Total XSect=0.013866
97234 incident electrons
[math]t_{sim}(50nA)=\frac{N_{in}}{\frac{50E-9\ A}{}\frac{1\ C}{1\ A}\frac{}{1\ s}\frac{1\ e^{-}}{1.602E-19\ C}}=\frac{97234\ e^{-}}{312,109,862,672\ e^{-}/s}=3.11E-7\ s[/math]
[math]t_{sim}(75nA)=\frac{N_{in}}{\frac{50E-9\ A}{}\frac{1\ C}{1\ A}\frac{}{1\ s}\frac{1\ e^{-}}{1.602E-19\ C}}=\frac{97234\ e^{-}}{468,164,794,007\ e^{-}/s}=2.07E-7\ s[/math]
[math]t_{sim}(100nA)=\frac{N_{in}}{\frac{50E-9\ A}{}\frac{1\ C}{1\ A}\frac{}{1\ s}\frac{1\ e^{-}}{1.602E-19\ C}}=\frac{97234\ e^{-}}{624,219,725,343\ e^{-}/s}=1.56E-7\ s[/math]
Method 1
CLAS12 Occupancy[math]\equiv\frac{N_{hits}}{N_{evt}}\frac{t_{sim}}{\Delta t}\frac{1}{112}\frac{100}{12}[/math]
Using the unweighted amounts
Occupancy(50nA)=[math]\frac{1274783}{92967}\frac{3.11E-7}{250E-9}\frac{1}{112}\frac{100}{12}=1.27\%[/math]
Occupancy(75nA)=[math]\frac{1274783}{92967}\frac{2.07E-7}{250E-9}\frac{1}{112}\frac{100}{12}=0.844\%[/math]
Occupancy(100nA)=[math]\frac{1274783}{92967}\frac{1.56E-7}{250E-9}\frac{1}{112}\frac{100}{12}=0.637\%[/math]
Using the weighted amounts
Occupancy(50nA)=[math]\frac{3698.7}{270}\frac{3.11E-7}{250E-9}\frac{1}{112}\frac{100}{12}=1.27\%[/math]
Occupancy(75nA)=[math]\frac{3698.7}{270}\frac{2.07E-7}{250E-9}\frac{1}{112}\frac{100}{12}=0.844\%[/math]
Occupancy(100nA)=[math]\frac{3698.7}{270}\frac{1.56E-7}{250E-9}\frac{1}{112}\frac{100}{12}=0.637\%[/math]
The non-time terms can be considered to be constant since they are either simple number such as 12 or functions which depend on the same variables such as the number of hits and number of events (Both terms are found by [math]\sigmaN_{in}\rho l[/math],thus are only multiples of each other). We can simplify this expression by:
Occupancy(100nA)=[math]1.01926\%frac{t_{sim}}{250E-9}[/math]
If 250ns is the time limit, then solving the time of simulation backwards will give the number of incident electrons within that window.
[math]t_{sim}(50nA)=\frac{N_{in}}{\frac{50E-9\ A}{}\frac{1\ C}{1\ A}\frac{}{1\ s}\frac{1\ e^{-}}{1.602E-19\ C}}=\frac{N_{in}}{312,109,862,672\ e^{-}/s}=250E-9\ s\rightarrow N_{in}=78027.5\ e^{-}[/math]
[math]t_{sim}(75nA)=\frac{N_{in}}{\frac{50E-9\ A}{}\frac{1\ C}{1\ A}\frac{}{1\ s}\frac{1\ e^{-}}{1.602E-19\ C}}=\frac{N_{in}}{468,164,794,007\ e^{-}/s}=250E-9\ s\rightarrow N_{in}=117041.2\ e^{-}[/math]
[math]t_{sim}(100nA)=\frac{N_{in}}{\frac{50E-9\ A}{}\frac{1\ C}{1\ A}\frac{}{1\ s}\frac{1\ e^{-}}{1.602E-19\ C}}=\frac{N_{in}}{624,219,725,343\ e^{-}/s}=250E-9\ s\rightarrow N_{in}=156054.9\ e^{-}[/math]
Method 2
CLAS12 Occupancy[math]\equiv\frac{N_{hits}}{N_{evt}}\frac{\Delta t}{t_{sim}}\frac{1}{112}\frac{100}{12}[/math]
Using the unweighted amounts
Occupancy(50nA)=[math]\frac{1274783}{92967}\frac{250E-9}{3.11E-7}\frac{1}{112}\frac{100}{12}=0.82\%[/math]
Occupancy(75nA)=[math]\frac{1274783}{92967}\frac{250E-9}{2.07E-7}\frac{1}{112}\frac{100}{12}=1.23\%[/math]
Occupancy(100nA)=[math]\frac{1274783}{92967}\frac{250E-9}{1.56E-7}\frac{1}{112}\frac{100}{12}=1.63\%[/math]
Using the weighted amounts
Occupancy(50nA)=[math]\frac{3698.7}{270}\frac{3.11E-7}{250E-9}\frac{1}{112}\frac{100}{12}=0.82\%[/math]
Occupancy(75nA)=[math]\frac{3698.7}{270}\frac{2.07E-7}{250E-9}\frac{1}{112}\frac{100}{12}=1.23\%[/math]
Occupancy(100nA)=[math]\frac{3698.7}{270}\frac{1.56E-7}{250E-9}\frac{1}{112}\frac{100}{12}=1.63\%[/math]
