Title: Insertions for an Isochronous, 8-16 turn, 8-20 GeV, Muon IFFAG
1Insertions for an Isochronous, 8-16 turn,
8-20 GeV, Muon IFFAG
2Pros 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
3Criteria 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. -
-
4Options 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
- Dispersion suppressors (2?) have not been
included - as too many are needed they are
non-isochronous
520 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 - There are four, 30 - cell superperiods,
with either - 20 or 22 normal cells, and hence 10 or 8
insertion cells. - New / old ring circumferences 920.0 or
889.6 / 1254.6 m
6Evaluation 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
7Lattice Functions at 14.75 GeV
8 Lattice Functions at 8 GeV
9 Lattice Functions near 20 GeV
10Superperiod 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
11Reference 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
12Insertion 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 (22) normal 10 (8)
insertion cells - 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 -
-
1320 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 and previous ring circumferences 27.0
and 29.25 m
14Electron Model 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 ?