Latest revision as of 02:30, 30 May 2019

Figure 5c: The experimental and theoretical Moller electron differential cross-section for an incident 11 GeV(Lab) electron in the Center of Mass frame of reference.

NH2 Target

Replacing the LH2 target with an NH3 target

Benchmark GEANT4's Moller scattering prediction with the theoretical cross section using NH3

Comparison of simulation vs. the theoretical Møller differential cross section using 11 GeV electrons impinging NH3

Theoretical and Simulated Moller Differential Cross-Section in Center of Mass Frame Frame

Figure 5c: The theoretical and simulated Moller electron differential cross-section for an incident 11 GeV(Lab) electron in the Center of Mass frame of reference for NH3 target.

LH2 Vs. NH3

Benchmark GEANT4's Moller scattering prediction for NH3 and LH2

Effects Due to Target Material

Atomic Mass and Electron Number Effects

Differential Cross-Section Offset

Figure 5c: The theoretical and simulated Moller electron differential cross-section for an incident 11 GeV(Lab) electron in the Center of Mass frame of reference for NH3 target. The theoretical differential cross-section has been adjusted to account for the 10 electrons within NH3.

Modeling the EG12 Drift Chamber

Mathematica Simulation

In the Detector Frame

Preparing Drift Chamber Efficiency Tests

Understanding GEMC Component Effects

rename "s/.stl/.junk/" *.stl

Mlr_Summ_TF

Results

DV_RunGroupC_Moller

Monte Carlo Binary Collision Approximation

@@ Line 3: / Line 3: @@
 =Moller Scattering=
 ==Moller Scattering Definition==
-===[[Variables_Used_in_Elastic_Scattering]]===
+==[[Relativistic Frames of Reference]]==
+===[[Relativistic Units]]===
+==[[4-vectors]]==
-===[[DV_Calculations_of_4-momentum_components]]===
+===[[4-momenta]]===
+===[[Frame of Reference Transformation]]===
+===[[4-gradient]]===
-==[[DV_XSECT|Moller Differential Cross-Section]]==
+==[[Mandelstam Representation]]==
+===[[s-Channel]]===
+===[[t-Channel]]===
+===[[u-Channel]]===
+===[[Limits based on Mandelstam Variables]]===
+====[[Limit of Energy in Lab Frame]]====
+====[[Limit of Scattering Angle Theta in Lab Frame]]====
-=GEANT4 Simulation of Moller Scattering=
+==Initial 4-momentum Components==
-==LH2 Target==
-=== [[LH2 target|Simulation Setup]]===
+===[[Initial Lab Frame 4-momentum components]]===
-==NH2 Target==
+===[[Initial CM Frame 4-momentum components]]===
+===[[Special Case of Equal Mass Particles]]===
+====[[Total Energy in CM Frame]]====
+====[[Scattered and Moller Electron Energies in CM Frame]]====
+==Final 4-momentum components==
+===[[Final Lab Frame Moller Electron 4-momentum components in XZ Plane]]===
+===[[Final Lab Frame Moller Electron 4-momentum components in XY Plane]]===
+====[[Momentum Components in the XY Plane Based on Angle Phi]]====
+===[[Final CM Frame Moller Electron 4-momentum components]]===
+===[[Final CM Frame Scattered Electron 4-momentum components]]===
+===[[Final Lab Frame Scattered Electron 4-momentum components]]===
-==LH2 Vs. NH3==
+==[[Summary of 4-momentum components]]==
+==[[Verification of 4-momentum components]]==
-==Effects Due to Target Material==
+==[[Feynman Calculus]]==
-===[[DV_Target_Density|Target Density]]===
+===[[Flux of Incoming Particles]]===
+===[[Invariant Lorentz Phase Space]]===
+===[[Relativistic Differential Cross-section]]===
-===[[DV_a_z_target|Atomic Mass and Electron Number Effects]]===
+==[[Scattering Amplitude]]==
-==Differential Cross-Section Offset==
+==[[Differential Cross-Section]]==
-=Weighted Isotropic Distribution in Lab Frame=
+==[[DV_XSECT|Moller Differential Cross-Section]]==
+===[[DV_Plotting_XSect | Plotting the Differential Cross-section]]===
+=GEANT4 Simulation of Moller Scattering of Target Material=
+==LH2 Target==
+=== [[LH2 target|6e7 incident electrons on 1cm square LH2 target Simulation Setup]]===
-=GEMC Simulation=
+=== [[LH2 target2|6e7 incident electrons on 5cm cylinder LH2 target Simulation Setup]]===
-==Drift Chamber==
+=== [[LH2 target3|6e7 incident electrons on 1mm cylinder LH2 target Simulation Setup]]===
-===[[Determining wire-theta correspondence]]===
+====[[Converting to barns|Converting the number of scattered electrons per scattering angle theta to a differential cross-section in barns.]]====
+====[[DV_Moller_LH2 | Benchmark GEANT4's Moller scattering prediction with the theoretical cross section using LH2]]====
-====[[CED Verification of DC Angle Theta and Wire Correspondance]]====
