HRRL 03-18-2011: Difference between revisions

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{| border="3"  cellpadding="20" cellspacing="0"
{| border="3"  cellpadding="20" cellspacing="0"
|V1 (Gun Vertical)||H1 (Gun Horizontal)|| Sol1 (Gun Sol) || V2 (Output Vertical) || H2 (Output horizontal || Sol 2 (Output solenoid)|| OTR Pict || FC pict
|Quad 1|| OTR Pict || FC pict
|-
|-
|(A)||(A) || (A) ||(A)||(A) || (A) || ||
|(A) || ||
|-
|-
| (-0.3)||+0 || 0 ||0||-0 || -0 ||[[File:OTR_Q1Scan03182011_SterOff.png | 100 px]] ||[[File:FC_Q1Scan03182011_SterOff.png | 100 px]]
| +0||[[File:OTR_Q1Scan03182011_10.png | 100 px]] ||[[File:FC_Q1Scan03182011_10.png | 100 px]]
|-
|-
| (-0.2)||+0.4 || 5.4 ||-0.5||-0.5 || 5.5 ||[[File:OTR_Q1Scan03182011_SterOn.png | 100 px]] ||[[File:FC_Q1Scan03182011_SterOon.png | 100 px]]
| +0.2||[[File:OTR_Q1Scan03182011_11.png | 100 px]] ||[[File:FC_Q1Scan03182011_11.png | 100 px]]
|-
|-
| (-0.2)||+0.4 || 6.8 ||-0.5||-0.5 || 5.5 ||[[File:OTR_Q1Scan03182011_1.png | 100 px]] ||[[File:FC_Q1Scan03182011_1.png | 100 px]]
| +0.4||[[File:OTR_Q1Scan03182011_12.png | 100 px]] ||[[File:FC_Q1Scan03182011_12.png | 100 px]]
|-
|-
| (-0.2)||+0.4 || 6.8 ||-0.5||-0.5 || 10.4 ||[[File:OTR_Q1Scan03182011_2.png | 100 px]] ||[[File:FC_Q1Scan03182011_2.png | 100 px]]
| +0.6||[[File:OTR_Q1Scan03182011_13.png | 100 px]] ||[[File:FC_Q1Scan03182011_13.png | 100 px]]
|-
|-
| +0.8||[[File:OTR_Q1Scan03182011_14.png | 100 px]] ||[[File:FC_Q1Scan03182011_14.png | 100 px]]
|-
| +1.0||[[File:OTR_Q1Scan03182011_15.png | 100 px]] ||[[File:FC_Q1Scan03182011_15.png | 100 px]]
|-
| +1.2||[[File:OTR_Q1Scan03182011_16.png | 100 px]] ||[[File:FC_Q1Scan03182011_16.png | 100 px]]
|-
| +1.4||[[File:OTR_Q1Scan03182011_17.png | 100 px]] ||[[File:FC_Q1Scan03182011_17.png | 100 px]]
|-
| +1.6||[[File:OTR_Q1Scan03182011_18.png | 100 px]] ||[[File:FC_Q1Scan03182011_18.png | 100 px]]
|-
| +1.8 ||[[File:OTR_Q1Scan03182011_19.png | 100 px]] ||[[File:FC_Q1Scan03182011_19.png | 100 px]]
|-
| +2.0 ||[[File:OTR_Q1Scan03182011_20.png | 100 px]] ||[[File:FC_Q1Scan03182011_20.png | 100 px]]
|}
|}


