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Scaling VFFAG eRHIC Design Progress Report 4 July 15, 2013Stephen Brooks, eRHIC FFAG meeting1

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Last time: Found FODO lattices rated for 9.4 and 9.5GeV – Extrapolation suggests both allow orbit excursions of less than 7cm (k=30m^-1) with <10^-6 losses But this is without alignment errors – Location relative to resonances understood 9.5GeV/80% packing factor lattice became baseline for scaling VFFAG arc magnet design Synchrotron radiation ~10MW to first order July 15, 2013Stephen Brooks, eRHIC FFAG meeting2

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I. Macroparticle Weighting July 15, 2013Stephen Brooks, eRHIC FFAG meeting3

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Greater accuracy for tail losses July 15, 2013Stephen Brooks, eRHIC FFAG meeting4 Generate macroparticles roughly uniformly as a function of normalised radius out to >10 Weights are w = f(r)/g(r) where: – f(r) is desired real phase space density function – g(r) is density of generated macroparticles Details available in the note on distributions: http://stephenbrooks.org/ral/report/2013- 9/4ddist.pdf http://stephenbrooks.org/ral/report/2013- 9/4ddist.pdf

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Comparison: 9.5GeV FODO lattice July 15, 2013Stephen Brooks, eRHIC FFAG meeting5

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Zoom: ‘resonance’ features remain July 15, 2013Stephen Brooks, eRHIC FFAG meeting6

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Comparison: 8GeV FODO lattice July 15, 2013Stephen Brooks, eRHIC FFAG meeting7

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Comparison: 9.4GeV FODO lattice July 15, 2013Stephen Brooks, eRHIC FFAG meeting8

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Comparison: 10GeV FODO lattice July 15, 2013Stephen Brooks, eRHIC FFAG meeting9

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II. Error Studies of FODO Lattice July 15, 2013Stephen Brooks, eRHIC FFAG meeting10

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Tracking with translational errors Random offsets were generated for each magnet in 500 cells (then reused) Error in each axis a normal distribution with mean 0 and standard deviation – RMS 3D distance offset = sqrt(3) ~ 1.73 – 99% single axis offset ~ 2.58 – 99% 3D distance offset ~ 3.37 Tracked 2 turns at 1.2GeV, disrupted beam July 15, 2013Stephen Brooks, eRHIC FFAG meeting11

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Beam loss vs. error sigma July 15, 2013Stephen Brooks, eRHIC FFAG meeting12

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Loss vs. k and for 9.5GeV lattice July 15, 2013Stephen Brooks, eRHIC FFAG meeting13

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=100um transmission July 15, 2013Stephen Brooks, eRHIC FFAG meeting14

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=100um beam centroid July 15, 2013Stephen Brooks, eRHIC FFAG meeting15

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=100um norm. RMS emittances July 15, 2013Stephen Brooks, eRHIC FFAG meeting16

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=10um transmission July 15, 2013Stephen Brooks, eRHIC FFAG meeting17

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=10um beam centroid July 15, 2013Stephen Brooks, eRHIC FFAG meeting18

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=10um norm. RMS emittances July 15, 2013Stephen Brooks, eRHIC FFAG meeting19

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=2.5um transmission July 15, 2013Stephen Brooks, eRHIC FFAG meeting20

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=2.5um beam centroid July 15, 2013Stephen Brooks, eRHIC FFAG meeting21

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=2.5um norm. RMS emittances July 15, 2013Stephen Brooks, eRHIC FFAG meeting22

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=1um transmission July 15, 2013Stephen Brooks, eRHIC FFAG meeting23

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=1um beam centroid July 15, 2013Stephen Brooks, eRHIC FFAG meeting24

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=1um norm. RMS emittances July 15, 2013Stephen Brooks, eRHIC FFAG meeting25

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=0 transmission July 15, 2013Stephen Brooks, eRHIC FFAG meeting26

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=0 beam centroid July 15, 2013Stephen Brooks, eRHIC FFAG meeting27

