Difference between revisions of "HRRL 03-17-2011"

From New IAC Wiki
Jump to navigation Jump to search
 
(77 intermediate revisions by 2 users not shown)
Line 1: Line 1:
−
;Accelerator Settings (Yujong Tune 11 am)
+
= Accelerator Tuning =
 +
= Good Tune Used for good Scan =
 +
 
 +
By Dr. Kim
 +
 
 
{| border="1"
 
{| border="1"
−
| Solenoid 1 || 6.8 A  
+
| 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)
 
|-
 
|-
−
|Solenoid 2 ||   10.4 A
+
|   RF frequency  || 2855.816 MHz
 
|-
 
|-
−
|Horzontal  In      || +0.4 A
+
|   Modulator HV Power Supply  || 4.42 (Knob Setting)
 
|-
 
|-
−
| Vertical In || -0.2 A
+
| RF macro Pulse Length (FWHM)  || 200 ns
 
|-
 
|-
−
|Horzontal out      || -1.4A
+
|  Peak Current on FC    || 37.2 mAmps
 
|-
 
|-
−
| Vertical Out || -0.5 A
+
| Scope on FC  || [[File:Scope_image_of_good_Accelarator_setting_by_Dr._Kim_Mar_17_2011.png | 100 px]]
 +
|-
 +
|  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 =
 +
 
  
 +
{| border="3"  cellpadding="20" cellspacing="0"
 +
| image || OTR image || cal_h (mm/px) || cal_v (mm/px)
 +
|-
 +
|[[File:HRRL_03-17-2011_cal_1_source.png | 200 px]]  || [[File:HRRL_03-17-2011_cal_1.png | 200 px]]  ||  0.04308  ||0.04204
 +
|-
 +
|[[File:HRRL_03-17-2011_cal_2_source.png | 200 px]]  || [[File:HRRL_03-17-2011_cal_2.png | 200 px]]  ||  0.04320  ||0.04228
 +
|-
 +
|[[File:HRRL_03-17-2011_cal_3_source.png | 200 px]]  || [[File:HRRL_03-17-2011_cal_3.png | 200 px]]  ||  0.04349  ||0.04181
 +
|-
 +
|[[File:HRRL_03-17-2011_cal_4_source.png | 200 px]]  || [[File:HRRL_03-17-2011_cal_4.png | 200 px]]  ||  0.04323  ||0.04196
 +
|-
 +
|[[File:HRRL_03-17-2011_cal_5_source.png | 200 px]]  || [[File:HRRL_03-17-2011_cal_5.png | 200 px]]  ||  0.04337  ||0.04212
 +
|-
 +
|  || || mean (mm/px) || mean (mm/px)
 +
|-
 +
|  || || <math> 0.04327 \pm 0.00016 </math>||  <math>  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
 +
 +
 +
 +
[[File:HRRL 03-17-2011_Results_Q1_42mA_Pos_SupGau_X.png | 300 px]]
 +
 +
//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
 +
 +
 +
[[File:HRRL 03-17-2011_Results_Q1_42mA_Pos_SupGau_Y.png | 300 px]]
 +
 +
//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 ===
 +
 +
[[File:HRRL 03-17-2011_Results_Q1_20mA_Pos_SupGau_X.png | 300 px]]
 +
 +
 +
 +
[[File:HRRL 03-17-2011_Results_Q1_20mA_Pos_SupGau_Y.png | 300 px]]
 +
 +
 +
 +
=== 10 mA, Positive Current, X projection ===
 +
 +
[[File:HRRL 03-17-2011_Results_Q1_10mA_Pos_SupGau_X.png | 300 px]]
 +
 +
 +
 +
[[File:HRRL 03-17-2011_Results_Q1_10mA_Pos_SupGau_Y.png | 300 px]]
 +
 +
=== 5 mA, Positive Current, X projection ===
 +
 +
[[File:HRRL 03-17-2011_Results_Q1_5mA_Pos_SupGau_X.png | 300 px]]
 +
 +
 +
[[File:HRRL 03-17-2011_Results_Q1_5mA_Pos_SupGau_Y.png | 300 px]]
 +
 +
== Q4 ==
 +
 +
=== 42 mA All Other Quads off ===
 +
 +
Haven't reach minimum.
 +
 +
=== 42 mA Q1_at_-2A, Q2_at_+8A, Q3_at_-6A ===
 +
 +
 +
[[File:HRRL 03-17-2011_Results_Q4_42mA_T1_On_Pos_SupGau_X.png | 300 px]]
 +
 +
x-projection:
 +
 +
 +
[[File:HRRL 03-17-2011_Results_Q4_42mA_T1_On_Pos_SupGau_Y.png | 300 px]]
 +
 +
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 [[https://wiki.iac.isu.edu/index.php/Second_Mapping_of_Quadruple_Magnets]].
 +
 +
=== X ===
 +
[[File:HRRL_Pos_Emit_test_Mar17_2011_Fit_after_2nd_quad_mapping_q1.png | 300 px]]
 +
 +
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> \sigma_x^2= (  \pm ) + ( \pm )k_1L + ( \pm )(k_1L)^2 </math>
 +
 +
<math> \epsilon_x =  \pm ~mm*mrad ~\Rightarrow~ \epsilon_{n,x} =  \pm ~mm*mrad</math>
 +
 +
<math> \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 ===
 +
 +
[[File:HRRL_Pos_Emit_test_Mar17_2011_Fit_after_2nd_quad_mapping_q2.png | 300 px]]
 +
 +
 +
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>\sigma_y^2 = ( \pm ) + ( \pm )k_1L + ( \pm )(k_1L)^2 </math>
 +
 +
<math> \epsilon_y =  \pm ~mm*mrad  ~\Rightarrow~  \epsilon_{n,y} =  \pm ~mm*mrad</math>
 +
 +
<math> \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 =
 +
 +
{| border="3"  cellpadding="20" cellspacing="0"
 +
| Dipole Current (A)|| Beam Energy (MeV) || FC current image || Current (mA)
 +
|-
 +
| 30.0000  ||  14.6469  || [[File:hrrl_17Mar2011_En_Scan_30MeV.png | 400 px]] || 0.6
 +
|-
 +
| 30.5000 ||  14.8240 ||  [[File:hrrl_17Mar2011_En_Scan_30p5MeV.png | 400 px]] || 1.2
 +
|-
 +
| 31.0000  ||  14.9985  || [[File:hrrl_17Mar2011_En_Scan_31MeV.png | 400 px]] || 3.2
 +
|-
 +
| 31.5000 ||  15.1704  || [[File:hrrl_17Mar2011_En_Scan_31p5MeV.png | 400 px]] || 3.0
 +
|-
 +
| 32.0000  ||  15.3398  || [[File:hrrl_17Mar2011_En_Scan_32MeV.png | 400 px]] || 2.4
 +
|-
 +
| 32.5000 ||  15.5066  || [[File:hrrl_17Mar2011_En_Scan_32p5MeV.png | 400 px]] || 1.3
 +
|-
 +
| 33.5000  ||  15.8325  || [[File:hrrl_17Mar2011_En_Scan_33p5MeV.png | 400 px]] || 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
 +
 +
 +
 +
[[File:hrrl_17Mar2012_15MeV_En_Spread.png | 400 px]]
 +
 +
 +
 +
 +
 +
 +
 +
 +
 +
 +
 +
 +
[[HRRL_Emittance_Measurements_March14-18-2011]]