-===[[DC Super Layer 1:Layer 1]]===
-===[[DC Binning Based On Wire Numbers]]===
+===Comparison of simulation vs. the theoretical Møller differential cross section using 11 GeV electrons impinging LH2===
-==Detector Occupancy==
+[[Converting to barns|Converting the number of scattered electrons per scattering angle theta to a differential cross-section in barns.]]
-==Comparing Rates==
-Using the values from Whitney:
-<center>[[File:Whitney_values.png‎]]</center>
+[[File:XSect_new_zoom.png|frame|center|alt=Experimental and Theoretical Moller Differential Cross-Section in Center of Mass Frame Frame|'''Figure 5c:''' The experimental and theoretical Moller electron differential cross-section for an incident 11 GeV(Lab) electron in the Center of Mass frame of reference.]]
-For a 5cm target of LH2:
+===[[Effects Due to Target Length]]===
-<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>
+==NH2 Target==
+===[[Replacing the LH2 target with an NH3 target]]===
+==[[DV_Moller_NH3|Benchmark GEANT4's Moller scattering prediction with the theoretical cross section using NH3]]==
+==Comparison of simulation vs. the theoretical Møller differential cross section using 11 GeV electrons impinging NH3==
-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>
+[[File:XSect_NH3.png|frame|center|alt=Theoretical and Simulated Moller Differential Cross-Section in Center of Mass Frame Frame|'''Figure 5c:''' The theoretical and simulated Moller electron differential cross-section for an incident 11 GeV(Lab) electron in the Center of Mass frame of reference for NH3 target.]]
+==LH2 Vs. NH3==
+===[[DV_Moller_NH3_LH2|Benchmark GEANT4's Moller scattering prediction for NH3 and LH2]]===
-Given the beam Luminosity of:
+==Effects Due to Target Material==
-<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>
+===[[DV_Target_Density|Target Density]]===
-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>
+===[[DV_a_z_target|Atomic Mass and Electron Number Effects]]===
-<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>
+==[[Calculating the differential cross-sections for the different materials, and placing them as well as the theoretical differential cross-section into a plot:|Differential Cross-Section Offset]]==
+[[File:Adjusted_MollerXSect_NH3.png‎|frame|center|alt=Theoretical and Simulated Moller Differential Cross-Section in Center of Mass Frame Frame|'''Figure 5c:''' The theoretical and simulated Moller electron differential cross-section for an incident 11 GeV(Lab) electron in the Center of Mass frame of reference for NH3 target.  The theoretical differential cross-section has been adjusted to account for the 10 electrons within NH3.]]
-Using the values from Whitney :
+=Modeling the EG12 Drift Chamber=
+==Drift Chamber==
+===[[Determining wire-theta correspondence]]===
-https://wiki.iac.isu.edu/index.php/CLAS12_RateEst_byWA
+====[[GEMC Verification]]====
-{| class="wikitable" align="center" border=1
+====[[CED Verification of DC Angle Theta and Wire Correspondance]]====
-|+ '''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
-|}
+====[[DC Super Layer 1:Layer 1]]====
+===[[DC Binning Based On Wire Numbers]]===
-<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>
+===[[Detector_Geometry Simulation]]===
-<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>
+====[[Conic Sections]]====
+=====[[Circular Cross Sections]]=====
+=====[[Elliptical Cross Sections]]=====
+====[[Determing Elliptical Components]]====
+====[[Determing Elliptical Equations]]====
+=====[[Test for Theta at 20 degrees and Phi at 0]]=====
+====[[In the Detector Plane]]====
+=====[[Test in Plane for Theta at 20 degrees and Phi at 0]]=====
+=====[[Test in Plane for Theta at 20 degrees and Phi at 1 degree]]=====
+===[[Function for change in x', Lab frame]]===
+===[[Wire Number Function]]===
+===Mathematica Simulation===
+====[[In the Detector Frame]]====
-[[File:CLAS12ExpWS_WA.pdf]]
+====In the wire frame====
+=====[[Points of Intersection]]=====
+=====[[The Wires]]=====
+=====[[Right Hand Wall]]=====
+=====[[Left Hand Wall]]=====
+=====[[The Ellipse]]=====
+====[[Plotting Different Frames]]====
+====[[Parameterizing the Ellipse Equation]]====
+====[[Change in Wire Bin Number]]====
+===One Hit per Wire Bin===
-<center>[[File:Whitney_2.png]][[File:Whitney_3.png]]</center>
+====[[One Hit Per Wire Bin|One Hit Per Wire Bin at phi=0]]====
+====[[Wire Bin Number as a function of Theta and Phi for Right Side]]====
