HRRL 03-18-2011

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

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:

emit=0.521 +- 0.013 mm*mrad, emit_norm=13.002 +- 0.330 mm*mrad

beta=0.884 +- 0.025, alpha=0.469 +-0.027

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:

emit=0.322 +- 0.001 mm*mrad, emit_norm=8.022 +- 0.033 mm*mrad

beta=3.110 +- 0.003, alpha=0.906 +-0.002

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:

emit=0.360 +- 0.001 mm*mrad, emit_norm=8.970 +- 0.031 mm*mrad

beta=1.993 +- 0.001, alpha=0.672 +-0.001

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:

emit=0.360 +- 0.001 mm*mrad, emit_norm=8.970 +- 0.031 mm*mrad

beta=1.993 +- 0.001, alpha=0.672 +-0.001

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:

emit=0.350 +- 0.001 mm*mrad, emit_norm=8.738 +- 0.032 mm*mrad

beta=1.344 +- 0.002, alpha=0.464 +-0.002

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

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

emit=0.370 +- 0.001 mm*mrad, emit_norm=9.225 +- 0.030 mm*mrad

beta=1.329 +- 0.001, alpha=0.754 +-0.001

2nd fit after cut off some points

emit=0.533 +- 0.002 mm*mrad, emit_norm=13.299 +- 0.046 mm*mrad

beta=1.954 +- 0.002, alpha=1.129 +-0.002