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G. H. Rees, ASTeC, RAL

FFAG’11 workshop FFAGs for R&D on injection, stacking and ejection, with potential as an ISIS injector. G. H. Rees, ASTeC, RAL. Linac test stand plus FFAG ring(s). Consider the Hˉ linac test stand extended to 20 MeV & 100 Hz. Add a 150 (180) MeV, FFAG with Hˉ injection, single H + bunch

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G. H. Rees, ASTeC, RAL

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  1. FFAG’11 workshopFFAGs for R&D on injection, stacking andejection, with potential as an ISIS injector. G. H. Rees, ASTeC, RAL

  2. Linac test stand plus FFAG ring(s) Consider the Hˉ linac test stand extended to 20 MeV & 100 Hz. Add a 150 (180) MeV, FFAG with Hˉ injection, single H+ bunch acceleration, stacking, 2nd acceleration, merging, re-bunching and ejection-transfer of the two bunches to ISIS at 50 Hz. Assume larger, mean outer orbit radius FFAG than the 5.12 m, D(-)oF(+)oD(-)O, scaling triplet ring at KURRI, Osaka.

  3. Compatibility with ISIS Let the ISIS & FFAG half-circumferences be L & L/p, where p, a ratio of integers, is set by a delay in 2nd bunch ejection (m, n more turns in ISIS & FFAG). Require:L(1+2m) =L(1+2n)/p. R/p > KURRI’s for longer bunches & lower long. space charge. R (ISIS) = L/π = 26.0 m , R/p (FFAG) = 10.0, 11.143 or 14.0 m for (m=2,n=6,p=13/5), (m=1,n=3,p=7/3) or (m=3,n=6,p=13/7).

  4. R&D topics Linac topics: ion source, LEBT, RFQ, MEBT, 20 MeV linac and a linac to ring, beam-line half funnel. FFAG: Hˉ injection, dynamic apertures, effects of errors, space charge, acceleration, stacking, re-bunching & delayed ejection. New injection scheme needs > ~600 (π) mm mr un-normalized acceptances, & for acceleration > 125 (π) mm mr, normalized, dynamic apertures. Tracking studies wIth errors required.

  5. R&D on one half of a 20 MeV funnel Lower space charge forces at all linac energiesSmaller excitation of higher-order cavity modesReduced growth of the beam emittance and halo

  6. Scaling D(-)F(+)D(-) triplet options B/Bo = (1+x/ro)KB/Bo = (1+αx/ro)K/α radially aligned edgesparallel triplet edges Field Bo at ro from ring centre and x a radial offset from ro D F D D(-) F(+) D(-) Set α for constant q(h)

  7. Parameters of scaling, DFD triplet ring Kinetic energy range for the protons = 20-150 (24-180) MeV, Number of identical D(-) o F(+) o D(-) O triplet cells =14 (19). Max. orbit radius & straights = 10.0 (14.0) & 1.92 (2.04) m. Field range for orbits = 0.3591 (0.3833) Tto 1.017 (1.042) T. Bending angle for the F magnet = 47.122º (41.661º). Bending angle for the D magnet = −10.704º (−11.357º). A “return yoke free triplet” is used, as at KEK, with poles offset relative to each other. Variation of q(v) with energy is restricted, using magnetic shields to adjust end field extents.

  8. FFAG10 data for radial & parallel edges α T(MeV) ro(m) str(m) ±Kn(m-2) Qh Qv Fext(m) 1.000 20.000 9.269 1.7834 0.8256 5.312 2.400 0.0421 1.000 55.576 9.628 1.8523 0.7653 5.312 2.400 0.0437 1.000 150.000 10.000 1.9240 0.7093 5.312 2.400 0.0454 0.957 20.000 9.277 1.5994 0.8221 5.312 2.402 0.0200 0.957 55.576 9.632 1.7585 0.7931 5.313 2.419 0.0600 0.957 150.000 10.000 1.9240 0.7650 5.312 2.438 0.1000

  9. More data for radial edged FFAG10 Radial alignment of edges gives the better results. A longer O straight is available for the Hˉ injection, and Qv is constant for a small range of end field extents, when K=12.7069 All orbits have similar lattice functions. At 55.576 MeV, beta(v) ranges from ~2.73 to 4.85 m,beta(h) from ~0.794 to 6.97 m, alphap(h) from ~0.657 to 0.705 m, andgamma-t = 3.7064, The 20 & 150 MeV closed orbits are ~ 0.7309 m apart and have respective bend radii of 1.66052 and 1.79145 m. while parallel edged triplets have constant bend radii = 1.8093 m.

  10. Hˉ multi-turn injection D(-) Hˉ F(+) Hº D(-) protons Hˉ ions protons foil

  11. Injection scheme for FFAG10 Merging of Hˉ ions & re-circulating protons occurs in a lattice bending-focusing region (the injection straight section is too short to house a bump magnet chicane), The foil location is in an o section between D(-) & F(+) units, within the end field region of the D(-). A field level is chosen so stripped eˉ bend to be collected outside the ring’s acceptance. Lattice functions at the foil: beta(v) = 4.72 m, alpha(v) = 1.54, beta(h) = 2.80 m, alpha(h) = -2.35 and alphap(h) = 0.659 m. An injection septum isn’t needed as the 20 MeV Hˉ ions bend and focus in an opposite sense to protons.

