1. Options for a 50Hz, 10 MW, Short Pulse Spallation Neutron Source G H Rees, ASTeC, CCLRC, RAL, UK

2. Premises  Kinetic energy for the 10 MW, proton beam (GeV) ≤ 3.2  Total proton pulse duration each 50 Hz pulse (  s) ≤ 2.2  The number of proton bunches in each 50 Hz pulse ≤ 8

3. Some Potential ISIS RCS Upgrades  ISIS injecting into a 50 Hz, 3.2 GeV RCS, for a 1 MW source  400 MeV Hˉ linac with the 3.2 GeV RCS, for a 2 MW source  800 MeV Hˉ linac with the 3.2 GeV RCS, for a 5 MW source (The ESS linac-compressor(s) appears better option at ≥ 2 MW) Limit for a single, 3.2 GeV RCS appears to be 5 MW (2 10 14 ppp)

4. 10 MW, 50 Hz Ring Options  A 3.2 GeV Hˉ linac feeding two, 3.2 GeV, 5 MW compressors: it is probably feasible, but is considered to be too difficult  A 0.8 GeV Hˉ linac feeding two, 3.2 GeV, 5 MW RCS rings: this option needs a delay of ~ 1 ms for one of the RCS  A 1 GeV Hˉ linac & compressor, & two 3.2 GeV, 5 MW NFFAG: some bunch compression in compressor before extraction

5. Schematic Layout for 3.2 GeV, 5 MW RCS 800 MeV H ˉ H ˉ, H° beam cavities collectors R = 65 m n = h = 4 N = 2 10 14 triplet dipoles 8° dipole dipoles extraction cavities

6. Choice of 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 a 50 Hz, 0.8-3.2 GeV RCS  Number of superperiods 4  Number of cells/superperiod 4(straights) + 3(bends)  Lengths of the cells 4(14.5004) + 3(14.7) m  Free length of long straights 16 x 11.0 m  Mean ring radius 65.0 m  Betatron tunes (Q v, Q h ) 6.38, 6.30 (  Q ~ 0.2)  Transition gamma 6.6202  Main dipole biased cosine fields 0.4208 to 1.1591 T  Secondary dipole fields 0.1252 to 0.3448 T  Triplet length/quad gradient 3.5 m / 2.2 to 6.2 T m -1

8. RCS Betatron and Dispersion Functions

9. RF Parameters for the 3.2 GeV RCS (Z/n = j 5 Ω, reduced g and η sc < 0.3)  Number of protons per cycle 2 10 14 (5.1 MW)  RF cavity straight sections 110 m  Frequency range for h = n = 4 2.4717 to 2.8597 MHz  Bunch area for h = n = 4 1.8 eV sec  Voltage &  p/p @ 0.8 GeV 61.4 kV & ± 3.9 10ˉ 3  Voltage &  p/p @1.96 GeV 717 kV & ± 4.6 10ˉ 3  Voltage &  p/p @ 3.2 GeV 470 kV & ± 5.3 10ˉ 3

10. FFAG Ring Types  Non-linear, scaling, non-isochronous FFAG  Linear, non-scaling, near isochronous -FFAG  Non-linear, non-scaling, isochronous IFFAG  Non-linear, non-scaling, non-isochronous NFFAG Radial, scaling, FFAG rings have BF(+) and BD(-) magnets Non-scaling, -FFAG rings have BF(-) and BD(+) magnets IFFAG & NFFAG rings have bd(-), BF(+) & BD(+) magnets Here, only bd-BF-BD-BF-bd cells for NFFAGs are considered Though of zero chromaticity, the tunes do vary with amplitude

11. 1.0 GeV Compressor Ring  Needed as NFFAG cells are unsuitable for Hˉ injection  Use a similar lattice to that for the 3.2 GeV, RCS rings  Replace the 8°dipoles by (2°, 4° and 2°) dipole sets  Optimise for Stark states 5, 6 with B(for 4°) = 0.1123 T  Separate injection fillings are required for each NFFAG  Some bunch compression is needed before extraction  High & low foils may be needed for lower temperatures

