Transcript Document

MUON LINAC
Solenoids Fringe Fields
M.Aslaninejad
J.Pasternak
J.Pozimski
21.04.2009,
Lancaster
M. Aslaninejad
Fast acceleration
Linear Pre-accelerator (244 MeV to 900 MeV)
RLA I - 4.5 pass, 0.6 GeV/pass, (0.9 GeV to 3.6 GeV )
RLA II - 4.5 pass, 2 GeV/pass (3.6 GeV to 12.6 GeV )
Non scaling FFAG - 8 revolutions (12.6 GeV to 25 GeV )
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SC Linac - 244 to 909 MeV. 25 cavities: First 6 cavities
each 0.744826 meters. Second 8 cavities each 1.489652.
Third 11 cavities each 2* 1.489652. Frequency 201 MHz
O pt iM - M AIN: - M :\c as a\a cc _ phys \boga c z\IDS \P re Lina c\Lina c_ s ol.opt
8 one meter solenoids.
ks=1
0
11 one meter solenoids. ks=0.83
0
6,one meter
solenoids.
ks=1.4
DISP_X&Y[m]
BETA_X&Y[m]
5
10
Tue Fe b 1 2 12 :4 7: 13 20 0 8
0
BE TA_X
BE TA_Y
DIS P _ X
DIS P _ Y
1 46
6 short cryos
8 medium cryos
11 long cryos
15 MV/m
17 MV/m
17 MV/m
1.1 Tesla solenoid
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2.4 Tesla solenoid
1.4 Tesla solenoid
M. Aslaninejad
Initial MADX
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MADXP, with Alex initial condition.
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Concern
Difference of beta functions between OptiM code and MADX
Source of the inconsistency:
1-Fringe fields for solenoids, not included in MADX yet.
2- Mismatch in optics:
 linac focusing without a periodic boundary condition. Small
mismatch at the beginning results in large beta beating.
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Ideal linear solenoid( zero aperture )transfer matrix:
Msol
 1 + cos(kL)

2

 - k sin(kL)

4
=
 - sin(kL)
2

 1 - cos(kL)
k
4

sin(kL)
k
1 + cos(kL)
2
1 - cos(kL)
k
sin(kL)
2
sin(kL)
2
1 - cos(kL)
-k
4
1 + cos(kL)
2
k sin(kL)
4
1 - cos(kL) 

k

sin(kL) 

2
sin(kL) 
k

1 + cos(kL) 

2

k = eB0 /pc
Non-zero aperture: correction due to the finite length of the edge.
It decreases the solenoid total focusing – via the effective length of:
1
L=
B0

 Bz (s) ds
-
 edge


1
k 2a
2
2
=   Bz (s) ds - B0 L   2  -
8

Medge
Msoft sol = Medge Msol Medge
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 1
 -
edge
=
 0

 0
0
0
1
0
0
1
0
-edge
0
0 
0

1
The first 6 solenoids, with the Alex initial conditions.
The strength of the 6th solenoids a bit smaller
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Lancaster
M. Aslaninejad
All cavities off. Different initial values. Different KS for matching solenoids
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Solenoid Fringe field
Thin solenoids defined in MADX can not resolve the
problem as they produce focusing in both planes.
Fringe fields for solenoids, not yet included in MADX.
But, it is ongoing through PTC.
Define an “arbitrary element matrix” in MADX
according to the fringe field defocusing matrix.
50 matrices have been defined. Two for each solenoids
according to the corresponding solenoids strength.
Radius of each solenoids=25 cm
21.04.2009,
Lancaster
M. Aslaninejad
21.04.2009,
Lancaster
M. Aslaninejad
21.04.2009,
Lancaster
M. Aslaninejad
21.04.2009,
Lancaster
M. Aslaninejad
Summary and future plans
• Main source of inconsistency was
identified – fringe fields of solenoids
• Effects of Cavities Focusing.
• Tracking in Field Maps For Solenoids
and RF.
21.04.2009,
Lancaster
M. Aslaninejad