Revision as of 20:11, 30 December 2016

@@ Line 43: / Line 43: @@
 ==Detector Occupancy==
-==Comparing Rates==
+==[[Comparing With Whitney Rates]]==
-Using the values from Whitney:
-<center>[[File:Whitney_values.png‎]]</center>
-For a 5cm target of LH2:
-<center><math>\rho_{target}\times l_{target}=\frac{70.85 kg}{1 m^3}\times \frac{1 mole}{2.02 g} \times \frac{1000g}{1 kg} \times \frac{6.022\times10^{23} molecules\ LH_2}{1 mole} \frac{2 atoms}{1\ molecule\ LH_2} \times \frac{1m^3}{(100 cm)^3} \times \frac{5 cm}{ }=2.11\times 10^{23} \times \frac{10^{-24} cm^{2}}{barn}=2.11\times 10^{-1}\ barns^{-1}</math></center>
-Using the beam current of 100nA,
-<center><math>\Phi_{beam}=\frac{100\times 10^{-9}\ A}{1} \times \frac{1\ C}{1\ A} \times \frac{1\ e^{-}}{1\ s} \times \frac{1}{1.602\times 10^{-19}C}\Rightarrow 6.2422\times 10^{11}\ \frac{1}{s}=\Phi_{e^{-}}</math></center>
-Given the beam Luminosity of:
-<center><math>\mathcal {L}=\frac{1.32\times 10^{35}}{cm^2 \cdot s}\frac{10^{-24} cm^{2}}{barn}=\frac{1.32\times 10^{11}}{barn\cdot s}=\Phi_{beam}\ \rho\ l_{target}</math></center>
-We can check to make sure the density makes sense
-<center><math>\Rightarrow \rho_{target}=\frac{1.32\times 10^{35}}{ \Phi_{beam}\ l_{target}cm^2 \cdot s}=\frac{1.32\times 10^{35}}{ 6.24\times 10^{11}\  \cdot 5cm^3}=\frac{4.23\times 10^{22}}{cm^3}</math></center>
-<center><math>\Rightarrow \rho_{target}=\frac{70.85 kg}{1 m^3}\times \frac{1 mole}{2.02 g} \times \frac{1000g}{1 kg} \times \frac{6.022\times10^{23} molecules\ LH_2}{1 mole} \times \frac{1m^3}{(100 cm)^3}\frac{2 atoms}{1\ molecule\ LH_2}=\frac{4.23\times 10^{22}}{cm^3}</math></center>
-Using the values from Whitney :
-https://wiki.iac.isu.edu/index.php/CLAS12_RateEst_byWA
-{| class="wikitable" align="center" border=1
-|+ '''Rates'''
-|-
-| Energy || 6 GeV || 11 GeV
-|-
-|Process || (nb) || (nb)
-|-
-|Moller || 22773001||75008636
-|-
-| DIS + radiative tail  || 128 || 83
-|-
-| Elastic e-p || 5511220 ||3670740
-|-
-|Elastic radiative tail || 24705 || 12944
-|-
-| π0 electro-production || 14802 ||17908
-|-
-| π0 photo-production || 569 || 852
-|-
-| π+ electro-production || 4032 || 5536
-|-
-| π+ photo-production || 282 || 487
-|-
-|  π− electro-production ||  2806 || 3843
-|-
-|  π− photo-production || 199 || 342
-|-
-|  Total || 2.83317E7 || 7.87214E7
-|}
-<center><math>R_{events}= \sigma_{events} \mathcal{L}=7.87\times 10^{-2}\ barn\ \cdot \frac{1.33\times 10^{11}}{barn\cdot s}=\frac{1.05\times 10^{10}events}{s}</math></center>
-<center><math>R_{Moller}= \sigma_{Moller} \mathcal{L}=7.50\times 10^{-2}\ barn\ \cdot \frac{1.33\times 10^{11}}{barn\cdot s}=\frac{9.97\times 10^{9}Moller}{s}</math></center>
-[[File:CLAS12ExpWS_WA.pdf]]
-<center>[[File:Whitney_2.png]][[File:Whitney_3.png]]</center>
-<center>[[File:Whitney_4.png]]</center>
-<center><math>\sigma=\frac{R}{\mathcal{L}}=\frac{dN}{dt}\cdot \frac{1}{\mathcal{L}}</math></center>
-<center><math>\Rightarrow \int\limits_{0}^{t}\, dt=\int\limits_{0}^{N}\frac{1}{\sigma \mathcal{L}}\, dN</math></center>
-<center><math>t_{simulated}=\frac{N_{events}}{\sigma_{events} \Phi \rho \ell}=\frac{1000000\ barn \cdot s}{7.87\times 10^{-2} \cdot 1.33\times 10^{11}\ barn}=9.54\times 10^{-5} s</math></center>
-<center><math>N_0=\Delta t \cdot R_{events}=\Delta t \cdot \frac{N_{events}}{t_{simulated}}=500\times 10^{-9}\ s \cdot \frac{1\times 10^6}{0.0954\times 10^{-3}\ s}=5240</math></center>
-<center><math>Occupancy=\frac{N_{hits}}{N_0}=\frac{N_{hits}}{\Delta t \cdot R_{events}}=\frac{t_{simulated}\cdot N_{hits}}{N_{events}\cdot \Delta t}=</math></center>
-Similarly,
-<center><math>N_{events} =R_{events}\cdot t_{simulated}=\frac{1.05\times 10^{10}events}{s} \cdot 9.54\times 10^{-5} s=1001700\ events</math></center>
-<center><math>N_{Moller} =R_{Moller}\cdot t_{simulated}=\frac{9.97\times 10^{9}Moller}{s} \cdot 9.54\times 10^{-5} s=951138\ Moller</math></center>
-<center><math>\sigma=\frac{N_{events}}{N_{incident}}\frac{1}{\rho \ell}\Rightarrow N_{incident}=\frac{N_{events}}{\sigma \rho \ell}=\frac{951138}{.075\cdot 2.11\times 10^{-1}}=6\times 10^7\ incident </math></center>
-<center><math>\left ( \frac{Number\ of\ hits}{Moller\ electron}\right ) \left (\frac{Moller\ electrons}{incidents\ electron} \right) \left (\frac{incident\ electrons}{sec} \right )</math></center>

Difference between revisions of "VanWasshenova Thesis"

Revision as of 20:11, 30 December 2016

Contents

Introduction

Moller Scattering

Moller Scattering Definition

Variables_Used_in_Elastic_Scattering

DV_Calculations_of_4-momentum_components

Moller Differential Cross-Section

GEANT4 Simulation of Moller Scattering

LH2 Target

Simulation Setup

NH2 Target

LH2 Vs. NH3

Effects Due to Target Material

Target Density

Atomic Mass and Electron Number Effects

Differential Cross-Section Offset

Weighted Isotropic Distribution in Lab Frame

GEMC Simulation

Drift Chamber

Determining wire-theta correspondence

CED Verification of DC Angle Theta and Wire Correspondance

DC Super Layer 1:Layer 1

DC Binning Based On Wire Numbers

Detector Occupancy

Comparing With Whitney Rates

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