  12. FFAG10 injection system details The Hˉ beam (~ ±10σ) is scraped at ±5σ in the input line, and directed on to a ring’s closed orbit, or to oscillate about one. It is directed at a fixed spot on the foil, which is set on v axis. Two injection steering magnets sweep the beam vertically over a range of incident angles. Painting also needs a programmed, collapsing horizontal orbit bump and an rf frequency ramp. Beam centre at foil is set at 5σ from adjacent foil corner edges, so a -ve steering error causes some input beam to miss the foil. Injection line, beta functions are set at ~ 1.66 m at the foil for a a spot size σ of ~ 1 mm. Lower beta values complicate the line.

  13. Horizontal injection painting for FFAG10 A steering magnet pair is needed on each side of the injection triplet set for a horizontal painting orbit bump. Unstripped Hˉ ions and partially stripped Ho atoms, which remain after the foil, pass via the following F magnet to the outside of the ring, as shown earlier. InjectIon turns & duration for 3 1013 ppp @ 100 Hz with a 40 mA Hˉ beam, chopped at 2/3 duty factor = 190, 196 μs.

  14. Double fast ejection pulse at 50 Hz Rise and fall times for two kicker pulses = 70 ns Approximate time extent of each bunch = 136 (200) ns Second pulse is delayed by 13/2 FFAG ring turns. 0 0.276 2.700 2.976 μs 0 0.340 3.510 3.850 μs

  15. Trapping, acceleration, stacking & re-bunching Let ratio of longitudinal space charge to rf focusing forces = ηsc Find V and longitudinal bunch area, A, in terms of ηscfrom: Vηsc= Negh2/(2FRεo γ2) V(1-ηsc) = πηc2h3A2/(128R2(Eoe)γα2) α = the area in ((dφ/Ωdt),φ) space, normalized by (√cos φs )/16. N = the number of particles per bunch, e = electronic charge, g = longitudinal space charge parameter, h = harmonic number, F = Hofmann-Pedersen dist. form factor, R = mean orbit radius, η = (γ−2 − γt−2)slip factor,εo = the permittivity of free space. c = the velocity of light, Eo = the proton rest mass energy.

  16. Rf trapping voltage for FFAG10 Rf frequency at 20 MeV injection (h = 1) = 0.96973 MHz Phase extent of the single bunch = ±113o Vηsc = 15.347 kV V(1-ηsc) = 61.89999 A2 kV ηsc(<0.4) = 0.34 V(pk) = 45.138 kV A = 0.69374 eV sec Δp/p (momentum spread of the bunch ) = ±19.45 10−3 Longitudinal painting is needed to provide the large Δp/p. The large dynamic aperture is needed for the large Δp/p.

  17. Rf system parameters for FFAG10 Rf frequencies for h = 1 acceleration = 0.9697 to 2.4173 MHz Time for 20-150 MeV acceleration = 6.0 ms Rf voltages for h = 1 acceleration = 45.1 to 60 to 13.7 kV Number of h=1 ferrite tuned cavities = 4 Frequencies for h = 2, 4 re-bunching = 4.8346, 9.6692 MHz Number of fixed frequency cavities = 2, 1

  18. De-bunching & re-bunching for FFAG10 De-bunching (h =1), 2-pulse stacking & re-bunching (h = 2 & 4). Phase extent of 150 MeV de-bunched bunch = ±180o A = 0.73 eV sec ηsc = 0.4700 V(pk) = 13.683 kV Re-bunching at 150 MeV (h = 2 & 4) for Δφ = ±113o A = 0.73 eV sec ηsc = 0.3184 V(pk) = 222.4 (111.2) kV Δp/p (momentum spread of the 2 bunches ) = ±13. 42 10−3

  19. FFAG14 or two FFAG10 for ISIS? Raise the energy range from 20-150 MeV to 24-180 MeV. Phase extent of FFAG14 bunch at injection = ±113o ηsc(<0.4) = 0.34 V(pk) = 31.277 kV A = 0.83180 eV sec Δp/p (momentum spread of the bunch) = ±14.86 10-3 Re-bunching at 180 MeV (h = 2 & 4) for Δφ= ±113o A = 0.870 eV sec ηsc = 0.2553 V(pk) = 135.0 (67.5) kV Bunches still too short & Δp/p (2 bunches) =±10.35 10-3 So, use 50 Hz linac & a single bunch in each of two FFAG10s.

  20. Summary Adding FFAGs to the RAL linac test stand has been studied. Outer orbit radii of 10 m and 14 m have been considered. Both are suitable for high space charge R&D experiments. The longitudinal space charge leads to large values of Δp/p. Re-bunched FFAG10 has bunches too short for the ISIS ring. FFAG14 bunches are better, but still not adequate for ISIS. Best is 50 Hz linac & single bunches in two FFAG10s (h=1, 2). Many topics (tracking, scrapers, instabilities) still to be studied.

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