To determine the timing properties of the pulses created in the PMT pixels of the present Whipple 10m camera and in proposed mirror and cameras for Veritas due to the shower PE's I have resorted to simulating in detail (.25 ns steps) the signal out that comes out of the base of the PMTs as a function of time. This is done by starting with a generic single pe pulse height profile, Figure 1, top plot. (the measured pulse profile was provided by John Finley). This pulse profile is given in .25ns steps and the peak has been normalized to 1. The risetime of this pulse is about 2 ns and the fall time is about 7.5 ns.

The modeling scheme is to take copies of this pulse profile, one for each pe generated in a particular PMT by a shower, and add them together shifted relative to each other as appropriate to their arrival times at the mirror focal plane. The model also simulates the relative pulse heights by choosing randomly for each pe pulse a pulse height from a single pe pulse height distribution as measured by C. Wilson, Figure 1, Middle plot. The mean of this distribution has been normalized to 1.0.

The sky shine 'NOISE' background to the pulses is simulated in a simular manner. Since we know the average arrival rate of the sky shine PE's at the PMT's (about .5 pe/ns/pixel in the 331 camera) we generate a random set of arrival times of sky shine photons, add the single pe profiles (again using the pulse height distribution) using these times the result is a typical plot of the background 'noise' that comes out of the pmt. The full model is realized by summing the sky shine 'noise' plot and the summed shower pe pulse.

As an example of this technique I show in the following figures results of a simulation study I made of the response of the Constant Fraction Discriminators (CFD) to a pulse of 20 pe's with 0 time spread impacting at random places on the Whipple 10m diameter 7.3m focal length mirror. The resultant time spread distribution can be see in Figure 1, Bottom plot. This distribution is due totally to the different path lengths the photons must travel to the focal plane when they impact at various places on the mirror. In the figures below the top plot is of the resultant pulse (which includes the afore mentioned individual pulse height variability) after undergoing these delays. The middle plot is the sky shine 'noise' plot generated for this event (a separate noise plot is generated for each shower pulse). The solid line in the bottom plot of the figure is of the sum of the noise and 'pure' pe pulse. To model the CFD's this solid plot is then delayed and amplified (in this particular case the delay was set to 2 ns and the amplification was 1.05). Where these two plots cross (after the first exceeds some threshold, set to 26 for this example) the CFD will fire. The middle plot in Figure 13 indicates how well the CFD's work and their insensitivity to the background noise and and variations in pulse height. This plot is the CFD trigger times for 10,000 20 pe pulses.

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Last updated: 24 Oct, 2005