# HRRL 03-17-2011

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# 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)

# Results

## Q1

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

### 42 mA, Positive Current, X projection

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

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


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

### 42 mA, Negative Current, Y projection

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

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


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

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.

## Q4

### 42 mA All Other Quads off

Haven't reach minimum.

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

## 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:

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


   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:

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


  -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

Relative Energy spread = 0.10378