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(ISS) Topics Studied at RAL G H Rees, RAL, UK

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ISS Work Areas 1. Bunch train patterns for the acceleration and storage of μ ± beams. 2. A 50Hz, 1.2 MW, 0.2 - 3 GeV, RCS booster for a proton driver. 3. A 50 Hz, 4 MW, 10 GeV, non-isochronous, FFAG proton driver. 4. Triangle and bow-tie designs for μ + to ν and μˉ to ν, decay rings. To ease the proton bunch compression, and the beam loading for the muon acceleration, there has been a change during the study from : 1 bunch train at 15 Hz, to 3 or 5 trains at 50 Hz.

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Bunch Train Patterns. Hˉ 1 RCS (R b ) NFFAG (2 R b ) 1 (h=3, n=3) (h=24, n=3) (h=5, n=5) (h=40, n=5) 32 Period T p = T d /2 23 μ ± bunch rotation P target Accel. of trains of 80 μ ± bunches NFFAG ejection delays: (p + m/n) T d for m = 1 to n (=3,5) Pulse 60 μs for solid targets Decay rings, T d h = 2 3 3 3 5 1 2 3 80 μˉ or μ + bunches

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Choice of 4 MW, 50 Hz, 10 GeV Proton Driver A linac, RCS & NFFAG permit adiabatic bunch compression and sequential bunch delays for either n = 3 or n = 5, bunch patterns NFFAG acceleration is over most of the cycle, for lower rf fields; NFFAG has metal, vacuum chambers while RCS needs ceramic The NFFAG concept is new, however, and needs further study and the construction of an electron model to prove its viability Two, 50 Hz boosters and two, 25 Hz drivers would be needed for an entire RCS driver scheme (for practical considerations) Ring radii & sequential bunch delay constraints lead to 3 or 5 compressors & large rf in linac-accumulator-compressor options

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Schematic Layout of 3 GeV, RCS Booster. 200 MeV H ˉ beam Low field injection dipole RF cavity systems Shielded beam loss collectors R = 63.788 m n = h = 3 or 5 Triplet quads Main dipoles Extraction system RF cavity systems

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Choice of Booster Lattice ESS-type, 3-bend achromat, triplet lattice chosen Lattice is designed around the Hˉ injection system Dispersion at foil to simplify the injection painting Avoids need of injection septum unit and chicane Separated injection; all units between two triplets Four superperiods, with >100 m for RF systems Locations for momentum and betatron collimation Common gradient for all the triplet quadrupoles Five quad lengths but same lamination stamping Bending with 20.5° main & 8° secondary dipoles

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Parameters for 50 Hz, 0.2 to 3 GeV Booster Number of superperiods 4 Number of cells/superperiod 4(straights) + 3(bends) Lengths of the cells 4(14.0995) + 3(14.6) m Free length of long straights 16 x 10.6 m Mean ring radius 63.788 m Betatron tunes (Q v, Q h ) 6.38, 6.30 Transition gamma 6.57 Main dipole fields 0.185 to 1.0996 T Secondary dipole fields 0.0551 to 0.327 T Triplet length/quad gradient 3.5 m/1.0 to 5.9 T m -1

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Booster RF Parameters Number of protons per cycle 5 10 13 (1.2 MW) RF cavity straight sections 106 m Frequency range for h = n = 5 2.117 to 3.632 MHz Bunch area for h = n = 5 0.66 eV sec Voltage at 3 GeV for η sc < 0.4 417 kV Voltage at 5 ms for φ s = 48° 900 kV Frequency range for h = n = 3 1.270 to 2.179 MHz Bunch area for h = n = 3 1.1 eV sec Voltage at 3 GeV for η sc < 0.4 247 kV Voltage at 5 ms for φ s = 52° 848 kV

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10 GeV, 50 Hz, 4 MW, Proton Driver 200 MeV Hˉ Linac Achromatic Hˉ Collimation Line 10 GeV NFFAG n = 5, h = 5 n = 5, h = 40 3 GeV RCS booster ΔT = 2 (p + m/5) T p for m = 1 to 5 2 5 R p = 2 R b = 2 x 63.788 m 3 4 1 1 5 2

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The Non-linear, Non-scaling NFFAG Non-isochronous FFAG : ξ v = 0 and ξ h = 0 Cells have the arrangement: O-bd-BF-BD-BF-bd-O The bending directions are : - + + + - Number of magnet types is: 3 Number of cells in lattice is: 66 The length of each cell is: 12.14 m The tunes, Q h and Q v,are: 20.308 & 15.231 Gamma-t is imaginary at 3 GeV and ~ 21 at 10 GeV Full analysis needs processing non-linear lattice data & ray tracing in 6-D simulation programs such as Zgoubi

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Adiabatic Bunch Compression at 10 GeV For 5 proton bunches: Longitudinal areas of bunches = 0.66 eV sec Frequency range for a h of 40 = 14.53-14.91 MHz Bunch extent for 1.18 MV/ turn = 2.1 ns rms Adding of h = 200, 3.77 MV/turn = 1.1 ns rms For 3 proton bunches: Longitudinal areas of bunches = 1.10 eV sec Frequency range for a h of 24 = 8.718-8.944 MHz Bunch extent for 0.89 MV/ turn = 3.3 ns rms Adding of h = 120, 2.26 MV/turn = 1.9 ns rms

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Non-linear Excitatations & Tune Choice Cells Q h /cell Q v /cell 3rd Order Higher Order 4 0.25 0.25 zero nQ h = nQ v & 4th order 5 0.20 0.20 zero nQ h = nQ v & 5th order 6 0.166 0.166 zero nQ h = nQ v & 6th order 9 0.222 0.222 zero nQ h = nQ v & 9th order 13 4/13 3/13 zero to 13th but for 3Q h =4Q v -t is imaginary at low energy and ~ 21 at 10 GeV. Use (13 x 5 ) + 1 = 66 of such cells for the NFFAG. (Use 13 such cells for the insertions of an NFFAGI)

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sin α = L 1 /2R sin θ = L 2 /2R L 1 ~ 3500 km, L 2 ~7500 km R the equatorial radius Vertical Plane Layout of 2 Isosceles Triangle Rings α θ ground level ν ν production efficiency ~ 49.6% ΔQ & collimation 10 cell arc 11 cell arc 10 cell arc α + θ = 52.8° C = 1608.8 m

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10 cell arcs Circumference 1608.8 m Tuning quads Depth ~ 300 m Efficiency 52.6% Beam loss collimators 425.16 m production straights Injection υ υ 52.8° Vertical Bow-tie Decay Rings

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Triangle vs Bow-tie? Bow-tie has the smaller depth (300 m compared with 435 m). Bow-tie has higher efficiency (52.6 % compared with 49.6%). Bow-tie has a greater choice of the opening angle around 50°. Bow-tie needs 40 bending cells cf with 31, but fewer quads. Bow-tie needs a scheme to remove the beam polarization. Bow-tie design becomes difficult at reduced circumferences. Both have a vertical tilt & a reduced ε for most detector pairs. Comparisons with racetrack rings to be given by C. Johnstone?

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