Difference between revisions of "Runs 4111(D2O)/4112(H2O)"

From New IAC Wiki
Jump to navigation Jump to search
 
(147 intermediate revisions by 2 users not shown)
Line 1: Line 1:
−
[[Simulation of n-flight pass]]
+
== Subtraction of stops for D2O ==
 +
 
 
Subtraction of the stops for each detector in the case of D2O target. The length of the active area (scintillator) of the detector is 75.3 cm.
 
Subtraction of the stops for each detector in the case of D2O target. The length of the active area (scintillator) of the detector is 75.3 cm.
  
 
[[File:run_4111_D2O_deltaT.png | 600 px]]
 
[[File:run_4111_D2O_deltaT.png | 600 px]]
 +
 +
== Subtraction of stops for H2O ==
  
 
Subtraction of the stops for each detector in the case of H2O target:
 
Subtraction of the stops for each detector in the case of H2O target:
  
 
[[File:run_4111_H2O_deltaT.png | 600 px]]
 
[[File:run_4111_H2O_deltaT.png | 600 px]]
 +
 +
== Subtraction of D2O and H2O ToF ==
  
 
Normalized superimposed timing spectra from D2O(black line)/H2O(red line) targets and bin-by-bin subtraction (green line) of D2O-H2O data:
 
Normalized superimposed timing spectra from D2O(black line)/H2O(red line) targets and bin-by-bin subtraction (green line) of D2O-H2O data:
Line 17: Line 22:
  
 
[[File:run_4111_subtr4.png | 600 px]]
 
[[File:run_4111_subtr4.png | 600 px]]
 +
 +
==Preliminary data analysis==
  
 
Neutron energy distribution data analysis for run 4111:
 
Neutron energy distribution data analysis for run 4111:
  
 
[[File:D2O_neutron_spectra.pdf]]
 
[[File:D2O_neutron_spectra.pdf]]
 +
 +
Correlation between the neutron energy and neutron energy uncertainty is plotted below:
 +
 +
[[File:Error_plot_detM.png | 400 px]]
 +
 +
The above plot may look better if you plot <math>Energy</math> -vs- (<math>Energy \pm Energy</math>)
 +
As the energy increased the uncertainty increases to the point the the error bar is as big as the magnitude of the energy.
 +
 +
 +
 +
== Neutron energy analysis ==
  
 
Errors on the neutron energy for the case of Det M:
 
Errors on the neutron energy for the case of Det M:
Line 26: Line 44:
 
<math>E_n \pm U(E_n)=m_nc^2/2 \cdot 1/c^2 \cdot (l_n/t_n)^2 \cdot [1 \pm 2 \sqrt{U^2(l_n)/l^2_n + U^2(t_n)/t^2_n}]</math>
 
<math>E_n \pm U(E_n)=m_nc^2/2 \cdot 1/c^2 \cdot (l_n/t_n)^2 \cdot [1 \pm 2 \sqrt{U^2(l_n)/l^2_n + U^2(t_n)/t^2_n}]</math>
  
−
Where uncertainty in the neutron flight pass due to the finite width of the detector (14.8 cm) <math>U(l_n) = 14.8cm/2 \cdot cos(\theta)</math> and uncertainty in zero time definition in neutron TOF spectrum <math>U(t_n)=10 ns</math>
+
Where uncertainty in the neutron flight pass due to the finite width of the detector <math>U(l_n)</math> was simulated using GEANT4 and uncertainty in zero time definition in neutron TOF spectrum <math>U(t_n)</math> was defined from the experimental data as sigma of the zero time photon peak.
 +
 
