1. ▪ Issues after KOBRA review meeting
01. 3 Tm for stage 2 is really required?  2 Tm
02. Vertical magnification at F5 is quite large (7.00)
03. Higher order aberration cannot be corrected especially for larger acceptance
04. More realistic calculation – field map etc
05. Simulation with whole system including target and detection system. Reaction ?
06. Available energy range ?
07. Background rejection issue
08. Usage of degrader (case of RCNP, Osaka)
09. After including realistic field map, ray-tracing calculation for WF is needed
10. Find best configuration for specific reactions, and adjust
11. Consider a degrader in stage 1. Uniform thickness degrader is recommended (ex 10 micron)
12. Calculate primary beam trajectories together with consideration for its intensity (4kW?)
13. Shorter is better because of the possibility of an imperfection
14. “Energy range of ±16%” it is unnecessary for low energy experiment
15. For Q3-Q6, ellipse can be considered
16. R~2900 ≠ requirement 10-4  Improve resolving power of stage 2 by adjusting D3

2. Stage 2 (last version) Mx=0.83 Dx=-2.7 2 m My=7.6
Q15-Q18: E.L m, aperture radius 0.12 m
D3 : radius 2.0 m, angle 60 deg, 0.12 m half gap
WF2 : Length 4 m
Mx=0.83
Dx=-2.7
2 m
My=7.6
(a|a)=(b|b)=0
(x|a)=(y|b)=0
(x|a)=(y|b)=0
Fitting constraint
Reasonable field strength, angular acceptance and resolving power
k-trace
mocadi
Vertical magnification at focal plane are not good.

3. Another Deflection Angle (Dipole 3) - Magnification(Mx), Dispersion(Dx)
Fit field of Q17 and Q18 with changing defection angle of D3. Fitting variable is (x|a)+(y|b).
* D3 : radius 2.0 m, 0.12 m half gap
60 deg
90 deg
110 deg
If Def. Ang. is changed, we can improve Mx by a factor of 2 without significant change of Dx. (but cost should be considered)

4. Another Deflection Angle (Dipole 3) – About My
shortest length in the condition of reasonable field strength
DL=3
DL=2
DL=1.5 My DL

5. With Short WF2 / Without WF2
Fitting constraint
(x|a)+(y|b)
Short WF2 (2m)
Mx=0.83
My=7.6
Without WF2
Upstream of QQD is not so related to magnification at final focal plane.
But the effect of higher order aberration would be high.
Mx=0.83
My=7.6

6. Another element which effects on My – Drift length
Fitting constraint
(x|a)+(y|b)
DL1
DL2
DL3
60 deg case
90 deg case
inverse proportion
inverse proportion
The regular pattern of vertical magnification appears with specific deflection angle, but irregular with angle
proportion
inverse proportion
proportion
inverse proportion

7. Another element which effects on My – Length of Magnet
Fitting constraint
(x|a)+(y|b)
50 cm
10 cm
Another element which effects on My – Fitting Constraint(Fitting Variables)
ORIGINAL F4 F5
Y|Y
B|Y
Y|Y
B|Y
Y|B
B|B
Y|B
B|B
(a|a)=(b|b)=0
(x|a)=(y|b)=0
(x|a)=(y|b)=0
In both cases, field strength is not reasonable, or angular acceptance decreases

8. Result R1st ~ >10000 Mx=0.29 Dx=-3.4 My=-4.3 0.1 1.7 1.1
With Single Quadrupole
Mx=0.29
Dx=-3.4
My=-4.3
drift length should be adjusted
0.4 T
0.08 T
1.0 T
R1st ~ >10000
take into account higher order aberration
5th order
5th order (original)
Mx and My are not changed

9. ▪ Summary of Design Procedure
Optimization of KOBRA configuration
Magnet/WF design &
manufacture
EL, Aperture(good field region), Field strength
Find best configuration for specific reactions
Resolving power
Realistic field information of magnets
Angular/Energy acceptance
Minimization of higher order aberrations
Apply the field information to codes
Primary beam dump
Fringe field, good field region  K-trace, GICOSY
Field map  GEANT4
GICOSY/MOCADI, K-trace is used.
K-trace provides suitable field region which is available beyond bore radius.
If we use also GICOSY for optimization, we first should make same condition such as definition of effective length and shape of fringe field.
In case of K-trace, it is clear.
We are not sure how GICOSY describes magnetic field. We need to understand.
More realistic calculation / Adjust
Construction

10. ▪ Magnetic Field of magnet in GICOSY
Quadruple
Quadruple
No fringe field
Matrices
. . .
values are determined based on the equation of motion. B
r=R
r=R/2 z
r=0
imagine what it look like on x-y coordinate at z=center of magnet y
r=R
perfect equal distance contour
(quadrupole magnet in ideal condition)
Can we imagine this magnetic field ? x
r=0

11. ? ▪ Higher order term in magnetic field / Higher order matrix elements
Higher order matrix of quadrupole magnet
Field in x-y coordinate ?
In real magnet, there are multipole magnet terms
higher order matrix elements
Are these related?
or, is the higher order matrix elements in GICOSY still perfect magnet?
z=center of magnet

12. ? ▪ Fringe field in GICOSY/K-trace
How to be describe the quadrupole field in K-trace
Field distribution calculated by TOSCA
Formula in K-trace well reproduces the realistic fringe field.
at z=center of magnet ?
perfect equal distance contour in K-trace?

13. ? ▪ Fringe field in GICOSY/K-trace
If we use fringe field command in GICOSY,
gicosyff.dat
coefficients for Enge function
We can modify that and get Enge function we want
This does not mean Bx, By, Bz, but h(z)
We can get additional matrix which is related to fringe field.
But we don’t know detailed field information.
We just know form of Enge function with given coefficients. ?
GICOSY can reproduce realistic fringe field like K-trace?