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Insertions for an Isochronous, 8-16 turn, 8-20 GeV, Muon FFAG

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Insertions for an Isochronous, 8-16 turn, 8-20 GeV, Muon FFAG G H Rees, RAL Pros and Cons for Insertions Pros: Reduced ring circumference Easier injection and ... – PowerPoint PPT presentation

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Title: Insertions for an Isochronous, 8-16 turn, 8-20 GeV, Muon FFAG


1
Insertions for an Isochronous, 8-16 turn,
8-20 GeV, Muon FFAG
  • G H Rees, RAL

2
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

3
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
  • There are nine parameters that need to be
    controlled.
  • These become six if x ? ah av 0 at the
    matching points.
  • Hence, match symmetrical cells at long straight
    centres, eg
  • Use the five-unit pumplets of the original
    isochronous design.
  • Use the non-linear lattice study technique
    adopted previously.

4
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 cell type, P2
  • P2 has the smallest closed orbit lever arm
  • Dispersion suppressors (2?) have not been
    included
  • as too many are needed they are
    non-isochronous

5
20 GeV, Normal Insertion Cell Layouts
  • 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
  • Four superperiods, each of 20 normal 10
    insertion cells
  • New and old ring circumferences 920.0
    and 1254.6 m

6
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
  • Almost exact dispersion matching is obtained

7
Lattice Functions at 14.75 GeV
8
Lattice Functions at 8 GeV
9
Lattice Functions near 20 GeV
10
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 -1.7
    -4.0 to -2.2
  • BF magnets 2.7 to -2.8
    2.7 to -2.3
  • BD magnets 3.0 to 5.0
    3.0 to 4.9
  • Range of the radial tunes
    16.11 to 42.04
  • Range of the vertical tunes
    12.77 to 14.39

11
Reference Orbit Separations (mm)
  • Energy range in GeV 9.5 to 20 8.75 to
    20 8.0 to 20
  • Long straight sections 181.2
    221.8 269.8
  • Insertion cell bd unit 180.4
    221.2 269.7
  • Normal cell bd unit 180.0
    220.7 269.0
  • Insertion cell BF quad 164.5
    206.6 267.9
  • Normal cell BF quad 160.8
    201.4 251.1
  • Insertion cell BD unit 106.7
    138.1 177.7
  • Normal cell BD unit 104.4
    134.6 172.7

12
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 20 normal and 10 insertion
    cells, and
  • all four have the same, small, acceptable
    ripple in ßh(max)
  • Ripple is ltlt than that of TRIUMFs KAON Factory,
    D ring
  • BD, BF bd magnet types are needed in the normal
    cells
  • Three slightly different types are needed for
    the insertions
  • Three, integer resonances are crossed in the
    vertical plane
  • and 26, integer resonances are crossed in
    the radial plane

13
20 MeV, Electron Model, Cell Layouts
  • bd(-) BF() BD()
    BF() bd(-)
  • O .04 .04
    .04 .04 O
  • .045 .062 .126
    .062 .045
  • .05 Normal cell (9.231º, 0.6
    m) .05
  • .20 Insertion cell (9.231º,
    0.9 m) .20
  • Three superperiods, each of 9 normal 4
    insertion cells
  • New and original ring circumferences 27.0
    and 29.25 m

14
Electron Model Design Studies
  • An e-model with insertions allows studies of
  • Matching between the insertions and normal cells
  • Emittance growth in fast slow resonance
    crossing
  • Isochronous properties of the 3 GHz, FFAG ring
  • Transient beam loading of the three, 3-cell
    cavities
  • Inject (s.c) extract from outermost side of the
    ring ?
  • Costs of injection, ejection over range 11-20
    MeV?
  • Diagnostics, with radial adjustment, in the
    insertions?
  • 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 ?
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