 +
The neutron flight path length was calculated using the following expression: <math>l_n = \sqrt{l_c^2 + (X_c-X_i)^2}</math>, where <math>X_c=75/2=37.5cm</math> is the coordinate of the middle of the neutron detector active area and <math>X_i</math> is the current x-coordinate extracted from time difference spectrum. <math>l_c</math> is the distance from the middle of the target to the middle of the neutron detector surface. The current coordinate can be defined as <math>X_i = (((TDC_{left}-TDC_{right}) \cdot 0.223 ns/ch) \pm S) \cdot R</math>, where <math>S</math> is a shift factor due to the difference in delays for the two channels and should be taken to be the lowest value in <math>(TDC_{left}-TDC_{right}) \cdot 0.223</math> spectrum. The coefficient <math>R</math> is equal to active area dimension divided by the total width of <math>(TDC_{left}-TDC_{right}) \cdot 0.223</math> spectrum measured at base,i.e. <math>R = \frac{ 75(cm)}{abs(MAX[(TDC_{left}-TDC_{right})(ch) \cdot 0.223(ns/ch)]-MIN[(TDC_{left}-TDC_{right})(ch) \cdot 0.223(ns/ch)])} </math> or it can be measured by moving a radioactive source along the neutron detector surface.
 +
 
 +
 
 +
 
 +
However, there is a question on how to define the uncertainty on the coefficient <math>R</math>. Calibration <math>R_{calibr}</math> does not correspond to the measured one <math>R_{data}</math> (measured w/ Co-60 source). As an example for Det M  we have (neutrons and photons combined together):
 +
 
 +
[[File:DetM_Calibr_data_mis.png]]
 +
 
 +
If we take into account only neutron region, we'll get
 +
 
 +
 
 +
[[File:DetM_Calibr_data_mis_nCut.png]]
 +
 
 +
 
 +
If we take into account only photon region, we'll get
 +
 
 +
 
 +
[[File:DetM_Calibr_data_mis_gCut.png]]
 +
 
 +
 
 +
Neutron ToF to the surface of the detector can be calculated as <math>t_n = 0.5 \cdot ((TDC_{left}+TDC_{right})-ToF_{sint+lg})</math>, where <math>ToF_{sint+lg}</math> is the total light ToF inside the detector and it was taken to be a const <math>ToF_{sint+lg} = 100cm \cdot \frac{1}{2.5 cm/ns} \simeq 40 ns</math>. So, the neutron ToF can be calculated as <math>t_n = 0.5 \cdot ((TDC_{left}+TDC_{right})-40)</math>
 +
 
 +
== Neutron Phi distribution analysis ==
 +
 
 +
Phi angle of the neutron hitting the surface of the detector can be found as
 +
<math>tan(\phi)=\frac{(((TDC_{left}-TDC_{right})(ch) \cdot 0.223(ns/ch)) \pm S(ns)) \cdot R(cm/ns)}{l_c}= \frac{X_i}{l_c}</math>
  
−
Correlation between the neutron energy and neutron energy uncertainty is plotted below:
+
The width of each channel is 0.223 ns and time walk of CF8000 is 0.25 ns. Hence the uncertainty on the x-coordinate can be calculated as <math>\delta X_i = \sqrt{(0.223(ns) \cdot R(cm/ns))^2 + (0.25(ns) \cdot R(cm/ns))^2}</math>.
 +
 
 +
For example, for the Det_M the coefficient <math>R=2.5 cm/ns</math> and <math>\delta X_i(Det_M) = \sqrt{(0.223(ns) \cdot 2.5(cm/ns))^2 + (0.25(ns) \cdot 2.5(cm/ns))^2}</math>.
  
−
[[File:Error_plot_detM.png | 400 px]]
+
Finally <math>\delta X_i(Det_M) = 0.84 cm</math>.
  
−
The above plot may look better if you plot <math>Energy</math> -vs- (<math>Energy \pm Energy</math>)
+
== Simulation of n-flight path. DetM. ==
−
As the energy increased the uncertainty increases to the point the the error bar is as big as the magnitude of the energy.
 
