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

G H Rees, RAL

Pros and Cons for InsertionsPros: 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 βh(max) ripple effects over a superperiod

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 α and β-functions on adding insertions Unchanged horizontal α and β-functions on adding insertions

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

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 β-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

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

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

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 βv and γ-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

Lattice Functions at 14.75 GeV

Lattice Functions at 8 GeV

Lattice Functions near 20 GeV

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

Reference Orbit Separations (mm)

Energy range in GeV 9.5 to 20 8.75 to 20 8.0 to 20

Long straight sections 181.2 221.8 269.8Insertion cell bd unit 180.4 221.2 269.7Normal cell bd unit 180.0 220.7 269.0Insertion cell BF quad 164.5 206.6 267.9Normal cell BF quad 160.8 201.4 251.1Insertion cell BD unit 106.7 138.1 177.7Normal cell BD unit 104.4 134.6 172.7

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 (22) normal + 10 (8) insertion cells & all four have the same, small, acceptable ripple in βh(max)

Ripple is << than that of TRIUMF’s 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

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 and previous ring circumferences: 27.0 and 29.25 m

Electron 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 ?