Isochronous, FFAG Rings with Insertions for Rapid Muon or Electron Acceleration

1
Isochronous, FFAG Rings with Insertions for Rapid
Muon or Electron Acceleration

• G H Rees, RAL

2
Non-scaling, Non-linear FFAGs

• Categories for FFAG Lattice Cells of Five
  Magnets
• 1. IFFAG isochronous, no Qvn and 2Qvn
  crossing
• 2. IFFAGI IFFAG with combined function
  insertions
• 3. NFFAG non-isochronous, high/imag ?-t, no Q
  varn
• 4. NFFAGI NFFAG with insertions, some Qh
  variation
• 1 and 2 rapid acceleration of muons or
  electrons
• 3 and 4 high power proton drivers or medical
  rings

3
Pros and Cons for Insertions

• Pros
• Reduced ring circumference
• Easier injection and extraction
• Space for beam loss collimators
• Fewer integer resonances crossed
• Easier acceleration system to operate
• Four times fewer, four-cell, 201 MHz cavities
• Cons
• Reduced ring periodicity
• More magnet types required 6, not 3 or 2
• Small ßh(max) ripple effects over a superperiod

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Criteria for Insertion Designs

• Isochronous conditions for the normal cells
• Isochronous conditions for the insertion cells
• Unchanged (x, x) closed orbits on adding
  insertions
• Minimising the separations of the radial closed
  orbits
• Unchanged vertical a and ß-functions on adding
  insertions
• Unchanged horizontal a and ß-functions on adding
  insertions
• Non-linear magnet, lattice study techniques are
  required.
• If x ah av 0 at match points, 6 control
  variables needed
• Match symmetrical, 5 unit, single cells, at long
  straight centres.
• Allow some small ripple in ßh (max) over a
  superperiod

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Options for the Insertion Designs

• Normal cell Insertion Magnet
  types
• Doublet D D1 T0 D2
  2 7
• Triplet T T1 T2 T1
  2 4
• Pumplet P1 P2
  3 3
• Easiest solution is to match the two, pumplet
  cells
• P1 has a smaller ß-range than either D or T
• The insertion has only one type of cell, P2
• P2 has the smallest closed orbit lever arm
  
• No 2? dispersion suppressors, as too many are
  needed

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8-20 GeV Muon, Normal Insertion Cells

• bd(-) BF() BD () BF()
  bd(-)
• O 0.5 0.5
  0.5 0.5
  O
• 0.45 0.62 1.26
  0.62 0.45
• 0.5 Normal cell (3º,
  6.4 m) 0.5
• 2.4 Insertion cell (3º,
  10.2 m) 2.4
• Lattice 4 superperiods of 22(20) normal 8(10)
  insertion cells
• New / old ring circumferences 889.6 or
  920.0 / 1254.6 m

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Evaluation of Non-linear Lattices

• First, at a reference energy for the insertion
  cell,
• a routine seeks a required value for Qv, and
  the
• value of gamma-t that provides for
  isochronism
• Next, adopting the same reference energy for the
• normal cell, a second routine searches for a
  match
• to the relevant ßv and ?-t values of the
  insertion cell
• Then, the normal cell is re-matched, using a
  revised
• field gradient in its bd, and this is
  continued until the
• two cells have identical, closed orbit, end
  positions
• Arrange for no Qvn, 2Qvn resonances to be
  crossed

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Lattice Functions at 14.75 GeV
9
Lattice Functions at 8 GeV
10
Lattice Functions near 20 GeV
11
Superperiod Parameters

• The insertion and normal cells are unlike those
  in other rings
• as they both have 3º closed orbit bend angles and
  use non-
• linear combined function magnets. The fields, in
  Tesla, are
• Insertion
  Normal cell
• bd magnets - 4.0 to - 1.6
  - 4.0 to - 2.1
• BF magnets 2.7 to - 3.0
  2.7 to - 2.4
• BD magnets 3.0 to 5.2
  3.0 to 5.0
• Range of radial tunes 15.06
  to 41.27
• Range of vertical tunes 13.72
  to 13.88

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Reference Orbit Separations (mm)

• Energy range in GeV 9.5 to 20 8.75 to
  20 8.0 to 20
• Long straight sections 185.9
  229.1 280.3
• Insertion cell bd unit 185.1
  228.6 280.4
• Normal cell bd unit 184.7
  228.0 279.6
• Insertion cell BF quad 169.5
  214.6 269.9
• Normal cell BF quad 165.3
  208.7 261.8
• Insertion cell BD unit 110.3
  144.1 187.0
• Normal cell BD unit 107.7
  140.1 181.1

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Insertion Design Summary

• Superperiods meet all nine, design criteria at
  15 GeV,
• but eight, only, for most of the energy
  range, 8 - 20 GeV
• A superperiod has 22 (20) normal 8 (10)
  insertion cells
• all four have the same, small, acceptable
  ripple in ßh(max)
• Ripple is ltlt than that of TRIUMFs KAON Factory,
  D ring
• Normal insertion cells require slightly
  different magnets
• From 8 to 20 GeV, no Qvn, 2Qv n resonances are
  crossed
• From 8 to 10 GeV, no Qhn resonances are
  crossed
• From 10 to 20 GeV, 26,Qhn resonances are
  crossed

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10.4 to 20 MeV Electron Model

• Model ring for 6-D electron tracking studies
• Computing time less than for 8-20 GeV muons
• Studies of F Meot F Lemuet now underway
• 3 superperiods of 9 normal 4 insertion cells
• 16 turns at 0.6 MeV/ turn 2997 MHz (h270)
• No full/ half integer vertical resonances crossed

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20 MeV, Electron Model, Cell Layouts

• bd(-) BF() BD() BF()
  bd(-)
• O .04 .04
  .04 .04 O
• .045 .062 .126
  .062 .045
• 0.05 Normal cell (9.231º,
  0.6 m) 0.05
• 0.20 Insertion cell (9.231º,
  0.9 m) 0.20
• Three superperiods, each of 9 normal and 4
  insertion cells
• New (previous) ring circumferences 27.0
  (29.2) m

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Electron Model Studies

• Matching between the insertions and normal cells
• Isochronous properties of the 3 GHz, FFAG ring
• Emittance growth in fast slow resonance
  crossing
• Transient beam loading of the three, 3-cell
  cavities
• Inject (s.c) extract from the outer side of
  the ring ?
• Figure of eight and C-type magnets for the
  insertion ?
• Long transmission line kickers, no septum
  magnets ?
• Larger aperture in magnets adjacent to fast
  kickers ?
• Diagnostics in the insertions, with radial
  adjustment ?