FFAG Studies at RAL G H Rees. FFAG Designs at RAL 1. 50 Hz, 4 MW, 3-10 GeV, Proton Driver (NFFAGI)...
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Transcript of FFAG Studies at RAL G H Rees. FFAG Designs at RAL 1. 50 Hz, 4 MW, 3-10 GeV, Proton Driver (NFFAGI)...
![Page 1: 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.](https://reader035.fdocuments.net/reader035/viewer/2022081811/5697bfed1a28abf838cb92ae/html5/thumbnails/1.jpg)
FFAG Studies at RAL
G H Rees
![Page 2: 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.](https://reader035.fdocuments.net/reader035/viewer/2022081811/5697bfed1a28abf838cb92ae/html5/thumbnails/2.jpg)
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
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4 MW, 10 GeV,
Proton Driver
![Page 4: 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.](https://reader035.fdocuments.net/reader035/viewer/2022081811/5697bfed1a28abf838cb92ae/html5/thumbnails/4.jpg)
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
![Page 5: 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.](https://reader035.fdocuments.net/reader035/viewer/2022081811/5697bfed1a28abf838cb92ae/html5/thumbnails/5.jpg)
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
![Page 6: 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.](https://reader035.fdocuments.net/reader035/viewer/2022081811/5697bfed1a28abf838cb92ae/html5/thumbnails/6.jpg)
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
![Page 7: 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.](https://reader035.fdocuments.net/reader035/viewer/2022081811/5697bfed1a28abf838cb92ae/html5/thumbnails/7.jpg)
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
![Page 8: 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.](https://reader035.fdocuments.net/reader035/viewer/2022081811/5697bfed1a28abf838cb92ae/html5/thumbnails/8.jpg)
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
![Page 9: 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.](https://reader035.fdocuments.net/reader035/viewer/2022081811/5697bfed1a28abf838cb92ae/html5/thumbnails/9.jpg)
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.
![Page 10: 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.](https://reader035.fdocuments.net/reader035/viewer/2022081811/5697bfed1a28abf838cb92ae/html5/thumbnails/10.jpg)
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.
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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
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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
![Page 13: 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.](https://reader035.fdocuments.net/reader035/viewer/2022081811/5697bfed1a28abf838cb92ae/html5/thumbnails/13.jpg)
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± ±