  
−
=Simulation of n-flight pass=
+
Simulation of the flight path length uncertainty <math>U(l_n)</math> for Det M(1,2) placed right below the target:
  
−
Simulation of the flight pass length uncertainty <math>U(l_n)</math> for Det M(1,2):
+
[[File:flight_pass_setup.png | 300 px]]
  
−
Cylindrical target with dimensions of real target was used. It was filled with liquid D2. 1 MeV neutrons were generated inside the target unoformly and isotropically. The shortest distance from the target to the detector surface was 97.4 cm (corresponds to zero in the plot of the Delta_L)
+
Cylindrical target with dimensions of real target was used. It was filled with liquid D2. 1 MeV neutrons were generated inside the target uniformly and isotropically. The shortest distance from the target to the detector surface was 97.4 cm (corresponds to zero in the plot of the Delta_L)
  
 
The whole range fit:
 
The whole range fit:
Line 51: Line 97:
 
As can be seen we have <math>U(l_n)</math> of ~ 3.3 cm for the whole detector (no binning).
 
As can be seen we have <math>U(l_n)</math> of ~ 3.3 cm for the whole detector (no binning).
  
−
The correlation of neutron energy <math>E_n = m_nc^2/2 \cdot 1/c^2 \cdot (l_n/t_n)^2</math> and its uncertainty <math>U(E_n)= 2 \sqrt{(3.3cm)^2/l^2_n + (10ns)^2/t^2_n} \cdot 100\%</math>, and neutron ToF cut [20,65] ns:
+
If we apply the binning (total # of events sampled <math>4 \cdot 10^5</math>):
 +
 
 +
{| cellpadding="2" style="border: 1px solid darkgray;"
 +
! width="400" | Region 4
 +
! width="400" | Region 3
 +
! width="400" | Region 2
 +
! width="400" | Region 1
 +
|- border="0"
 +
| [[File:Region4_DetM.png|300px|Region 1]]
 +
| [[File:Region3_DetM.png|300px|Region 2]]
 +
| [[File:Region2_DetM.png|300px|Region 3]]
 +
| [[File:Region1_DetM.png|300px|Region 4]]
 +
|- align="center"
 +
| x <= -18.97 cm|| 0 >= x >= -18.97 cm|| 0 <= x <= 18.97 cm || x >= 18.97 cm
 +
|}
 +
 
 +
== Experimental data Det M ==
 +
 
 +
The correlation of neutron energy <math>E_n = m_nc^2/2 \cdot 1/c^2 \cdot (l_n/t_n)^2</math> and its uncertainty <math>U(E_n)= 2 \sqrt{(3cm)^2/l^2_n + (8.8ns)^2/t^2_n} \cdot 100\%</math> for the case neutron ToF cut [25,65] ns:
  
 
[[File:DetM_neutron_energy.png | 600 px]]
 
[[File:DetM_neutron_energy.png | 600 px]]
 +
 +
Correlation plot of neutron energy vs neutron Phi angle (experimental data, cuts on time applied):
 +
 +
[[File:Det_M_PhiEn_corr.png | 600 px]]
 +
 +
  
 
If we consider the neutron time of flight uncertainty <math>U(t_n) = 7 ns</math> and <math>U(l_n) = 3.3 cm</math> then the correlation plot changes to
 
If we consider the neutron time of flight uncertainty <math>U(t_n) = 7 ns</math> and <math>U(l_n) = 3.3 cm</math> then the correlation plot changes to
Line 64: Line 134:
  
 
It can be concluded that the neutron energy uncertainty is really sensitive to the neutron ToF uncertainty. In our case we had a long tail in photon peak which could possibly distort the zero time definition and the precision of neutron energy calculation.
 