= Scan Quad 4 =
= Scan Quad 4 =
= Calibration =
 
Estimate the error in the above calibration
{| border="3"  cellpadding="20" cellspacing="0"
| image || OTR image || Calibration
|-
|[[File:HRRL_03-18-2011_cal_1_source.png | 200 px]]  || [[File:HRRL_03-18-2011_cal_1.png | 200 px]]  ||cal_h = 31.75 mm / 737 px = 0.04308 mm/px; cal_v = 31.75 mm / sqrt(2) / 531 px = 0.04228 mm/px;
|-
|[[File:HRRL_03-18-2011_cal_2_source.png | 200 px]]  || [[File:HRRL_03-18-2011_cal_2.png | 200 px]]  || cal_h = 31.75 mm / 738 px = 0.04302 mm/px; cal_v = 31.75 mm / sqrt(2) / 535 px = 0.04196 mm/px;
|-
|[[File:HRRL_03-18-2011_cal_3_source.png | 200 px]]  || [[File:HRRL_03-18-2011_cal_3.png | 200 px]]  || cal_h = 31.75 mm / 735 px = 0.04320 mm/px; cal_v = 31.75 mm / sqrt(2) / 532 px = 0.04220 mm/px;
|-
|[[File:HRRL_03-18-2011_cal_4_source.png | 200 px]]  || [[File:HRRL_03-18-2011_cal_4.png | 200 px]]  || cal_h = 31.75 mm / 735 px = 0.04320 mm/px; cal_v = 31.75 mm / sqrt(2) / 536 px = 0.04189 mm/px;
|-
|[[File:HRRL_03-18-2011_cal_5_source.png | 200 px]]  || [[File:HRRL_03-18-2011_cal_5.png | 200 px]]  || cal_h = 31.75 mm / 749 px = 0.04239 mm/px; cal_v = 31.75 mm / sqrt(2)) / 539 px = 0.04165  mm/px
|-
|[[File:HRRL_03-18-2011_cal_6_source.png | 200 px]]  || [[File:HRRL_03-18-2011_cal_6.png | 200 px]]  || cal_h = 31.75 mm / 732 px = 0.04337 mm/px; cal_v = 31.75 mm / sqrt(2) / 536 px = 0.04189 mm/px
|-
|[[File:HRRL_03-18-2011_cal_7_source.png | 200 px]]  || [[File:HRRL_03-18-2011_cal_7.png | 200 px]]  || cal_h = 31.75 mm / 735 px = 0.04320 mm/px; cal_v = 31.75 mm / sqrt(2)) / 532 px = 0.04220 mm/px
|-
|}
{| border="3"  cellpadding="20" cellspacing="0"
|- 
|cal_h (mm/px) || cal_v (mm/px) ||
|- 
|0.04308|| 0.04228 ||
|-
|0.04302 || 0.04196 ||
|- 
|0.04320  || 0.04220 ||
|- 
|0.04320 || 0.04189 ||
|- 
|0.04239 ||  0.04165 ||
|-
|0.04337 || 0.04189 ||
|-
|0.04320 || 0.04220 ||
|-
|  mean (mm/px) || mean (mm/px) ||
|-
|  <math> 0.04307 \pm 0.00032 </math>||  <math> 0.04201 \pm  0.00023 </math> ||
|}
= Data Analysis =
== Preliminary results==
Here is the study on how to fit non_Gaussian curve. I fitted for whole image as well as parts of the image.
Here is beam profile, which is non-Gaussian.
Fits for whole image:
[[File:HRRL_03-18-2011_Data_Analysis_Preliminary_Results_non-Gauss_profile_1.png | 300 px]]
Fits for x=[362,404] and y=[241,301]:
[[File:HRRL_03-18-2011_Data_Analysis_Preliminary_Results_non-Gauss_profile_2.png | 300 px]]
=== Gaussian fitted for whole image ===
12.74 MeV
Fitted Gaussian for whole image
x-projection:
[[File:HRRL_03-18-2011_Data_Analysis_Preliminary_Results_Gauss_Fitted_Whole_Image.png | 300 px]]
=== Gaussian fitted for part 1 of the image ===
Fitted Gaussian for part 1 of the image
        xl = 362;% center at 382
        xr = 404;
        yl = 241;% center at 271
        yr = 301;
xl: x left, xr: x right. yl: y left, yr: y right.
x-projection:
[[File:HRRL_03-18-2011_Data_Analysis_Preliminary_Results_Gauss_Fitted_Part_1_Image.png | 300 px]]
=== Gaussian fitted for part 2 of the image ===
Fitted Gaussian for part 2 of the image
        xl = 342;% center at 382
        xr = 424;
        yl = 241;% center at 271
        yr = 301;
x-projection:
[[File:HRRL_03-18-2011_Data_Analysis_Preliminary_Results_Gauss_Fitted_Part_2_Image.png | 300 px]]
=== Gaussian fitted for part 3 of the image ===
Fitted Gaussian for part 3 of the image
        xl = 342;% center at 382
        xr = 424;
        yl = 221;% center at 271
        yr = 321;
       
