An Alternative to Grahame Rees

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An Alternative to Grahame Rees Isochronous FFAG
Lattice for the Acceleration of Muons from 10
20 GeV
Horst Schönauer, CERN
Proposed FFAG-type Muon Accelerators
Type Proposals Features Isochronous
Linear, scaling Japan, YM et al Qx,y const Far from
Linear, non-scaling CJ, AS, EK, SB et al Qx,y cross integers nearly
Non-linear, non-scaling GHR 123 cell ? t ? ? Qx,y cross integers exactly
Non-linear, non-scaling Modif. GHR  HS 66 cell Qx,y , ?t ? const. (not yet) exactly
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GHR 123 Cell Lattice 8-20 GeV
Length m B, Bmax T
Cell 19.35
O3 3
B 0.7 4
O2 1
F 1.2 1.9
O1 0.5
D 1 -2.3
O0 2
b 0.32 -1
Proposed 66 Cell Lattice 10 20 GeV
Reference Orbit 15 GeV
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• Design Principles
• Extended Triplet Cell
• One high-field SC homogenous bending per half
  cell
• One low-field room temp. homogenous bending per
  half cell
• Approx. Constant Tune no integer crossing
• Simple Elements (for tracking ) Rectang. F, D
  magnets
• Local Phase Slip accepted ? Off-crest acceleration

Basic Parameters Basic Parameters
Energy Range 10 20 GeV
Circumference 1257.52 m
Number of Cells 66
Inverted Bending b / B -1/8
Long Straight Sections 6 m
T 10 15 20 GeV
B? 33.68 50.35 67.02 Tm
B 8.42 12.59 16.75 T/m for kF, kD 0.25
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Consequences of kF,D ? const.
At y 0 (Central Energy, T 15 GeV), B0 and
B B0
10
PBF
,
gPBF
,
y
,
YFmin
,
YFmax
Evaluate
Plot
As the Gradients B are given by k (0.25 m-2) ,
the maximum fields can be lt 2T if ymax, min lt
0.1m
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10 15 10 GeV Orbits and Magnets
Superimposed (AGILE Code Results)
T Gev L Halfcell Qx Qy Gamma-t
10 19.3449 25.282 16.318 33.721
15 19.3563 26.773 15.559 22.835
20 19.3486 25.647 15.557 19.502
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Cell ToF for lin. Dx -0.37, -0.36, -0.34 m
Playing with Mathematica..
B?
Error in Cell ToF for Rectangular inverse b
Magnet with added quadratic Dx component ps
tps
Evaluate
.
Init15T
.
Incom
.
Dx70
0.37
,
0.36
,
0.34
.
Plot
-
-
-
e20
0
,
B
,
B
min
,
B
max
,
-gt
r
r
r
kF
B?
B?
Plot
Evaluate
kFeff
.
Incom
.
Init15T
,
B
,
B
min
,
B
max
Plot
Evaluate
tps0
tps
.
Init15T
.
Incom
,
B
,
B
min
,
B
max
r
r
r
-
r
r
r
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BeamOptics Representation
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BeamOptics Representation
25
20
15
m
D
m
?
10
5
0
0
5
10
15
s
m
OpticsPlot
Graphics
,
SigmaEnd
Sigma
14.3333
,
0.
,
Sigma
8.07818
,
0.
,




Tunes
0.389993
0.243576
DVectorEnd
DVector
0.304343
0.
,
Path
0.0164295
RelativeTimeDispersion
0.000849186
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(No Transcript)
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• Open Questions
• (After finalizing and optimizing the lattice)
• Consequences of local ? ? ?t
• Classical acceleration at high ?s feasible?
• RF acceptance
• Orbit control in isochronous lattice
• Dynamic aperture (Sextupole!)

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T 10 15 20 GeV
B? 33.68 50.35 67.02 Tm
B 8.42 12.59 16.75 T/m for kF, kD 0.25

Length m Bmax T
Cell 19.35
O3 3
B 0.7 4
O2 1
F 1.2 1.9
O1 0.5
D 1 -2.3
O0 2
b 0.32 1