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Zoom out: L_F vs. L_D plot from 0 to 5m
(1,1) beta~5m, 6-7GeV
(2,1) beta~20-50m, 10-11GeV
(3,1)beta~10000m!16GeV
DFD (2,2)beta<5m??11GeV
DFD (2,1)Beta~80-200m13-14GeV
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IV. eRHIC Energy Limit Formula
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“Maximum GeV” for a Lattice
• Reference case: 60% packing factor, 0.43*2/3 = 0.2867T, Eref=20GeV
• Synchrotron power P proportional to E^2B^2• <P> = E^2<B^2>• So Emax^2<((Emax/E)B)^2> = Eref^2<Bref^2>• (Emax^4/E^2)<B^2> = Eref^2<Bref^2>• Emax = sqrt(E Eref Brmsref/Brms)
– = Eref sqrt(E/Brms)/sqrt(Eref/Brmsref)
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Maximum GeV Examples
• The non-FFAG eRHIC with separate beamlines (no reverse bend) has Emax=20GeV and C=1
• Having a circumference factor multiplies up the required fields (Brms) by C for a given energy, so E/Brms is divided by C
• Square root means Emax is divided by sqrt(C)• Existing C=3.241 case gets to 11.1GeV
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V. Future Work
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Where to go next
• Try to find scaling VFFAG at lower energy (~5GeV) but with enough dynamic aperture– Perhaps alignment error studies too– Acts as a back-stop
• A few places remain to optimise the scaling VFFAG but since the tunes do not matter a non-scaling machine has more freedom
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