x-projection:
[[File:HRRL_03-18-2011_Data_Analysis_Preliminary_Results_Gauss_Fitted_Part_3_Image.png | 300 px]]
=== Gaussian fitted for part 4 of the image ===
Fitted Gaussian for part 4 of the image
        xl = 322;% center at 382
        xr = 444;
        yl = 221;% center at 271
        yr = 321;
x-projection:
[[File:HRRL_03-18-2011_Data_Analysis_Preliminary_Results_Gauss_Fitted_Part_4_Image.png | 300 px]]
== Analysis with root ==
===  Q1_Scan, 42mA peak current, Scan Coil Current at positive 1.8_Amp ===
Image
[[File:HRRL-03-18-2011-Analysis-with-root-Q1_Scan-42mA-peak-current-Scan-Coil-Current-at-positive-1.8_Amp-signal.png | 200 px]]
Back grounds
[[File:HRRL-03-18-2011-Analysis-with-root-Q1_Scan-42mA-peak-current-Scan-Coil-Current-at-positive-1.8_Amp-bg-1.png | 100 px]]
[[File:HRRL-03-18-2011-Analysis-with-root-Q1_Scan-42mA-peak-current-Scan-Coil-Current-at-positive-1.8_Amp-bg-2.png | 100 px]]
[[File:HRRL-03-18-2011-Analysis-with-root-Q1_Scan-42mA-peak-current-Scan-Coil-Current-at-positive-1.8_Amp-bg-3.png | 100 px]]
[[File:HRRL-03-18-2011-Analysis-with-root-Q1_Scan-42mA-peak-current-Scan-Coil-Current-at-positive-1.8_Amp-bg-4.png | 100 px]]
[[File:HRRL-03-18-2011-Analysis-with-root-Q1_Scan-42mA-peak-current-Scan-Coil-Current-at-positive-1.8_Amp-bg-5.png | 100 px]]
[[File:HRRL-03-18-2011-Analysis-with-root-Q1_Scan-42mA-peak-current-Scan-Coil-Current-at-positive-1.8_Amp-bg-6.png | 100 px]]
[[File:HRRL-03-18-2011-Analysis-with-root-Q1_Scan-42mA-peak-current-Scan-Coil-Current-at-positive-1.8_Amp-bg-7.png | 100 px]]
[[File:HRRL-03-18-2011-Analysis-with-root-Q1_Scan-42mA-peak-current-Scan-Coil-Current-at-positive-1.8_Amp-bg-8.png | 100 px]]
[[File:HRRL-03-18-2011-Analysis-with-root-Q1_Scan-42mA-peak-current-Scan-Coil-Current-at-positive-1.8_Amp-bg-9.png | 100 px]]
[[File:HRRL-03-18-2011-Analysis-with-root-Q1_Scan-42mA-peak-current-Scan-Coil-Current-at-positive-1.8_Amp-bg-10.png | 100 px]]
{| border="1"
| Signal || Background
|-
| [[File:HRRL-03-18-2011-Analysis-with-root-Q1_Scan-42mA-peak-current-Scan-Coil-Current-at-positive-1.8_Amp-signal.png | 300 px]]    || [[File:HRRL-03-18-2011-Analysis-with-root-Q1_Scan-42mA-peak-current-Scan-Coil-Current-at-positive-1.8_Amp-bg-1.png | 300 px]]
|-
|These MATLAB fits are set to fit at 0.7 times above height of the peak.
|-
|  Matlab fit to x profile || Matlab fit to y profile
|-
|[[File:HRRL-03-18-2011-Analysis-with-root-Q1_Scan-42mA-peak-current-Scan-Coil-Current-at-positive-1.8_Amp-signal-Matlab_Fit-x.png | 300 px]]  ||  [[File:HRRL-03-18-2011-Analysis-with-root-Q1_Scan-42mA-peak-current-Scan-Coil-Current-at-positive-1.8_Amp-signal-Matlab_Fit-y.png | 300 px]]
|-
|sigma_x = 24.97 px || sigma_y = 44.45 px
|-
| Blue: Signal, Red Background, Black: Subtraction || [[File:HRRL-03-18-2011-Analysis-with-root-Q1_Scan-42mA-peak-current-Scan-Coil-Current-at-positive-1.8_Amp-signal_bg_sg-bg.png | 300 px]]
|-
|signal || [[File:HRRL-03-18-2011-Analysis-with-root-Q1_Scan-42mA-peak-current-Scan-Coil-Current-at-positive-1.8_Amp-surf-sg.png | 300 px]]
|
|-
|background || [[File:HRRL-03-18-2011-Analysis-with-root-Q1_Scan-42mA-peak-current-Scan-Coil-Current-at-positive-1.8_Amp-surf-bg.png | 300 px]]
|
|-
| signal - background|| [[File:HRRL-03-18-2011-Analysis-with-root-Q1_Scan-42mA-peak-current-Scan-Coil-Current-at-positive-1.8_Amp-surf-sg-bg.png | 300 px]]
|
|-
|signal || [[File:HRRL-03-18-2011-Analysis-with-root-Q1_Scan-42mA-peak-current-Scan-Coil-Current-at-positive-1.8_Amp-contour-sg.png | 300 px]]
|-
|background || [[File:HRRL-03-18-2011-Analysis-with-root-Q1_Scan-42mA-peak-current-Scan-Coil-Current-at-positive-1.8_Amp-contour-bg.png | 300 px]]
|
|-
