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 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$^{0.8}$.
3. Electron rate in Enge was evaluated by two methods: one by EGS code and the other by Light body code, which agreed more or less to each other.
4. Pion rate in Enge was calculated based on the EPC code, and normalized by the same factor used for hadron rates in HKS.

The estimated rates for the three targets at the beam intensity of 30 $\mu$A are summarized in Table 8. 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 HKS is placed at an angle off 0 degrees. The singles rate of the ENGE hodoscope is expected almost two orders of magnitude less than that of E89-009.

表 8: Singles rates for 100 mg/cm$^2$ targets

	Beam	HKS				Enge
Target	Intensity	$e^+$ rate	$\pi^+$ rate	$K^+$ rate	$p$ rate	$e^-$ rate	$\pi^-$ rate
	($\mu$A)	(MHz)	(kHz)	(Hz)	(kHz)	(MHz)	(kHz)
$^{12}$C	30	-	800	340	280	2.6	2.8
$^{28}$Si	30	-	800	290	240	5.1	2.8
$^{51}$V	30	-	770	260	230	6.9	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 4 $\times$ $10^{-4}$,
4. Enge singles rate is dominated by $e^-$ rate and it is less than 10 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,

$$\begin{eqnarray*} Trigger\: rate & = & (Kaon\: Arm) \times (Electron\: Arm) \tim... ... (50 \times 10^{-9}) \: \mbox{[s]}\\ & = & 400 \: \mbox{[Hz]}. \end{eqnarray*}$$

The total trigger rate of 400 Hz can be easily handled with a conventional data taking system, but it is essential to install highly efficient Cerenkov counters to veto protons and pions in the kaon arm as assumed above. The trigger counter system is designed to meet this requirement as described in the detector section.