Weighted Occupancy

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]

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]