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=0 norm. RMS emittances July 15, 2013Stephen Brooks, eRHIC FFAG meeting28

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III. Synchrotron Radiation Losses July 15, 2013Stephen Brooks, eRHIC FFAG meeting29

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Compensation-free designs FFAG arcs transmit a continuum of energies so don’t strictly speaking need compensation of synchrotron energy losses – All examples given for “9.5GeV” FODO lattice – Assumed FFAG straights radiate same rate as arcs Constraints: – My FFAG arcs won’t transmit beam below 1.2GeV – Assumed ring linac won’t transmit below 100MeV July 15, 2013Stephen Brooks, eRHIC FFAG meeting30

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Schematic changes July 15, 2013Stephen Brooks, eRHIC FFAG meeting31 Before Source, 10?MeV dump 100MeV ERL 1.1GeV ERL Compensation RF After ~200MeV linac 1.xGeV ERL 100MeV ERL?

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9-pass 10GeV (worst) July 15, 2013Stephen Brooks, eRHIC FFAG meeting32

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9-pass 9GeV July 15, 2013Stephen Brooks, eRHIC FFAG meeting33

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6-pass 10GeV July 15, 2013Stephen Brooks, eRHIC FFAG meeting34

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6-pass 9GeV (<10MW) July 15, 2013Stephen Brooks, eRHIC FFAG meeting35

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6-pass 9GeV to 13.5GeV, 6.1mA July 15, 2013Stephen Brooks, eRHIC FFAG meeting36

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6-pass 9GeV to 14.9GeV, 3.3mA July 15, 2013Stephen Brooks, eRHIC FFAG meeting37

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This may or may not be practical? July 15, 2013Stephen Brooks, eRHIC FFAG meeting38 Source, dump Overdrive mode 197MeV linac 1.474GeV not quite ERL 100MeV ERL RF

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4-pass 10GeV (~10MW, long linac) July 15, 2013Stephen Brooks, eRHIC FFAG meeting39

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IV. VFFAG Options Comparison July 15, 2013Stephen Brooks, eRHIC FFAG meeting40

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FFAG type Synchrotron radiation Dynamic aperture / error tolerance Time of flight Energy range / multiple rings Vertical (nonlinear) scaling ** # 10MW at 9- 10GeV Not impossible but difficult 1-beta effect only Infinite / one ring Vertical linear nonscaling * ## Potentially to 20GeV 50mA Better? Unknown but better than horizontal FFAG Probably factor 3x / two rings for 10GeV, three rings for 20-30 Vertical nonlinear nonscaling *** ### Potentially to 20GeV 50mA Also bad? At least as good as linear nonscaling VFFAG Horizontal linear nonscaling * ## 20GeV OKLinear magnetsProblematicTwo/three rings Non-FFAG20GeV OKPresumably goodEach ring exactToo many rings July 15, 2013Stephen Brooks, eRHIC FFAG meeting41 *, **, *** indicate complexity of magnets and correction #, ##, ### indicate conceptual difficulty

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V. Future Work July 15, 2013Stephen Brooks, eRHIC FFAG meeting42

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Next steps (if scaling VFFAG) Develop “straight” cell for full ring lattice Work with magnet and FFAG splitter designers Decide on RF/linac energies Open issues: – Emittance growth from SR photon emission – Coherent synchrotron radation? “End-to-end” tracking of full ring – Eventually track with fieldmaps from magnet July 15, 2013Stephen Brooks, eRHIC FFAG meeting43

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Next steps (if non-scaling VFFAG) Try linear field NS-VFFAG first (“Davidtron”) – Much less synchrotron radiation – Expect better dynamic aperture – Easier to build (correct and understand!) magnets – Will likely need a cascade of rings 1-3, 3-10 etc. Develop quadrupole field models for Muon1 and/or VFFAG tracker code Try to search and understand lattice space July 15, 2013Stephen Brooks, eRHIC FFAG meeting44

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