| signal - background|| [[File:HRRL-03-18-2011-Analysis-with-root-Q1_Scan-42mA-peak-current-Scan-Coil-Current-at-positive-1.8_Amp-contour-sg-bg.png | 300 px]]
|
|}
[[File:TF_Q1_1.8_03182011_NOCUTS.png| 200 px]][[File:TF_Q1_1.8_03182011.png| 200 px]]
The red line is the background above which seems to be larger than the signal.  Why?
Below I zoom in on channel 250 where you can see that for this channel the background is larger.  I then plot, on the right, all the elements along the x direction what are added up to get the values on the right.
[[File:TF_Q1_1.8_03182011Problem.png| 200 px]]
Why isn't the addition making sense?
===  Q6_Scan, 42mA peak current, Scan Coil Current at negative 2.5_Amp ===
{| border="1"
| Signal || Background
|-
| [[File:HRRL-03-18-2011-Analysis-with-root-Q6_Scan-42mA-peak-current-Scan-Coil-Current-at-negative-2.5_Amp-signal.png | 300 px]]    || [[File:HRRL-03-18-2011-Analysis-with-root-Q6_Scan-42mA-peak-current-Scan-Coil-Current-at-negative-2.5_Amp-bg-1.png | 300 px]]
|-
|  Matlab fit to x profile || Matlab fit to y profile
|-
| set to fit at 0.2 times above height of the peak. || set to fit at 0.7 times above height of the peak.
|-
|[[File:HRRL-03-18-2011-Analysis-with-root-Q6_Scan-42mA-peak-current-Scan-Coil-Current-at-negative-2.5_Amp-signal-Matlab_Fit-x.png | 300 px]]  ||  [[File:HRRL-03-18-2011-Analysis-with-root-Q6_Scan-42mA-peak-current-Scan-Coil-Current-at-negative-2.5_Amp-signal-Matlab_Fit-y.png | 300 px]]
|-
|sigma_x = 31.37 px || sigma_y = 18.63 px
|}
[[File:TF_Q6_2.5_03182011.png| 200px]]
== Lorentzian Fitting ==
Basic MATLAB Codes to fit Lorentzian:
[[File:Trial_my_Lorentzian_fit.txt]]
[[File:desum.txt]]
My MATLAB Fit code for beam
[[File:my_Lorentzian_fit.txt]]
[[File:desum.txt]]
Here is an example fitting:
{| border="1"
| Signal || Background || fit
|-
| [[File:HRRL_03-18-2011_Lorentzian_Fitting_Example_sg.png| 300 px]] || [[File:HRRL_03-18-2011_Lorentzian_Fitting_Example_bg.png| 300 px]]  || [[File:HRRL_03-18-2011_Lorentzian_Fitting_Example_1.png| 300 px]]
|-
| height of the peak || location of the peak ||  half-width at half-maximum (HWHM)
|-
| 1.6935e+006 || 358.9910 ||  45.4280
|}
If we were to apply the relation of the Gaussian rms to its FWHM to Lorentzian, we will get the sigma (or rms) of Lorentzian to be:
<math> \frac {2 \times 45.4280}{ 2.3548} = 38.5833192 </math>
== Super Gaussian Fitting ==
Beam Distributions Beyond RMS:
[[File:Beam_Distributions_Beyond_RMS.pdf]]
Bib: http://www.osti.gov/bridge/product.biblio.jsp?osti_id=82539#
Basic MATLAB Codes to fit Super Gaussian:
[[File:Trial_my_Super_Gaussian_fit.txt]]
[[File:SupGau_desum.txt]]
My MATLAB Fit code for beam
[[File:my_Super_Gaussian_fit.txt]]
[[File:SupGau_desum.txt]]
Here is an example fitting:
{| border="1"
| Signal || Background || fit
|-
| [[File:HRRL_03-18-2011_Lorentzian_Fitting_Example_sg.png| 300 px]] || [[File:HRRL_03-18-2011_Lorentzian_Fitting_Example_bg.png| 300 px]]  || [[File:HRRL_03-18-2011_SupGau_Fitting_Example_1.png| 300 px]]
[[HRRL_Emittance_Measurements_March14-18-2011]]
|-
| base || Amplitude ||  center
|-
| 202 || 8.0480e+003 ||  359.6730
|-
| sigma_0 || N ||  sigma
|-
| 20.92 || 0.8494 ||  38.56
|}
If we were to apply the relation of the Gaussian rms to its FWHM to Lorentzian, we will get the sigma (or rms) of Lorentzian to be:
<math> \frac {2 \times 45.4280}{ 2.3548} = 38.5833192 </math>
This is very close to the sigma we got from Super Gaussian, which is 38.56
= Results =
== Q1 ==
=== Positive Current, X projection ===
==== 1st fit ====
[[File:HRRL 03-18-2011_Results_Q1_42mA_Pos_X.png | 300 px]]
==== 2nd fit after cut off some points ====
[[File:HRRL 03-18-2011_Results_Q1_42mA_Pos_X_2.png | 300 px]]
== Q4 ==
Did not reach minimum.




