# PowerPoint Presentation

Document Sample

```					               MUON LINAC
Solenoids Fringe Fields

J.Pasternak
J.Pozimski

Lancaster
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 )

Lancaster
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
Tue Feb 12 12:47:13 2008    OptiM - MAIN: - M:\casa\acc_phys\bogacz\IDS \PreLinac\Linac_sol.opt
10

5
BE TA_ X&Y [m]

DISP _X&Y [m]
8 one meter solenoids.
ks=1                                              11 one meter solenoids. ks=0.83
6,one meter
solenoids.
ks=1.4
0

0
0        BE TA_X      BE TA_Y       DISP_X      DISP_Y                                                                        146

6 short cryos                    8 medium cryos                                                       11 long cryos

15 MV/m                         17 MV/m                                                            17 MV/m

1.1 Tesla solenoid                                         1.4 Tesla solenoid                                             2.4 Tesla solenoid

Lancaster

Lancaster

Lancaster
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.

Lancaster
Ideal linear solenoid( zero aperture )transfer matrix:
 1 + cos(kL)      sin(kL)          sin(kL)       1 - cos(kL) 
      2               k                 2              k     
                                                             
 - k sin(kL)   1 + cos(kL)
-k
1 - cos(kL)     sin(kL) 
       4              2                   4            2             k = eB0 /pc
=
sin(kL) 
Msol
 - sin(kL)     -
1 - cos(kL)     1 + cos(kL)                 
       2               k                2              k     
 1 - cos(kL)       sin(kL)         k sin(kL)     1 + cos(kL) 
k                -               -                           
       4               2                 4             2     

Non-zero aperture: correction due to the finite length of the edge.
It decreases the solenoid total focusing – via the effective length of:
 1          0      0     0
 -                      0
1                    
                              
k 2a                            1      0
=                          
1
L=       B (s) ds         edge =   Bz (s) ds - B0 L   -
2          2
Medge
edge

B0   -
z
2  -                      8                  0          0      1     0
                          
 0
            0   -edge   1


Msoft sol = Medge Msol Medge

Lancaster
The first 6 solenoids, with the Alex initial conditions.
The strength of the 6th solenoids a bit smaller

Lancaster
All cavities off. Different initial values. Different KS for matching solenoids

Lancaster
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.

Lancaster
Lancaster
Lancaster
Lancaster
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.