HRRL 03-17-2011

Good Tune Used for good Scan

By Dr. Kim

Solenoid 1	6.8 A
Solenoid 2	10.4 A
Gun Ver	-0.2 A
Gun Hor	+0.4 A
Output Hor	-1.4A
Output Ver	-0.5 A
Gun HV	+9.75 (Knob Setting)
Gun Grid Voltage	5.25 (Knob Setting)
RF frequency	2855.816 MHz
Modulator HV Power Supply	4.42 (Knob Setting)
RF macro Pulse Length (FWHM)	200 ns
Peak Current on FC	37.2 mAmps
Scope on FC
e- Beam Energy	14 MeV

Scan Description

This is scan for 14 MeV beam. 40 mAmps peak current. Q1 is on, All other quads are off.

1) Scan from -5 Amps to 5 Amps

2) Increment at 0.2 Amps.

3) Name images by numbers start from 1. Then go on.

Like: -5 Amp is 1, -4.8 Amp is 2, and so on til 5 Amp is named 51.

4) Scan multipole times from -5 to 5 Amps, and put them in different folders.

5) For each time, take back ground images. It should be done when RF is on and gun is off.

6) After the scan take a scope image for the current of the FC after the OTR screen.

Calibration

image	OTR image	cal_h (mm/px)	cal_v (mm/px)
		0.04308	0.04204
		0.04320	0.04228
		0.04349	0.04181
		0.04323	0.04196
		0.04337	0.04212
		mean (mm/px)	mean (mm/px)
		[math]\displaystyle{ 0.04327 \pm 0.00016 }[/math]	[math]\displaystyle{ 0.04204 \pm 0.00018 }[/math]

Results

Q1

At lower current background subtraction gets worse, because singal/noise drops.

42 mA, Positive Current, X projection

emit=0.388 +- 0.008 mm*mrad, emit_norm=10.64 +- 0.22 mm*mrad

beta=1.285 +- 0.024, alpha=0.94 +-0.03

//K1*L(1/m)   er K1*L    sgima^2(mm)   er sigma^2

Media:2011_Mar_Emit_fit_data_x.txt

parabola fit for x-projection:

parabola fit for y-projection (y in mm unit):

y = (3.69167 +-0.02346) + (-3.89000+-0.12250)*x + (4.79738+-0.13309)*x.*x

Data created from parabola fit

Media:2011_Mar_Emit_data_from_fit_x.txt

42 mA, Negative Current, Y projection

emit=0.266 +- 0.018 mm*mrad, emit_norm=7.30 +- 0.50 mm*mrad

beta=0.918 +- 0.068, alpha=0.19 +-0.06

//K1*L(1/m)   er K1*L    sgima^2(mm)   er sigma^2

Media:2011_Mar_Emit_fit_data_y.txt

parabola fit for y-projection (y in mm unit):

y = (2.81806 +-0.03890) + (0.52202+-0.26284)*x + (2.35025+-0.34553)*x.*x

Data created from parabola fit

Media:2011_Mar_Emit_data_from_fit_y.txt

X and Y emittances are different. The parabola in X reaches min around 0.4, while in Y reaches around 0.15. Which suggests quadrupole strengths of X and Y are way different for same coil current. Which might suggest beam is not centered, because when beam is off-centered we have this can occur.

20 mA, Positive Current, X projection

10 mA, Positive Current, X projection

5 mA, Positive Current, X projection

Q4

42 mA All Other Quads off

Haven't reach minimum.

42 mA Q1_at_-2A, Q2_at_+8A, Q3_at_-6A

x-projection:

y-projection:

Fits After the Second Mapping of the Quad

I mapped the quad to find effective length of the quad for different currents. Results are at: Second Mapping of Quadruple Magnets

MATLAB Scripts

Media:hrrl_2011_marc_emit_test_marc17_SuperGaussian_Fit.txt

Media:hrrl_2011_marc_emit_test_marc17_SupGau_devsum.txt

Media:hrrl_2011_marc_emit_test_marc17_Emit_Parabola_Fit_kl_XProjection.txt

Media:hrrl_2011_marc_emit_test_marc17_Emit_Parabola_Fit_kl_YProjection.txt

Media:hrrl_2011_marc_emit_test_marc17_Trial_my_superGaussian_Fit.txt

Media:hrrl_2011_marc_emit_test_marc17_Plot_Beam_Spot.txt

Media:hrrl_2011_marc_emit_test_marc17_Three_d_surface_plotter.txt

Media:hrrl_2011_marc_emit_test_marc17_my_superGaussian_Fit.txt

Media:hrrl_2011_marc_emit_test_marc17_devsum.txt

Media:hrrl_2011_marc_emit_test_marc17_countor_plotter.txt

With thin lens approximation method

Why y projection has bigger error?

