Optics and detector geometries

The TRANSPORT calculations were performed to optimize the magnetic fields for the various configuration of the HKS magnets (Q1, Q2 length, the distance between magnets and other geometrical configurations). The calculation took into account the second order effect and the fringe field effect with the Graphical Transport which was modified at PSI. With the optimized parameters, a GEANT Monte-Carlo simulation was carried out and the HKS momentum resolution and the solid angle were estimated. Table 5 summarized the optimized magnetic field parameters and the geometrical conditions for the HKS magnets.

表 5: Summary of the HKS TRANSPORT calculation

Item	Given or Optimized values
Q1 length (cm)	84
Q1 bore radius (cm)	12
Q1 Field Gradient (T/m)	-5.43
Q1 Integral Field Gradient (T/m$\cdot$m)	-5.20
Q2 bore radius (cm)	14.5
Q2 Field Gradient (T/m)	3.32
Q2 Integral Field Gradient (T/m$\cdot$m)	2.47
Dipole Field (T)	1.44

Red lines shown in Figure 4 shows particle trajectories in the horizontal plane ($\theta$ = 7$^\circ$, 7$\pm2.7^\circ$), obtained with the simulation code. Horizontal focusing property of the HKS is clearly seen.

Active areas of the HKS detectors are determined to cover the momentum acceptance of 1.2 GeV/$c \pm 12.5$% and to maximize the geometrical acceptance. Figure 8 shows beam profiles at each detector position. The active area of each detector is indicated by a square in the figure and listed in Table 11. Geometries and conditions used in the simulation are summarized in Table 6.