Difference between revisions of "Weighted Occupancy"

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<center><math> \underline{\textbf{Navigation} }</math>
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[[Uniform_distribution_in_Energy_and_Theta_LUND_files|<math>\vartriangleleft </math>]]
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[[VanWasshenova_Thesis#Moller_Scattering|<math>\triangle </math>]]
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[[Relativistic_Units|<math>\vartriangleright </math>]]
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</center>
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<pre>Total XSect=0.013866</pre>
 
<pre>Total XSect=0.013866</pre>
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=97234 incident electrons=
 
[[File:Nin97234stats.png]]
 
[[File:Nin97234stats.png]]
  
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<center><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></center>
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<center><math>t_{sim}(75nA)=\frac{N_{in}}{\frac{75E-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></center>
 
 
  
<center><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></center>
 
  
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<center><math>t_{sim}(100nA)=\frac{N_{in}}{\frac{100E-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></center>
  
  
<center>CLAS12 Occupancy=<math>\frac{N_{hits}}{N_{evt}}\frac{t_{sim}}{\Delta t}\frac{1}{112}\frac{100}{12}</math></center>
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==Method 1==
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<center>CLAS12 Occupancy<math>\equiv\frac{N_{hits}}{N_{evt}}\frac{t_{sim}}{\Delta t}\frac{1}{112}\frac{100}{12}</math></center>
  
  
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<center>Occupancy(100nA)=<math>\frac{3698.7}{270}\frac{1.56E-7}{250E-9}\frac{1}{112}\frac{100}{12}=0.637\%</math></center>
 
<center>Occupancy(100nA)=<math>\frac{3698.7}{270}\frac{1.56E-7}{250E-9}\frac{1}{112}\frac{100}{12}=0.637\%</math></center>
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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>\sigma N_{in}\rho l</math>,thus are only multiples of each other).  We can simplify this expression by:
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<center>Occupancy=<math>1.01926\%\frac{t_{sim}}{250E-9}</math></center>
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If 250ns is the time limit, then solving the time of simulation backwards will give the number of incident electrons within that window.
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<center><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></center>
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<center><math>t_{sim}(75nA)=\frac{N_{in}}{\frac{75E-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></center>
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<center><math>t_{sim}(100nA)=\frac{N_{in}}{\frac{100E-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></center>
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CEBAF has a bunch redition rate of 499MHz for hall B.  For a current of 50nA, this implies:
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<center><math>\frac{\frac{50E-9\ A}{}\frac{1C}{1A}\frac{}{1s}\frac{1\ e^{-}}{1.602E-19\ C}}{499E6\ Hz}=\frac{\frac{312,109,863,672\ e^{-}}{s}}{499E6\ Hz}=625\ e^{-}</math></center>
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If we declare that every 2ns consists of a bunch of 625 electrons each, then
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<center><math>\frac{78027.5\ e^{-}}{\left(\frac{625\ e^{-}}{2E-9\ s}\right)}=124.844\times 2E-9\ s=2.50E-7\ s</math></center>
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<center><math>\frac{117041.2\ e^{-}}{\left(\frac{625\ e^{-}}{2E-9\ s}\right)}=187.266\times 2E-9\ s=3.75E-7\ s</math></center>
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<center><math>\frac{156054.9\ e^{-}}{\left(\frac{625\ e^{-}}{2E-9\ s}\right)}=249.688\times 2E-9\ s=4.99E-7\ s</math></center>
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If we use these times as the times of simulation:
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<center>Occupancy(50nA)=<math>1.01926\%\frac{2.50E-7\ s}{250E-9}=1\%</math></center>
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<center>Occupancy(75nA)=<math>1.01926\%\frac{3.75E-7\ s}{250E-9}=1.5\%</math></center>
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<center>Occupancy(100nA)=<math>1.01926\%\frac{4.99E-7\ s}{250E-9}=2\%</math></center>
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==Method 2==
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<center>CLAS12 Occupancy<math>\equiv\frac{N_{hits}}{N_{evt}}\frac{\Delta t}{t_{sim}}\frac{1}{112}\frac{100}{12}</math></center>
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Using the unweighted amounts
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<center>Occupancy(50nA)=<math>\frac{1274783}{92967}\frac{250E-9}{3.11E-7}\frac{1}{112}\frac{100}{12}=0.82\%</math></center>
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<center>Occupancy(75nA)=<math>\frac{1274783}{92967}\frac{250E-9}{2.07E-7}\frac{1}{112}\frac{100}{12}=1.23\%</math></center>
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<center>Occupancy(100nA)=<math>\frac{1274783}{92967}\frac{250E-9}{1.56E-7}\frac{1}{112}\frac{100}{12}=1.63\%</math></center>
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Using the weighted amounts
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<center>Occupancy(50nA)=<math>\frac{3698.7}{270}\frac{250E-9}{3.11E-7}\frac{1}{112}\frac{100}{12}=0.82\%</math></center>
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<center>Occupancy(75nA)=<math>\frac{3698.7}{270}\frac{250E-9}{2.07E-7}\frac{1}{112}\frac{100}{12}=1.23\%</math></center>
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<center>Occupancy(100nA)=<math>\frac{3698.7}{270}\frac{250E-9}{1.56E-7}\frac{1}{112}\frac{100}{12}=1.63\%</math></center>
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----
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<center><math> \underline{\textbf{Navigation} }</math>
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 +
[[Uniform_distribution_in_Energy_and_Theta_LUND_files|<math>\vartriangleleft </math>]]
 +
[[VanWasshenova_Thesis#Moller_Scattering|<math>\triangle </math>]]
 +
[[Relativistic_Units|<math>\vartriangleright </math>]]
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</center>