It can be concluded that the neutron energy uncertainty is really sensitive to the neutron ToF uncertainty. In our case we had a long tail in photon peak which could possibly distort the zero time definition and the precision of neutron energy calculation.
 +
 +
== Data analysis for DetH ==
 +
 +
===Simulation of n-flight path. DetH.===
 +
 +
Simulated neutron flight pass lenrgth distribution is presented below:
 +
 +
[[File:Fit_whole_range_detH.png | 600 px]]
 +
 +
The width of the distribution is about 10 cm wide.
 +
 +
The active area of the detector is ~ 75 cm. If we bin the detector in four, we will get for <math>4 \cdot 10^5</math> generated events
 +
 +
 +
{| cellpadding="2" style="border: 1px solid darkgray;"
 +
! width="400" | Region 4
 +
! width="400" | Region 3
 +
! width="400" | Region 2
 +
! width="400" | Region 1
 +
|- border="0"
 +
| [[File:Region4_DetH.png|300px|Region 1]]
 +
| [[File:Region3_DetH.png|300px|Region 2]]
 +
| [[File:Region2_DetH.png|300px|Region 3]]
 +
| [[File:Region1_DetH.png|300px|Region 4]]
 +
|- align="center"
 +
| x <= -18.97 cm|| 0 >= x >= -18.97 cm|| 0 <= x <= 18.97 cm || x >= 18.97 cm
 +
|}
 +
 +
So it can be seen that the neutron flight path uncertainty, if taken to be the RMS in a flight path spectrum, is <math>U(l_n) \simeq 3.5 cm</math>.
 +
 +
===Experimental data===
 +
 +
Data with no binning:
 +
 +
[[File:Exp_data1_detH.png | 600 px]]
 +
 +
After binning the detector and taking for the neutron flight path uncertainty <math>U(l_n) = 3.5 cm</math> we got:
 +
 +
{| cellpadding="2" style="border: 1px solid darkgray;"
 +
! width="400" | Region 4
 +
! width="400" | Region 3
 +
! width="400" | Region 2
 +
! width="400" | Region 1
 +
|- border="0"
 +
| [[File:Region4_exp_DetH.png|300px|Region 1]]
 +
| [[File:Region3_exp_DetH.png|300px|Region 2]]
 +
| [[File:Region2_exp_DetH.png|300px|Region 3]]
 +
| [[File:Region1_exp_DetH.png|300px|Region 4]]
 +
|- align="center"
 +
| x <= -18.97 cm|| 0 >= x >= -18.97 cm|| 0 <= x <= 18.97 cm || x >= 18.97 cm
 +
|}
 +
 +
According to my observation the uncertainty in the neutron flight path does not influence the uncertainty in neutron energy too much. Main contribution is from the zero-time definition in ToF spectrum.
 +
 +
Correlation plot of neutron energy vs neutron Phi angle (experimental data, cuts on time applied):
 +
 +
[[File:Det_H_PhiEn_corr.png | 600 px]]
 +
 +
== Data analysis for Det_E ==
 +
 +
Simulated neutron flight path for detector F w/o binning and <math>2 \cdot 10^5</math> events simulated:
 +
 +
[[File:Det_E_sim_flightpath_nobinning.png | 400 px]]
 +
 +
The uncertainty in neutron flight path is RMS = 2.36 cm.
 +
 +
 +
Phi-angular distribution of hits (experimental data, no cuts on time):
 +
 +
[[File:Det_E_angl_distr.png | 400 px]]
 +
 +
Correlation plot of neutron energy vs neutron Phi angle (experimental data, cuts on time applied):
 +
 +
[[File:Det_E_PhiEn_corr.png | 600 px]]
 +
 +
 +
If we apply the binning:
 +
 +
{| cellpadding="2" style="border: 1px solid darkgray;"
 +
! width="400" | Region 4
 +
! width="400" | Region 3
 +
! width="400" | Region 2
 +
! width="400" | Region 1
 +
|- border="0"
 +
| [[File:Region4_DetE.png|300px|Region 1]]
 +
| [[File:Region3_DetE.png|300px|Region 2]]
 +
| [[File:Region2_DetE.png|300px|Region 3]]
 +
| [[File:Region1_DetE.png|300px|Region 4]]
 +
|- align="center"
 +
| x <= -18.97 cm|| 0 >= x >= -18.97 cm|| 0 <= x <= 18.97 cm || x >= 18.97 cm
 +
|}
 +
 +
 +
[[File:Det_E_data_nobinning.png | 600 px]]