[[HRRL_Emittance_Measurements_March14-18-2011]]
[[HRRL_Emittance_Measurements_March14-18-2011]]

Latest revision as of 19:13, 11 January 2012

Tune parameters

Previous Tune at the higher energy

Solenoid 1 5.4 A
Solenoid 2 5.5 A
Gun Ver -0.2 A
Gun Hor +0.4 A
Output Hor -0.5 A
Output Ver -0.5 A
Gun HV +9.75 (Knob Setting)
Gun Grid Voltage 5.25 (Knob Setting)
RF frequency 2855.813 MHz
Modulator HV Power Supply 4.11 (Knob Setting)
RF macro Pulse Length (FWHM) 200 ns

Solenoid comparison with yesterdays higher energy tune

V1 (Gun Vertical) H1 (Gun Horizontal) Sol1 (Gun Sol) V2 (Output Vertical) H2 (Output horizontal Sol 2 (Output solenoid) OTR Pict FC pict
(A) (A) (A) (A) (A) (A)
(-0.3) +0 0 0 -0 -0
(-0.2) +0.4 5.4 -0.5 -0.5 5.5
(-0.2) +0.4 6.8 -0.5 -0.5 5.5
(-0.2) +0.4 6.8 -0.5 -0.5 10.4

Quad Scans

To test reproducibility from yesterday. Scan at 40, 20, 10, 5 mA peak currents. Scan twice on each Current.

Do Energy Scan

Bend the beam through 45 bending dipole, take images on the scope of FC and YAG images.

D1 current Energy FC peak Volt Pic
(A) MeV mV
28 11.85 39
29 12.3 74
30 12.74 93
30.5 12.96 65
30.7 large uncertainty 22

Quad 1 Scan

Quad 1 OTR Pict FC pict
(A)
+0
+0.2
+0.4
+0.6
+0.8
+1.0
+1.2
+1.4
+1.6
+1.8
+2.0

Scan Quad 4

Calibration

Estimate the error in the above calibration


image OTR image Calibration
cal_h = 31.75 mm / 737 px = 0.04308 mm/px; cal_v = 31.75 mm / sqrt(2) / 531 px = 0.04228 mm/px;
cal_h = 31.75 mm / 738 px = 0.04302 mm/px; cal_v = 31.75 mm / sqrt(2) / 535 px = 0.04196 mm/px;
cal_h = 31.75 mm / 735 px = 0.04320 mm/px; cal_v = 31.75 mm / sqrt(2) / 532 px = 0.04220 mm/px;
cal_h = 31.75 mm / 735 px = 0.04320 mm/px; cal_v = 31.75 mm / sqrt(2) / 536 px = 0.04189 mm/px;
cal_h = 31.75 mm / 749 px = 0.04239 mm/px; cal_v = 31.75 mm / sqrt(2)) / 539 px = 0.04165 mm/px
cal_h = 31.75 mm / 732 px = 0.04337 mm/px; cal_v = 31.75 mm / sqrt(2) / 536 px = 0.04189 mm/px
cal_h = 31.75 mm / 735 px = 0.04320 mm/px; cal_v = 31.75 mm / sqrt(2)) / 532 px = 0.04220 mm/px


cal_h (mm/px) cal_v (mm/px)
0.04308 0.04228
0.04302 0.04196
0.04320 0.04220
0.04320 0.04189
0.04239 0.04165
0.04337 0.04189
0.04320 0.04220
mean (mm/px) mean (mm/px)
[math]\displaystyle{ 0.04307 \pm 0.00032 }[/math] [math]\displaystyle{ 0.04201 \pm 0.00023 }[/math]

Data Analysis

Preliminary results

Here is the study on how to fit non_Gaussian curve. I fitted for whole image as well as parts of the image.

