Momentum and angular resolution

Position of the first chamber and the distance between the two chambers were optimized for two factors, the angular resolution due to chamber position resolution and the multiple scattering. As a result, two chambers are placed at 50 cm upstream and 50 cm downstream from the first order focal plane (235 cm downstream from dipole exit).

Table 7 shows materials taken into account in the simulation. From the target to the exit of the dipole vacuum chamber (just before the first chamber) is vacuum. Figure 12 summarizes the contribution of the chamber spatial resolution and multiple scattering effects to the HKS momentum resolution. Even for a modest position resolution of 250 $\mu$m (rms), the simulation shows that momentum resolution of better than 2 $\times 10^{-4}$ FWHM ($\sigma$ = 100 keV/$c$) and scattering angular resolution of better than 0.5 mr are achieved.

表 6: Parameters used in the HKS GEANT simulation

Item	Condition
Collimator size	14 cm $\times$ 14 cm
Q1 aperture	$\vert x\vert{\leq}24$ cm
	$\vert y\vert{\leq}12$ cm
	$\vert xy\vert{\leq}(11.5)^2/2$ cm$^2$
Q2 aperture	$\vert x\vert{\leq}40$ cm
	$\vert y\vert{\leq}15$ cm
	$\vert xy\vert{\leq}(14)^2/2$ cm$^2$
Dipole aperture	$\vert x\vert{\leq}45$ cm$^*$
	$\vert y\vert{\leq}10$ cm
Momentum of	1.2 GeV/$c\pm$12.5% (Simulation for the detector size)
generated particles	1.2 GeV/$c\pm$15% (Simulation for the momeutum acceptance)
Angle $\theta$$^{**}$ of	$0^\circ\leq\theta\leq15^\circ$
generated particles

* Narrower than the actual aperture ($\vert x\vert{\leq}$ 60 cm) to estimate 'good field region' solid angle.
** Theta is defined with respect to 1.2 GeV/$c$ 0$^\circ$ ray.

表 7: Material list and properties included in the simulation

Item	$t$	$\rho$	$X_0$	thickness (/radiation length)
	(cm)	(g/cm$^3$)	(g/cm$^2$)
Dipole Exit Window
Kevlar(C$_{14}$N$_2$O$_2$H$_{10}$)	0.02	0.74	55.2	2.68 ${\times}10^{-4}$
Mylar(C$_{10}$O$_4$H$_8$)	0.01+0.0025	1.39	39.95	4.35 ${\times}10^{-4}$
SDC1
Mylar	0.012	1.39	39.95	4.18 ${\times}10^{-4}$
Ar gas	5.08	1.78 ${\times}10^{-3}$	19.55	4.63 ${\times}10^{-4}$
SDC1-SDC2 gap
He gas	94.5	1.79 ${\times}10^{-4}$	94.32	1.79 ${\times}10^{-4}$
SDC2
Mylar	0.012	1.39	39.95	4.18 ${\times}10^{-4}$
Ar gas	5.08	1.78 ${\times}10^{-3}$	19.55	4.63 ${\times}10^{-4}$