Difference between revisions of "Defining Occupancy"
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<center><math>t_{sim} \equiv </math> Time of simulation = <math>\frac{N_{incident}}{I(A)}\frac{1A}{1C}\frac{1s}{}\frac{1.602E-19\ C}{1\ e^{-}}</math></center> | <center><math>t_{sim} \equiv </math> Time of simulation = <math>\frac{N_{incident}}{I(A)}\frac{1A}{1C}\frac{1s}{}\frac{1.602E-19\ C}{1\ e^{-}}</math></center> | ||
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+ | When applying the Moller differential cross-section as a weight, this gives the "Weighted Occupancy" as: | ||
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+ | <center>''Weighted'' CLAS12 DC occupancy <math>\equiv \frac{N_{hits}}{N_{evt}}\frac{\Delta t}{t_{sim}}\frac{1}{112}\frac{1}{12}</math></center> | ||
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− | + | Since the expression for the differential cross-section for Moller Scattering is well know, we can solve for the minimum angle detected by the DC (5 degrees in Theta). | |
− | + | <center><math>(\theta=5^{\circ}) \frac{d\sigma}{d\Omega}=\frac{\frac{N_{scattered}{solid\ angle}}{\frac{N_{incident}}{area}}</math></center> | |
− | <center> |
Revision as of 04:17, 23 July 2018
The occupancy measures the number of particles interactions per a detector cell per an event. For the CLAS12 drift chamber, there are 112 wires on each layer, with 12 layers within a region, giving 1344 cells. This can simply be defined as the "Unweighted Occupancy" for the CLAS12 DC and follows the equation:
where
The registering of a "hit" takes a finite time in which the detector and its associated electronics are not able to register an additional signal if it occurs. This time window is known as the "dead time" during which only limited events are registered. For Region 1:
Since the events are simulated outside the dead time constraints of the DC, we can factor in the number of event windows that occur by dividing the dead time window per region by the time that would have been required to produce the number of incident electrons given a known current.
When applying the Moller differential cross-section as a weight, this gives the "Weighted Occupancy" as:
Using the definition of the cross-section:
where the flux is defined as:
Making some assumptions that the flux can be taken over an same time range as the time found in the cross-section, which allows
For a LH2 target of length 5cm.
Additionally, for Moller Scattering, we can assume that almost 100% of the incident electrons occur as events.
This allows us to rewrite the cross-section expression as,
Since the expression for the differential cross-section for Moller Scattering is well know, we can solve for the minimum angle detected by the DC (5 degrees in Theta).