Here is beam profile, which is non-Gaussian.

Fits for whole image:

Fits for x=[362,404] and y=[241,301]:


Gaussian fitted for whole image

12.74 MeV

Fitted Gaussian for whole image x-projection:

Gaussian fitted for part 1 of the image

Fitted Gaussian for part 1 of the image 

       xl = 362;% center at 382
       xr = 404;
       yl = 241;% center at 271
       yr = 301;

xl: x left, xr: x right. yl: y left, yr: y right.

x-projection:


Gaussian fitted for part 2 of the image

Fitted Gaussian for part 2 of the image 

       xl = 342;% center at 382
       xr = 424;
       yl = 241;% center at 271
       yr = 301;

x-projection:



Gaussian fitted for part 3 of the image

Fitted Gaussian for part 3 of the image 

       xl = 342;% center at 382
       xr = 424;
       yl = 221;% center at 271
       yr = 321;

x-projection:



Gaussian fitted for part 4 of the image

Fitted Gaussian for part 4 of the image 

       xl = 322;% center at 382
       xr = 444;
       yl = 221;% center at 271
       yr = 321;

x-projection:




Analysis with root

Q1_Scan, 42mA peak current, Scan Coil Current at positive 1.8_Amp

Image


Back grounds


Signal Background
These MATLAB fits are set to fit at 0.7 times above height of the peak.
Matlab fit to x profile Matlab fit to y profile
sigma_x = 24.97 px sigma_y = 44.45 px
Blue: Signal, Red Background, Black: Subtraction
signal
background
signal - background
signal
background
signal - background

The red line is the background above which seems to be larger than the signal. Why?

Below I zoom in on channel 250 where you can see that for this channel the background is larger. I then plot, on the right, all the elements along the x direction what are added up to get the values on the right.

Why isn't the addition making sense?

Q6_Scan, 42mA peak current, Scan Coil Current at negative 2.5_Amp

Signal Background
Matlab fit to x profile Matlab fit to y profile
set to fit at 0.2 times above height of the peak. set to fit at 0.7 times above height of the peak.
sigma_x = 31.37 px sigma_y = 18.63 px

Lorentzian Fitting

Basic MATLAB Codes to fit Lorentzian:

File:Trial my Lorentzian fit.txt

File:Desum.txt

My MATLAB Fit code for beam

File:My Lorentzian fit.txt

File:Desum.txt

Here is an example fitting:

Signal Background fit
height of the peak location of the peak half-width at half-maximum (HWHM)
1.6935e+006 358.9910 45.4280

If we were to apply the relation of the Gaussian rms to its FWHM to Lorentzian, we will get the sigma (or rms) of Lorentzian to be: [math]\displaystyle{ \frac {2 \times 45.4280}{ 2.3548} = 38.5833192 }[/math]


Super Gaussian Fitting

Beam Distributions Beyond RMS: File:Beam Distributions Beyond RMS.pdf

Bib: http://www.osti.gov/bridge/product.biblio.jsp?osti_id=82539#


Basic MATLAB Codes to fit Super Gaussian:

File:Trial my Super Gaussian fit.txt

File:SupGau desum.txt

My MATLAB Fit code for beam

File:My Super Gaussian fit.txt

File:SupGau desum.txt

Here is an example fitting:

Signal Background fit


HRRL_Emittance_Measurements_March14-18-2011

base Amplitude center
202 8.0480e+003 359.6730
sigma_0 N sigma
20.92 0.8494 38.56


If we were to apply the relation of the Gaussian rms to its FWHM to Lorentzian, we will get the sigma (or rms) of Lorentzian to be: [math]\displaystyle{ \frac {2 \times 45.4280}{ 2.3548} = 38.5833192 }[/math]

This is very close to the sigma we got from Super Gaussian, which is 38.56

Results

Q1

Positive Current, X projection

1st fit


2nd fit after cut off some points

Q4

Did not reach minimum.




HRRL_Emittance_Measurements_March14-18-2011

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