Latest revision as of 09:16, 10 August 2012

Accelerator Tuning

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 Scope image of good Accelarator setting by Dr. Kim Mar 17 2011.png
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)
HRRL 03-17-2011 cal 1 source.png HRRL 03-17-2011 cal 1.png 0.04308 0.04204
HRRL 03-17-2011 cal 2 source.png HRRL 03-17-2011 cal 2.png 0.04320 0.04228
HRRL 03-17-2011 cal 3 source.png HRRL 03-17-2011 cal 3.png 0.04349 0.04181
HRRL 03-17-2011 cal 4 source.png HRRL 03-17-2011 cal 4.png 0.04323 0.04196
HRRL 03-17-2011 cal 5 source.png HRRL 03-17-2011 cal 5.png 0.04337 0.04212
mean (mm/px) mean (mm/px)
[math] 0.04327 \pm 0.00016 [/math] [math] 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


HRRL 03-17-2011 Results Q1 42mA Pos SupGau X.png 

//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


HRRL 03-17-2011 Results Q1 42mA Pos SupGau Y.png 

//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

HRRL 03-17-2011 Results Q1 20mA Pos SupGau X.png


HRRL 03-17-2011 Results Q1 20mA Pos SupGau Y.png


10 mA, Positive Current, X projection

HRRL 03-17-2011 Results Q1 10mA Pos SupGau X.png


HRRL 03-17-2011 Results Q1 10mA Pos SupGau Y.png

5 mA, Positive Current, X projection

HRRL 03-17-2011 Results Q1 5mA Pos SupGau X.png


HRRL 03-17-2011 Results Q1 5mA Pos SupGau Y.png

Q4

42 mA All Other Quads off

Haven't reach minimum.

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

HRRL 03-17-2011 Results Q4 42mA T1 On Pos SupGau X.png

x-projection:


HRRL 03-17-2011 Results Q4 42mA T1 On Pos SupGau Y.png

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

HRRL Pos Emit test Mar17 2011 Fit after 2nd quad mapping q1.png

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

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

[math] \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

HRRL Pos Emit test Mar17 2011 Fit after 2nd quad mapping q2.png


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

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

[math] \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 Hrrl 17Mar2011 En Scan 30MeV.png 0.6
30.5000 14.8240 Hrrl 17Mar2011 En Scan 30p5MeV.png 1.2
31.0000 14.9985 Hrrl 17Mar2011 En Scan 31MeV.png 3.2
31.5000 15.1704 Hrrl 17Mar2011 En Scan 31p5MeV.png 3.0
32.0000 15.3398 Hrrl 17Mar2011 En Scan 32MeV.png 2.4
32.5000 15.5066 Hrrl 17Mar2011 En Scan 32p5MeV.png 1.3
33.5000 15.8325 Hrrl 17Mar2011 En Scan 33p5MeV.png 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 17Mar2012 15MeV En Spread.png







HRRL_Emittance_Measurements_March14-18-2011

Retrieved from "https://wiki.iac.isu.edu/index.php?title=HRRL_03-17-2011&oldid=76478"