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

2. 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.

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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)

13. 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

14. 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

15. 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?