Effective Spill # EFFECTIVE SPILL

The effective spill is a measure of the uniformity of the arrival times of the beam particles. Typically an experiment has a deadtime, once a trigger has occurred. Any particle that comes inside that deadtime will effectively be lost. For a given number of particles N and a total spill length T, the best one can do is a uniform distributiuon of particles, provided the deadtime is shorter than T/N.
Deviations from uniformity can occur at high frequencies (e.g. related to RF), medium frequencies (multiples of 50 Hz) or slow variations over the spill, e.g. if the beam moves slowly over small apertures. In that case the data-taking capability of the experiment may be reduced as if the same number of particles N were arriving over a shorther time, the so-called effective spill.

Ususally the effective spill is measured by taking the coincidence of a singles rate with a delayed copy of itself, as illustrated below: As one sees already in the figure, coincidences occur preferentially if the instantaneous singles rate is high. In fact the effective spill can be estimated as

## Eff.Spill = Gate x Singles2 / Del.Coincidence

.

And indeed one observes that the effective spill decreases when the coincidence rate goes up.
The formula can be understood as follows:

• For every single signal a gate of with Gate is opened. The total time occupied by these gates is Topen = Singles x Gate.
• The number of coincidences in this time Topen is C, which is a fraction F = C/S of the total number of possible coincidences.
• The singles rate suffers also from deadtime with the same probability. Therefore Topen = Eff.Spill * F, which gives the formula quoted above
The gate should be chosen as typical for the deadtime of the experiment. Typical values are of the order of 10 nsec.
The delay is related to the highest frequencies that can be sampled. Typical values are of the order of 50 nsec.

The effective spill measurement of an experiment can be shown on page-1. The experiment should provide two NIM signals into experimental scalers and define the gate width. The EA physicists can declare the equipment numbers of the scalers, using the p1spill interface (SingleSpill for the singles, RateSpill for the delayed coincidence), as well as the Gate width in nsec.
Typical values of the effective spill range from 1.5 to 2.0 seconds for a nominal spill length T of 2.38 seconds.

From L. Gatignon

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