 +
 +
== Data analysis for Det_F ==
 +
 +
Simulated neutron flight path for detector F w/o binning and <math>2 \cdot 10^5</math> events simulated:
 +
 +
[[File:Det_F_sim_flightpath_nobinning.png | 600 px]]
 +
 +
The uncertainty in neutron flight path is RMS = 2.5 cm.
 +
 +
 +
If we apply the binning:
 +
 +
{| cellpadding="2" style="border: 1px solid darkgray;"
 +
! width="400" | Region 4
 +
! width="400" | Region 3
 +
! width="400" | Region 2
 +
! width="400" | Region 1
 +
|- border="0"
 +
| [[File:Region4_DetF.png|300px|Region 1]]
 +
| [[File:Region3_DetF.png|300px|Region 2]]
 +
| [[File:Region2_DetF.png|300px|Region 3]]
 +
| [[File:Region1_DetF.png|300px|Region 4]]
 +
|- align="center"
 +
| x <= -18.97 cm|| 0 >= x >= -18.97 cm|| 0 <= x <= 18.97 cm || x >= 18.97 cm
 +
|}
 +
 +
Experimental data
 +
 +
[[File:Det_F_data_nobinning.png | 600 px]]
 +
 +
Correlation plot of neutron energy vs neutron Phi angle (experimental data, cuts on time applied):
 +
 +
[[File:Det_F_PhiEn_corr.png | 600 px]]
 +
 +
== Data analysis for Det_G ==
 +
 +
Simulated neutron flight path for detector F w/o binning and <math>2 \cdot 10^5</math> events simulated:
 +
 +
[[File:Det_G_sim_flightpath_nobinning.png | 600 px]]
 +
 +
The uncertainty in neutron flight path is RMS = 3.24 cm.
 +
 +
 +
If we apply the binning:
 +
 +
{| cellpadding="2" style="border: 1px solid darkgray;"
 +
! width="400" | Region 4
 +
! width="400" | Region 3
 +
! width="400" | Region 2
 +
! width="400" | Region 1
 +
|- border="0"
 +
| [[File:Region4_DetG.png|300px|Region 1]]
 +
| [[File:Region3_DetG.png|300px|Region 2]]
 +
| [[File:Region2_DetG.png|300px|Region 3]]
 +
| [[File:Region1_DetG.png|300px|Region 4]]
 +
|- align="center"
 +
| x <= -18.97 cm|| 0 >= x >= -18.97 cm|| 0 <= x <= 18.97 cm || x >= 18.97 cm
 +
|}
 +
 +
 +
[[File:Det_G_data_nobinning.png | 600 px]]
 +
 +
Correlation plot of neutron energy vs neutron Phi angle (experimental data, cuts on time applied):
 +
 +
[[File:Det_G_PhiEn_corr.png | 600 px]]
 +
 +
== Data analysis for Det_K ==
 +
 +
[[File:Det_K_data_non.png | 600 px]]
 +
 +
== Data analysis for Det_I ==
 +
 +
Simulated neutron flight path for detector F w/o binning and <math>4 \cdot 10^5</math> events simulated:
 +
 +
[[File:Det_I_sim_flightpath_nobinning.png | 600 px]]
 +
 +
The uncertainty in neutron flight path is RMS = 4.27 cm.
 +
 +
 +
If we apply the binning:
 +
 +
{| cellpadding="2" style="border: 1px solid darkgray;"
 +
! width="400" | Region 4
 +
! width="400" | Region 3
 +
! width="400" | Region 2
 +
! width="400" | Region 1
 +
|- border="0"
 +
| [[File:Region4_DetI.png|300px|Region 1]]
 +
| [[File:Region3_DetI.png|300px|Region 2]]
 +
| [[File:Region2_DetI.png|300px|Region 3]]
 +
| [[File:Region1_DetI.png|300px|Region 4]]
 +
|- align="center"
 +
| x <= -18.97 cm|| 0 >= x >= -18.97 cm|| 0 <= x <= 18.97 cm || x >= 18.97 cm
 +
|}
 +
 +
[[File:Det_I_data_nobinning.png | 600 px]]
 +
 +
The uncertainty on the zero time is <math>U(t_n) \simeq 24 ns</math>. Squared value <math>U(t_n)^2 = 576 ns</math> which is comparable to <math>t_n^2</math> and the uncertainty is big while the neutron flight path uncertainty for the whole detector is ~ 3 cm and its squared value is much less than the squared value of the distance traveled by neutrons, e.g. <math>3^2/253^2 = 9/64009 \simeq 1.4 \cdot 10^{-4}</math>
 +
 +
Correlation plot of neutron energy vs neutron Phi angle (experimental data, cuts on time applied):
 +
 +
[[File:Det_I_PhiEn_corr.png | 600 px]]