13. Pumplet Cell for the 3.2 GeV NFFAG Ring bd(-) BF(+) BD(+) BF(+) bd(-) 2.32 0.65 1.00 1.40 (m) 1.00 0.65 2.32 –3.2086° 6.6043° 3.2086° 6.6043° –3.2086° Lengths and angles for the 36 cells of the 3.2 GeV closed orbit

14. NFFAG Non-linear Lattice Code  A linear lattice code is modified for estimates to be made of the non-linear fields in a group of FFAG magnets.  Bending radii are found from average field gradients between adjacent orbits & derived dispersion values, D.  D is a weighted, averaged, normalized dispersion of a new orbit relative to an old, and the latter to the former.  A first, homing routine obtains specified betatron tunes. A second routine is for exact closure of reference orbits  A final, limited-range, orbit-closure routine homes for  -t. Accurate estimates are made for reference orbit lengths.  Full analysis needs processing the lattice output data & ray tracing in 6-D simulation programs such as Zgoubi.

15. Non-linear Fields and Reference Orbits  Low ampl. Twiss parameters are set for a max. energy cell.  Successive, adjacent, lower energy reference orbits are then found, assuming linear, local changes of the field gradients.  Estimates are repeated, varying the field gradients for the required tunes, until self-consistent values are obtained for: the bending angle for each magnet of the cell the magnet bending radii throughout the cell the beam entry & exit angle for each magnet the orbit lengths for all the cell elements, and the local values of the magnet field gradients

16. 3.2 GeV Betatron & Dispersion Functions 0.6 m 0.0 m

17. NFFAG Combined Function Magnet Data  bd bend field range(-) 1.0490 to 1.1583 T  bd gradient range 0.2546 to 0.0134 T m -1  BF bend field range 0.1945 to 1.5497 T  BF gradient range(-) 2.1936 to 4.9487 T m -1  BD bend field range 1.4004 to 0.5378 T  BD gradient range 2.0690 to 5.7518 T m -1  BF units approximate four poles of a sextupole

18. Reduction of Non-linear Effects Cells Q h Q v 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  9 0.222 0.222 zero nQ h =nQ v & 9th order  13 4/13 3/13 zero to 13 th, except 3Q h =4Q v Use (13 x 3 ) - 1 = 38 such cells for the NFFAG (36) Betatron tune variations with amplitude still remain Gamma-t = 14.02 (j) at 1.0 GeV & 12.43 at 3.2 GeV

19. RF Parameters for the 3.2 GeV NFFAG (Z/n = j 5 Ω, reduced g and η sc < 0.3)  Number of protons per cycle 2 10 14 (5.1 MW)  RF cavity straight sections 110 m  Frequency range for h = n = 4 2.5717 to 2.8597 MHz  Bunch area for h = n = 4 1.8 eV sec  Voltage &  p/p @ 1.0 GeV 99.5 kV & ± 4.1 10ˉ 3  Voltage &  p/p @1.96 GeV 290 kV & ± 3.3 10ˉ 3  Voltage &  p/p @ 3.2 GeV 258 kV & ± 3.9 10ˉ 3  Compare to the 3.2 GeV RCS 717 kV & ± 5.3 10ˉ 3

20. Vertical Loss Collection in an FFAG Loss collectors Y X 1.0 GeV proton beam 3.2 GeV proton beam  Coupling may limit the horizontal beam growth  ΔP loss collection requires beam in gap kickers

21. 3.2 GeV: NFFAG versus RCS Pros:  Volts per turn for acceleration is less than half  No need for a biased ac magnet power supply  No need for an ac design for the ring magnets  No need for a ceramic chamber with rf shields  Gives more flexibility for the holding of bunches Cons:  Requires a larger (~ 0.27 m) radial aperture  Needs an electron model to confirm viability  Needs a 1.0 GeV, Hˉ injection compressor ring

22. Conclusions re a 50 Hz, 10 MW Source  A 3.2 GeV Hˉ linac & two compressors looks a difficult option  A 0.8-3.2 GeV RCS option needs 2 rings & large, ~3 MHz, rf  A 3.2 GeV NFFAG needs a 1 GeV compressor and two rings NFFAGs offer the potential of greater reliability, but R and D is needed on electron models & new space charge tracking codes.