Dead-time and Yield vs Beam Intensity

To map out the dependence on beam intensity of the yield of true-tagged events, use is made of a model of the Radphi trigger that is described in detail elsewhere Ref. [2]. Without further comment I reproduce here Table 1 from that note, with values of the parameters updated based upon the measurements taken in 1999. The fact that several of the background suppression factors in Table 3 are much smaller than initially supposed explains why the rate of events to tape is so much smaller than predicted.

Table 3: Parameters supplied as input to the model, calibrated using the rates measured at 125nA and 5.5GeV endpoint in 1999.

	parameter		value		method
	$r_{_T}$		$4.00\cdot 10^5$		/s/nA		fit to TDC data
	$r_{_R}$		$5.00\cdot 10^3$		/s/nA		fit to TDC data
	$r_{_U}$		$4.5\cdot 10^4$		/s/nA		fit to TDC data
	$r_{_C}$		$3.0\cdot 10^5$		/s/nA		fit to TDC data
	$t_{_T}$		$3.0\cdot 10^{-8}$		s		TDC spectra
	$t_{_C}$		$0.0\cdot 10^{-8}$		s		(disabled)
	$d_{_T}$		$1.0\cdot 10^{-8}$		s		fit to scaler data
	$d_{_C}$		$4.0\cdot 10^{-9}$		s		fit to scaler data
	$d_2$		$1.1\cdot 10^{-5}$		s		measured on scope
	$d_{_{DAQ}}$		$3.0\cdot 10^{-4}$		s		measured on scope
	$f_s$		$5.5\cdot 10^{-3}$				measured at low rates
	$f_n$		$5.5\cdot 10^{-1}$				from TDC spectra
	$f_c$		$1.1\cdot 10^{-2}$				measured at low rates
	$f_p$		$3.3\cdot 10^{-1}$				from TDC spectra
	$f_{2s}$		$1.0\cdot 10^{-1}$				from TDC spectra
	$f_{2n}$		$8.0\cdot 10^{-3}$				from TDC spectra
	$f_{2c}$		$3.2\cdot 10^{-1}$				from TDC spectra
	$f_{2p}$		$3.3\cdot 10^{-2}$				from TDC spectra
	$f_{3s}$		$0.5\cdot 10^{-2}$				from TDC spectra
	$f_{3n}$		$0.1\cdot 10^{-3}$				from TDC spectra
	$f_{3c}$		$0.9\cdot 10^{-2}$				from TDC spectra
	$f_{3p}$		$2.8\cdot 10^{-4}$				from TDC spectra

The model gives good agreement with the measured rates at 125nA and 20nA taken during July-August 1999. Using the model it is now possible to extrapolate to beam currents where there are no measurements, and decide what is the optimum beam current at which to run. The experimental live-time fraction is shown in Fig. 4 under the conditions of 1999 running. The dead-time contributions from each of DAQ, level 3 and level 2 are shown by the stacked curves. Level 2 is clearly the most important. As mentioned above, we have a scheme in hand that will enable us to reduce the level 2 dead-time per event by a factor of 2. The new live-time curve from this modification resulting resulting from this modification is shown in Fig. 5.

Figure 4: Calculated live time vs beam current under the conditions for 1999 running, calibrated using the measurements described in this report.

Figure 5: Improved live-time vs beam current profile, after reducing the level-1 dead time as described in the text.

The bottom line is determined by the number of true-coincidence events being written to tape per second. This quantity is plotted vs beam current if Fig. 6. The point represented by $5\cdot 10^7$ photons/s is 125nA in this figure. The curve is still rising at this current, indicating that the trigger is still some distance from saturation.

From these results we conclude that the Radphi trigger is now capable of taking data at the luminosity listed in the proposal. Some improvements over the performance obtained in 1999 can yet be obtained by streamlining the level 2 trigger and optimizing the relative timing of the tagger and BSD counters. A further study is planned to investigate how much acceptance can be gained by reducing the diameter of the target. Using the data on tape from the 1999 run it will be possible to refine the choice of the BSD threshold to maintain good acceptance for protons while improving somewhat the background rejection at level 1.

Figure 6: Rate of writing signal events to tape vs beam current under conditions foreseen for running during Y2K. Signal events are defined as those generated from a photon within the tagging energy range, and which did not include a charge track.