Latest revision as of 15:35, 4 October 2012

Subtraction of stops for D2O

Subtraction of the stops for each detector in the case of D2O target. The length of the active area (scintillator) of the detector is 75.3 cm.

Run 4111 D2O deltaT.png

Subtraction of stops for H2O

Subtraction of the stops for each detector in the case of H2O target:

Run 4111 H2O deltaT.png

Subtraction of D2O and H2O ToF

Normalized superimposed timing spectra from D2O(black line)/H2O(red line) targets and bin-by-bin subtraction (green line) of D2O-H2O data:

Run 4111 subtr1.png

Run 4111 subtr2.png

Run 4111 subtr3.png

Run 4111 subtr4.png

Preliminary data analysis

Neutron energy distribution data analysis for run 4111:

File:D2O neutron spectra.pdf

Correlation between the neutron energy and neutron energy uncertainty is plotted below:

Error plot detM.png 

The above plot may look better if you plot [math]Energy[/math] -vs- ([math]Energy \pm Energy[/math]) 
As the energy increased the uncertainty increases to the point the the error bar is as big as the magnitude of the energy.


Neutron energy analysis

Errors on the neutron energy for the case of Det M:

[math]E_n \pm U(E_n)=m_nc^2/2 \cdot 1/c^2 \cdot (l_n/t_n)^2 \cdot [1 \pm 2 \sqrt{U^2(l_n)/l^2_n + U^2(t_n)/t^2_n}][/math]

Where uncertainty in the neutron flight pass due to the finite width of the detector [math]U(l_n)[/math] was simulated using GEANT4 and uncertainty in zero time definition in neutron TOF spectrum [math]U(t_n)[/math] was defined from the experimental data as sigma of the zero time photon peak.

The neutron flight path length was calculated using the following expression: [math]l_n = \sqrt{l_c^2 + (X_c-X_i)^2}[/math], where [math]X_c=75/2=37.5cm[/math] is the coordinate of the middle of the neutron detector active area and [math]X_i[/math] is the current x-coordinate extracted from time difference spectrum. [math]l_c[/math] is the distance from the middle of the target to the middle of the neutron detector surface. The current coordinate can be defined as [math]X_i = (((TDC_{left}-TDC_{right}) \cdot 0.223 ns/ch) \pm S) \cdot R[/math], where [math]S[/math] is a shift factor due to the difference in delays for the two channels and should be taken to be the lowest value in [math](TDC_{left}-TDC_{right}) \cdot 0.223[/math] spectrum. The coefficient [math]R[/math] is equal to active area dimension divided by the total width of [math](TDC_{left}-TDC_{right}) \cdot 0.223[/math] spectrum measured at base,i.e. [math]R = \frac{ 75(cm)}{abs(MAX[(TDC_{left}-TDC_{right})(ch) \cdot 0.223(ns/ch)]-MIN[(TDC_{left}-TDC_{right})(ch) \cdot 0.223(ns/ch)])} [/math] or it can be measured by moving a radioactive source along the neutron detector surface.


However, there is a question on how to define the uncertainty on the coefficient [math]R[/math]. Calibration [math]R_{calibr}[/math] does not correspond to the measured one [math]R_{data}[/math] (measured w/ Co-60 source). As an example for Det M we have (neutrons and photons combined together):

DetM Calibr data mis.png

If we take into account only neutron region, we'll get


DetM Calibr data mis nCut.png


If we take into account only photon region, we'll get


DetM Calibr data mis gCut.png


Neutron ToF to the surface of the detector can be calculated as [math]t_n = 0.5 \cdot ((TDC_{left}+TDC_{right})-ToF_{sint+lg})[/math], where [math]ToF_{sint+lg}[/math] is the total light ToF inside the detector and it was taken to be a const [math]ToF_{sint+lg} = 100cm \cdot \frac{1}{2.5 cm/ns} \simeq 40 ns[/math]. So, the neutron ToF can be calculated as [math]t_n = 0.5 \cdot ((TDC_{left}+TDC_{right})-40)[/math]

