▪ 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

Stage 2 (last version) Mx=0.83 Dx=-2.7 2 m My=7.6 Q15-Q18: E.L. 0.45 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.

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)

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

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

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

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

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

▪ 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

▪ 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

? ▪ 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

? ▪ 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?

? ▪ 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?