FFAG Studies at RAL

1
FFAG Studies at RAL

• G H Rees

2
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
  Lemuet
• Ring 3 (IFFAGI) is now being tracked by F Lemuet

3
4 MW, 10 GeV, Proton Driver
4
Features of S2, 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 ßh ßv (max) in 13
  cell insertions

5
Resonance Crossing (Qv13.72, Qh19.2-19.36)

• Crossing of the 3rd order resonance 3Qh
  58
• Insertion and arc 3(Qh ) values 3Qh
  3(4, 5? )
• 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, 5? )
• Some small 4th order excitation for 4Qh
  77

6
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 m
• Lattice has space for only 7 pumplet (5 unit)
  cells,
• with the straight sections having a length 0.6
  m
• Drift tube system a possibility for acceleration
• Horizontal and vertical tunes 2.177 and 1.290
• Lattice maxima ßv 4 m, ßh 1.8 m, Dh 0.8 m
• An initial study has spanned range 60 to 38 MeV
• Entry exit angles become too big below 38 MeV
• It does not then make a good model for an NFFAG

7
Isochronous IFFAG and IFFAGI

• The vertical betatron tunes are kept constant
• The horizontal tunes change for ?-t gamma
• Tracking shows losses when the cell Qh 1/3
• Similar effect in linacs unless Qh is kept lt 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 lt 1/3

8
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

9
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 a
• single 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.

10
Optimum Switch-on of S/C Cavities
Cavity Impedance
RF Generator
C

• .

Load R Z
Beam Z V/(Ib cos fs)
Pmin P beam loading
Use detuned cavity matched Z for minimum
generator power. For isochronous FFAG, fs 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.
11
Optimum Switch-on for Isochronous Ring

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

12
Options for an N-Pass Cooler

• N RF cavities Absorbers ?E / pass
• 1 n n
  ?E
• gt1 n / N n
  ?E / N
• gt1 n n
  ?E
• 3(eg) n/2 n
  ?E/2
• Reduced cost of RF, or more cooling, or both

13
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
K1 off/on
K2 on/off
?
?
Cooling Channel
Isochronous turn(s)
Isochronous turn(s)
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 ? 0 (NFFAG) or ? gt 0 (IFFAG)