Neutron Phi distribution analysis

Phi angle of the neutron hitting the surface of the detector can be found as [math]tan(\phi)=\frac{(((TDC_{left}-TDC_{right})(ch) \cdot 0.223(ns/ch)) \pm S(ns)) \cdot R(cm/ns)}{l_c}= \frac{X_i}{l_c}[/math]

The width of each channel is 0.223 ns and time walk of CF8000 is 0.25 ns. Hence the uncertainty on the x-coordinate can be calculated as [math]\delta X_i = \sqrt{(0.223(ns) \cdot R(cm/ns))^2 + (0.25(ns) \cdot R(cm/ns))^2}[/math].

For example, for the Det_M the coefficient [math]R=2.5 cm/ns[/math] and [math]\delta X_i(Det_M) = \sqrt{(0.223(ns) \cdot 2.5(cm/ns))^2 + (0.25(ns) \cdot 2.5(cm/ns))^2}[/math].

Finally [math]\delta X_i(Det_M) = 0.84 cm[/math].

Simulation of n-flight path. DetM.

Simulation of the flight path length uncertainty [math]U(l_n)[/math] for Det M(1,2) placed right below the target:

Flight pass setup.png

Cylindrical target with dimensions of real target was used. It was filled with liquid D2. 1 MeV neutrons were generated inside the target uniformly and isotropically. The shortest distance from the target to the detector surface was 97.4 cm (corresponds to zero in the plot of the Delta_L)

The whole range fit:

Fit whole range.png

Central region fit:

Fit peak.png

As can be seen we have [math]U(l_n)[/math] of ~ 3.3 cm for the whole detector (no binning).

If we apply the binning (total # of events sampled [math]4 \cdot 10^5[/math]):

Region 4 Region 3 Region 2 Region 1
Region 1 Region 2 Region 3 Region 4
x <= -18.97 cm 0 >= x >= -18.97 cm 0 <= x <= 18.97 cm x >= 18.97 cm

Experimental data Det M

The correlation of neutron energy [math]E_n = m_nc^2/2 \cdot 1/c^2 \cdot (l_n/t_n)^2[/math] and its uncertainty [math]U(E_n)= 2 \sqrt{(3cm)^2/l^2_n + (8.8ns)^2/t^2_n} \cdot 100\%[/math] for the case neutron ToF cut [25,65] ns:

DetM neutron energy.png

Correlation plot of neutron energy vs neutron Phi angle (experimental data, cuts on time applied):

Det M PhiEn corr.png


If we consider the neutron time of flight uncertainty [math]U(t_n) = 7 ns[/math] and [math]U(l_n) = 3.3 cm[/math] then the correlation plot changes to

Tof 7ns uncertty.png

If we consider the neutron time of flight uncertainty [math]U(t_n) = 1 ns[/math] and [math]U(l_n) = 3.3 cm[/math] then the correlation plot changes to

Tof 1ns uncertty.png

It can be concluded that the neutron energy uncertainty is really sensitive to the neutron ToF uncertainty. In our case we had a long tail in photon peak which could possibly distort the zero time definition and the precision of neutron energy calculation.

Data analysis for DetH

Simulation of n-flight path. DetH.

Simulated neutron flight pass lenrgth distribution is presented below:

Fit whole range detH.png

The width of the distribution is about 10 cm wide.

The active area of the detector is ~ 75 cm. If we bin the detector in four, we will get for [math]4 \cdot 10^5[/math] generated events


Region 4 Region 3 Region 2 Region 1
Region 1 Region 2 Region 3 Region 4
x <= -18.97 cm 0 >= x >= -18.97 cm 0 <= x <= 18.97 cm x >= 18.97 cm

So it can be seen that the neutron flight path uncertainty, if taken to be the RMS in a flight path spectrum, is [math]U(l_n) \simeq 3.5 cm[/math].