For data look at here: HRRL-03-17-2011-fit-error-ana

From the data we can see that sigma (rms) of Y-projection are more spread, 
ie. has bigger standard deviation, than the of X-projection. 

I think this is due to the beam profile in Y-projection contains less pixels than X- projection. 
(This is due to Y-projection observed with 45 degree angle, so Y-profile got squeezed).

So, Y-projection has less data for fitting, thus this creates bigger standard deviation for sigma (rms) value of the Y-projection.

Quad was mapping for the second time to find effective length for the different currents. Link is at [[1]].

X

x-projection:

emit=0.395 +- 0.021 mm*mrad, emit_norm=11.59 +- 1.31 mm*mrad

beta=1.50 +- 0.06 m, alpha=1.01 +- 0.06 rad

parabola fit for y-projection (y in mm unit):

y = (3.23007 +-0.01742) + (-3.96786+-0.18396)*x + (5.67591+-0.38307)*x.*x 

[math]\displaystyle{ \sigma_x^2= ( \pm ) + ( \pm )k_1L + ( \pm )(k_1L)^2 }[/math]

[math]\displaystyle{ \epsilon_x = \pm ~mm*mrad ~\Rightarrow~ \epsilon_{n,x} = \pm ~mm*mrad }[/math]

[math]\displaystyle{ \beta_x= \pm , \alpha_x= \pm }[/math]

   0.0234    3.1441    0.0204
   0.0524    3.0306    0.0231
   0.0817    2.9492    0.0174
   0.1116    2.8507    0.0204
   0.1429    2.7718    0.0212
   0.1733    2.7313    0.0362
   0.2049    2.6626    0.0301
   0.2362    2.6097    0.0237
   0.2679    2.5767    0.0287
   0.2955    2.5523    0.0222
   0.3283    2.5355    0.0338
   0.3594    2.5371    0.0221
   0.3920    2.5499    0.0401
   0.4227    2.5586    0.0360
   0.4535    2.6033    0.0259
   0.4849    2.6336    0.0463

Y

y-projection:

emit=0.315 +- 0.044 mm*mrad, emit_norm=9.25 +- 1.59 mm*mrad

beta=1.25 +- 0.14 m, alpha=0.26 +- 0.07 rad

parabola fit for y-projection (y in mm unit):

y = (2.47210 +-0.02580) + (0.83973+-0.32422)*x + (3.78259+-0.84657)*x.*x 

[math]\displaystyle{ \sigma_y^2 = ( \pm ) + ( \pm )k_1L + ( \pm )(k_1L)^2 }[/math]

[math]\displaystyle{ \epsilon_y = \pm ~mm*mrad ~\Rightarrow~ \epsilon_{n,y} = \pm ~mm*mrad }[/math]

[math]\displaystyle{ \beta_y= \pm , \alpha_y= \pm }[/math]

  -0.3969    2.7679    0.0693
  -0.3665    2.6659    0.0384
  -0.3341    2.5621    0.0552
  -0.3040    2.5487    0.0430
  -0.2743    2.5598    0.0333
  -0.2429    2.4948    0.0558
  -0.2137    2.4538    0.0365
  -0.1810    2.4705    0.0359
  -0.1500    2.4126    0.0762
  -0.1212    2.4144    0.0295
  -0.0902    2.4162    0.0620
  -0.0600    2.4181    0.0396
  -0.0301    2.4533    0.0472
  -0.0020    2.4801    0.0313

Energy Measurement

Dipole Current (A)	Beam Energy (MeV)	FC current image	Current (mA)
30.0000	14.6469		0.6
30.5000	14.8240		1.2
31.0000	14.9985		3.2
31.5000	15.1704		3.0
32.0000	15.3398		2.4
32.5000	15.5066		1.3
33.5000	15.8325		0.4

Energy     Current
(MeV)      (mA)
14.6469    0.6
14.8240    1.2
14.9985    3.2
15.1704    3.0
15.3398    2.4
15.5066    1.3
15.8325    0.4

Here used dipole mapping Kiwi_Dipole_Mappings#Estimation_for_En_vs_I

Amplitude = 3.23464, mean = 15.14254, sigma = 0.26190 

Gaussian Fit for Electron Beam Energy: 
En = 3.23464exp(-(En-15.14254)^2) / (2*0.26190^2) 

Gaussian Energy peak = 15.14254 

Energy spread = 1.57142 
rms Energy spread = 0.26190 

Relative Energy spread = 0.10378 
Relative rms Energy spread = 0.01730 

HRRL_Emittance_Measurements_March14-18-2011