FFAG Studies at RAL

G H Rees

FFAG Designs at RAL

1. 50 Hz, 4 MW, 3-10 GeV, Proton Driver (NFFAGI)2. 50 Hz,1 MW, 0.8-3.2 GeV, ISIS Upgrade (NFFAG)3. 50 Hz, 8-20 GeV,16 turn, ± accelerator (IFFAG,I)4. 50 Hz, 3.2-8 GeV, 8 turn, ± accelerator (IFFAG)5. 1 Hz, 10.4-20 MeV,16 turn, electron-model (IFFAG)6. 1 Hz,10.4-20 MeV,16 turn, electron-model (IFFAGI)7. 50 Hz, low energy, 3 or 5 turn, cooler (N or I FFAG)

Rings 3, & 5 have been tracked by F Meot & F LemuetRing 3 (IFFAGI) is now being tracked by F Lemuet

4 MW, 10 GeV,

Proton Driver

Features of S=2, NFFAGI, Proton Driver

• Equal bend, normal and insertion, pumplet cells are used• Approx matching is found for a normal and an insertion cell • Integer, insertion tunes are then used, viz Qh = 4 & Qv = 3• The 21, normal cells of each arc become exactly matched

• Unchanged closed orbits are obtained on adding insertions by varying the field gradients and tunes of the normal cells• Then, dispersion is matched almost exactly for insertions • A small ripple remains in βh & βv (max) in 13 cell insertions

Resonance Crossing (Qv=13.72, Qh=19.2-19.36)

Crossing of the 3rd order resonance: 3Qh = 58 • Insertion and arc 3(Qh ) values: 3Qh = 3(4, 5⅔ )• Hence, no 3rd order excitation for: 3Qh = 58

Crossing of 4th order resonance: 2Qh + 2Qv = 66• Insertion and arc values for: 2(Qh + Qv ) = 2(7, 9½ )• So, no 4th order excitation for: 2Qh + 2Qv = 66

Crossing of the 4th order resonance: 4Qh = 77 • Insertion and arc 4(Qh ) values: 4Qh = 4(4, 5⅝ )• Some small 4th order excitation for: 4Qh = 77

Need for an NFFAG Model

Electron model much preferred to a proton model Is the proton ring for irradiation of mice suitable?Circumference for the outermost orbit ≈ 20 mLattice has space for only 7 pumplet (5 unit) cells,with the straight sections having a length ≈ 0.6 mDrift tube system a possibility for accelerationHorizontal and vertical tunes: 2.177 and 1.290Lattice maxima: βv ≈ 4 m, βh ≈ 1.8 m, Dh ≈ 0.8 m An initial study has spanned range 60 to 38 MeVEntry & exit angles become too big below 38 MeVIt does not then make a good model for an NFFAG

Isochronous IFFAG and IFFAGI

The vertical betatron tunes are kept constant

The horizontal tunes change for γ-t = gamma

Tracking shows losses when the cell Qh = 1/3

Similar effect in linacs unless Qh is kept < 1/4

(Non-linear space charge not non-linear fields)

Insertion, not normal, cell needs the lower tune

120 144 cells in the IFFAGI so that Qh is < 1/3

Collimation in IFFAGI

Collimation is required for both the + and beams

Primary collimators are set at a minimum acceptance

Secondary collimators are set outwards by ~ 1 mm

3 collimator cells are needed on each side of primary

Vertical collimation requires a constant vertical tune

Horiz collimation planned only at inner & outer orbits

Vertical collimators are tapered across the aperture

15 to 30 m is needed for stopping high energy muons

Beam Loading in IFFAGI

Proton driver (50 Hz?): 4.0 MW (n = 5 proton bunches) 8 - 20 GeV Muon ring: ≈ 1.0 MW (combined and ─) 20-50 GeV Muon ring: ≈ 2.5 MW (combined and ─) 20,50 GeV Storage rings: ≈ 0.5,1.25 MW (separate and ─)

Peak beam loading at the fundamental, ring RF frequency for asingle train of 80 muon bunches in the 8-20 GeV.16-turn ring, is:

≈ 50 MW (50 Hz, C = 900 m, n = 5 proton bunches. I = 2 x Idc )

≈ 1000 MW (25 Hz, C = 450 m, n = 1 proton bunch, I = 2 x Idc )

Beam loading compensation is practical only for the former case.

Optimum Switch-on of S/C Cavities

. Cavity Impedance

Load R = Z

RF Generator C

Beam Z = V/(Ib cos φs)Pmin = P beam loading

Use detuned cavity & matched Z for minimum generator power.

For isochronous FFAG, φs = 0, and no cavity detuning needed.

Input coupler must handle peak loading & 20% control power.

Use amplitude & phase modulation of Ig for cavity switch-on.

For an isochronous FFAG, no phase modulation is required.

Use max gen power (= Pbeam loading ) for optimum switch-on.

Optimum Switch-on for Isochronous Ring

Step function pulsing of Ig at maximum power level.V rises with exponential time constant, 2Q(loaded)/ω,towards 2ZIg (= 2ZIb = 2V),with no phase modulation.Ib is injected at T = (2Q/ ω) loge2, when V is reached.

During switch-on, circulator load absorbs the power.Power for switch-on = (T/ t) x beam loading power.t = time that n muon bunch trains circulate in the ring.Av. power estimates for 50 Hz, 8-20 GeV, n =5, ring: Beam loading: 0.58 MW, Switch-on: 2.7 MW RF power is ≈ half that needed for proton driver

Options for an N-Pass Cooler

N RF cavities Absorbers ∆E / pass

1 n n ∆E

>1 n / N n ∆E / N

>1 n n ∆E

3(eg) n/2 n ∆E/2 Reduced cost of RF, or more cooling, or both

Three or Five Pass Cooling

Previous ring coolers had kickers beyond the state of the art, and were incompatible with the trains of 80 muon bunches. Consider ≈300 ns kicker field rise and fall times in following:

Possibility for 400 MHz RF cavities in later FFAG stages. Design kickers as an integral part of the dog-bone lattices. Design to be at transition with ξ = 0 (NFFAG) or ξ > 0 (IFFAG)

Isochronous turn(s) Isochronous turn(s)

Cooling Channel

K1 off/on K2 on/off± ±