Singles rates for HKS, ENGE and coincidence triggers

The procedures to evaluate singles rates of each particle in HKS and Enge spectrometers are explained in the following:

1. The $\pi^+$ and proton rates in HKS were calculated based on the EPC code, and they were normalized by the experimental values measured in E89-009 for a carbon target at 2.2 degrees.
2. Quasifree kaon production cross section was assumed to scale as A$^{0.8}$. The index of 0.8 was taken from the effective proton numbers of the $^{12}$C($\gamma$, K$^+$) reaction.
3. Positron rate in HKS was evaluated with the GEANT simulation code using $1.7 \times 10^4$ positron events (corresponds to 1.9 $\times 10^9$ beam electrons bombarding 100mg/cm$^2$ carbon target, i.e. 30$\mu$A beam for 10$\mu$s) generated by EGS code. No positrons passed through the dipole.
4. Electron rate in Enge was evaluated by two methods, one by EGS code and the other by Lightbody's code, which agreed more or less to each other.
5. Pion rate in Enge was calculated based on the EPC code, and normalized by the same factor used for the hadron rates in HKS.

The estimated rates for the three targets at the beam intensity of 30 $\mu$A are summarized in table 10. As shown, the singles rate of HKS is dominated by positive pions, while that for Enge by electrons. The positron rate in HKS is expected low since we setup HKS at an angle off 0 degrees. The estimated singles rate of the ENGE hodoscope is almost two orders of magnitude less than that of E89-009.

表 10: Singles rates

	Beam	HKS				Enge
Target	Intensity	$e^+$ rate	$\pi^+$ rate	$K^+$ rate	$p$ rate	$e^-$ rate	$\pi^-$ rate
	($\mu$A)	(kHz)	(kHz)	(kHz)	(kHz)	(kHz)	(kHz)
$^{12}$C	30	-	420	0.38	150	1,000	2.8
$^{28}$Si	30	-	420	0.32	130	1,900	2.8
$^{51}$V	30	-	410	0.29	120	2,650	3.0

With the estimated rates, the hardware coincidence between the electron arm and the kaon arm can form good triggers. The coincidence trigger rate was evaluated assuming:

1. The $\pi^+$, K$^+$, proton rates in HKS are 1 MHz, 500 Hz and 0.5 MHz, respectively,
2. Aerogel Cerenkov counter pion rejection efficiency is 1 $\times$ $10^{-4}$,
3. Water Cerenkov counter proton rejection efficiency is 5 $\times$ $10^{-4}$,
4. Enge singles rate is dominated by $e^-$ rate and it is less than 5 MHz,
5. Coincidence trigger is mainly produced by the accidental coincidence between kaon and electron arm signals,
6. Hardware coincidence time window is 50 ns,

$$\begin{eqnarray*} Trigger\: rate & = & (Kaon\: Arm) \times (Electron\: Arm) \ti... ...50 \times 10^{-9}) \: \mbox{[s]}\\ & = & 200 \: \mbox{[Hz]}. \end{eqnarray*}$$

The total trigger rate of 200 Hz can be easily handled by the Hall C data acquisition system. It is essential to install Cerenkov counters to veto protons and pions with high efficiency. The trigger counter system is designed to meet this requirement as described in the detector section.