-<center>[[File:Whitney_4.png]]</center>
+====[[Wire Bin Number as a function of Theta and Phi for Left Side]]====
+=[[Preparing Drift Chamber Efficiency Tests]]=
+==[[Uniform distribution in Energy and Theta LUND files]]==
-<center><math>\sigma=\frac{R}{\mathcal{L}}=\frac{dN}{dt}\cdot \frac{1}{\mathcal{L}}</math></center>
+===[[1000 Events per degree in the range 5 to 40 degrees for Lab Frame]]===
+===[[Isotropic Spread in CM for 5 to 40 degrees in Lab Frame|Isotropic Spread in CM for 5 to 40 degrees in Lab Frame at Phi=0]]===
+===[[Isotropic Spread  in Lab Frame for 5 to 40 degrees in Theta and for Phi between -30 and 30 Degrees]]===
+===[[Reading_LUND_files]]===
+===[[Run GEMC Isotropic Theta and Phi for Sector 1 DC]]===
-<center><math>\Rightarrow \int\limits_{0}^{t}\, dt=\int\limits_{0}^{N}\frac{1}{\sigma \mathcal{L}}\, dN</math></center>
+===[[Analysis of evio files]]===
+====[[Little Runs]]====
+====[[Bin Test]]====
+====[[Field Test]]====
+====[[Bin Shapes]]====
+====[[Limit Adjustment on Walls]]====
+===[[HITs in DC]]===
+===[[Hits with Changing Torus Field and 0T Solenoid]]===
+====[[Too Large Events]]====
-<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>
+===[[Hits with -5T Torus and Changing Solenoid Field]]===
+===[[Weight]]===
+==Detector Occupancy==
+===[[Defining Occupancy]]===
+====[[Unweighted Occupancy]]====
+====[[Weighted Occupancy]]====
+====[[Rates]]====
+=====[[Gamma Event Vertex]]=====
+===[[Comparing With Whitney Rates|Whitney Rates]]===
+===[[GEANT Moller Simulations Comparison|GEANT Moller Simulations]]===
-<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>
+===[[Comparison of GEANT Simulation to Whitney Data]]===
-<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,
+===[[Occupancy for Sector 1]]===
-<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>
+===[[Rates for Sector 1]]===
+===[[Rates for Different Currents]]===
+====[[Rates for Different Solenoid Strengths]]====
+====[[Rates for all Sectors based on Initial Sector 1 incident Moller electrons]]====
+====[[Changing Solenoid Field Rates in Sector 1]]====
+====[[Pb Cylinder (AKA "Temp Shield")]]====
+=[[Understanding GEMC Component Effects]]=
+<pre>rename "s/.stl/.junk/" *.stl</pre>
+==[[Forward Chamber]]==
+==[[Drift Chamber]]==
+==[[Magnets]]==
+===[[Solenoid]]===
+===[[Torus]]===
+===[[CAD Components]]===
+====[[BoreShield]]====
+====[[CenterTube]]====
+====[[DownstreamShieldingPlate]]====
+====[[DownstreamVacuumJacket]]====
+====[[Hub001]]====
+====[[Plates 1-6]]====
+====[[Shields 1-7]]====
-<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>
+====[[UpstreamShieldingPlate]]====
+====[[UpstreamVacuumJacket]]====
+====[[WarmBoreTube]]====
+====[[coils 1-6]]====
+====[[shell 1-6 a/b]]====
+====[[dc supports sectors 1-6 region 1]]====
+====[[dc back sectors 1-6 region 1]]====
+====[[apex]]====
+==[[Beamline]]==
+===[[CadBeamline]]===
+====[[innerShieldAndFlange]]====
+====[[outerFlange]]====
+====[[outerMount]]====
+====[[nut 1-9]]====
+====[[taggerInnerShield]]====
+====[[main-cone]]====
+====[[adjuster 1-3]]====
+====[[DSShieldFrontLead]]====
+====[[DSShieldBackLead]]====
+====[[DSShieldInnerAss]]====
+====[[DSShieldBackAss]]====
+====[[DSShieldFrontAss]]====
+====[[DSShieldBackCover]]====
+====[[DSShieldFrontCover]]====
+====[[DSShieldFlangeAttachment]]====
+====[[DSShieldFlange]]====
+===[[VacuumLine]]===
+====[[ConnectUpstreamToTorusPipe]]====
+====[[connectTorusToDownstreamPipe]]====
+====[[downstreamPipeFlange]]====
+=[[Mlr_Summ_TF]]=
-<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>
+=[[Results]]=
+[[DV_RunGroupC_Moller]]
-<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>
+=[[Monte Carlo Binary Collision Approximation]]=

Difference between revisions of "VanWasshenova Thesis"

Latest revision as of 02:30, 30 May 2019

Introduction

Moller Scattering

Moller Scattering Definition

Initial 4-momentum Components

Final 4-momentum components

GEANT4 Simulation of Moller Scattering of Target Material

LH2 Target

Comparison of simulation vs. the theoretical Møller differential cross section using 11 GeV electrons impinging LH2

NH2 Target

Comparison of simulation vs. the theoretical Møller differential cross section using 11 GeV electrons impinging NH3

LH2 Vs. NH3

Effects Due to Target Material

Modeling the EG12 Drift Chamber

Drift Chamber

Mathematica Simulation

In the wire frame

One Hit per Wire Bin

Detector Occupancy