Latest revision as of 19:59, 29 December 2018

[math] \underline{\textbf{Navigation} }[/math]

[math]\vartriangleleft [/math] [math]\triangle [/math] [math]\vartriangleright [/math]

Total XSect=0.013866

97234 incident electrons

Nin97234stats.png


[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{75E-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{100E-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]\sigma N_{in}\rho l[/math],thus are only multiples of each other). We can simplify this expression by:


Occupancy=[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{75E-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{100E-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]


CEBAF has a bunch redition rate of 499MHz for hall B. For a current of 50nA, this implies:

[math]\frac{\frac{50E-9\ A}{}\frac{1C}{1A}\frac{}{1s}\frac{1\ e^{-}}{1.602E-19\ C}}{499E6\ Hz}=\frac{\frac{312,109,863,672\ e^{-}}{s}}{499E6\ Hz}=625\ e^{-}[/math]


If we declare that every 2ns consists of a bunch of 625 electrons each, then

[math]\frac{78027.5\ e^{-}}{\left(\frac{625\ e^{-}}{2E-9\ s}\right)}=124.844\times 2E-9\ s=2.50E-7\ s[/math]


[math]\frac{117041.2\ e^{-}}{\left(\frac{625\ e^{-}}{2E-9\ s}\right)}=187.266\times 2E-9\ s=3.75E-7\ s[/math]


[math]\frac{156054.9\ e^{-}}{\left(\frac{625\ e^{-}}{2E-9\ s}\right)}=249.688\times 2E-9\ s=4.99E-7\ s[/math]


If we use these times as the times of simulation:


Occupancy(50nA)=[math]1.01926\%\frac{2.50E-7\ s}{250E-9}=1\%[/math]


Occupancy(75nA)=[math]1.01926\%\frac{3.75E-7\ s}{250E-9}=1.5\%[/math]


Occupancy(100nA)=[math]1.01926\%\frac{4.99E-7\ s}{250E-9}=2\%[/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{250E-9}{3.11E-7}\frac{1}{112}\frac{100}{12}=0.82\%[/math]


Occupancy(75nA)=[math]\frac{3698.7}{270}\frac{250E-9}{2.07E-7}\frac{1}{112}\frac{100}{12}=1.23\%[/math]


Occupancy(100nA)=[math]\frac{3698.7}{270}\frac{250E-9}{1.56E-7}\frac{1}{112}\frac{100}{12}=1.63\%[/math]




[math] \underline{\textbf{Navigation} }[/math]

[math]\vartriangleleft [/math] [math]\triangle [/math] [math]\vartriangleright [/math]