Experimental data

Data with no binning:

Exp data1 detH.png

After binning the detector and taking for the neutron flight path uncertainty [math]U(l_n) = 3.5 cm[/math] we got:

Region 4 Region 3 Region 2 Region 1
Region 1 Region 2 Region 3 Region 4
x <= -18.97 cm 0 >= x >= -18.97 cm 0 <= x <= 18.97 cm x >= 18.97 cm

According to my observation the uncertainty in the neutron flight path does not influence the uncertainty in neutron energy too much. Main contribution is from the zero-time definition in ToF spectrum.

Correlation plot of neutron energy vs neutron Phi angle (experimental data, cuts on time applied):

Det H PhiEn corr.png

Data analysis for Det_E

Simulated neutron flight path for detector F w/o binning and [math]2 \cdot 10^5[/math] events simulated:

Det E sim flightpath nobinning.png

The uncertainty in neutron flight path is RMS = 2.36 cm.


Phi-angular distribution of hits (experimental data, no cuts on time):

Det E angl distr.png

Correlation plot of neutron energy vs neutron Phi angle (experimental data, cuts on time applied):

Det E PhiEn corr.png


If we apply the binning:

Region 4 Region 3 Region 2 Region 1
Region 1 Region 2 Region 3 Region 4
x <= -18.97 cm 0 >= x >= -18.97 cm 0 <= x <= 18.97 cm x >= 18.97 cm


Det E data nobinning.png

Data analysis for Det_F

Simulated neutron flight path for detector F w/o binning and [math]2 \cdot 10^5[/math] events simulated:

Det F sim flightpath nobinning.png

The uncertainty in neutron flight path is RMS = 2.5 cm.


If we apply the binning:

Region 4 Region 3 Region 2 Region 1
Region 1 Region 2 Region 3 Region 4
x <= -18.97 cm 0 >= x >= -18.97 cm 0 <= x <= 18.97 cm x >= 18.97 cm

Experimental data

Det F data nobinning.png

Correlation plot of neutron energy vs neutron Phi angle (experimental data, cuts on time applied):

Det F PhiEn corr.png

Data analysis for Det_G

Simulated neutron flight path for detector F w/o binning and [math]2 \cdot 10^5[/math] events simulated:

Det G sim flightpath nobinning.png

The uncertainty in neutron flight path is RMS = 3.24 cm.


If we apply the binning:

Region 4 Region 3 Region 2 Region 1
Region 1 Region 2 Region 3 Region 4
x <= -18.97 cm 0 >= x >= -18.97 cm 0 <= x <= 18.97 cm x >= 18.97 cm


Det G data nobinning.png

Correlation plot of neutron energy vs neutron Phi angle (experimental data, cuts on time applied):

Det G PhiEn corr.png

Data analysis for Det_K

Det K data non.png

Data analysis for Det_I

Simulated neutron flight path for detector F w/o binning and [math]4 \cdot 10^5[/math] events simulated:

Det I sim flightpath nobinning.png

The uncertainty in neutron flight path is RMS = 4.27 cm.


If we apply the binning:

Region 4 Region 3 Region 2 Region 1
Region 1 Region 2 Region 3 Region 4
x <= -18.97 cm 0 >= x >= -18.97 cm 0 <= x <= 18.97 cm x >= 18.97 cm

Det I data nobinning.png

The uncertainty on the zero time is [math]U(t_n) \simeq 24 ns[/math]. Squared value [math]U(t_n)^2 = 576 ns[/math] which is comparable to [math]t_n^2[/math] and the uncertainty is big while the neutron flight path uncertainty for the whole detector is ~ 3 cm and its squared value is much less than the squared value of the distance traveled by neutrons, e.g. [math]3^2/253^2 = 9/64009 \simeq 1.4 \cdot 10^{-4}[/math]

Correlation plot of neutron energy vs neutron Phi angle (experimental data, cuts on time applied):

Det I PhiEn corr.png

Retrieved from "https://wiki.iac.isu.edu/index.php?title=Runs_4111(D2O)/4112(H2O)&oldid=78151"