# Design

New deisign: We changed to use just one magnet.

HRRL had steer magnets on itself. We don't need external steer magnets. But Dr. Chouffani said that we might need them after quads, if the quads are not on axis. He will think about it.

Beam Line design on 27th, Jul. 2010:

Optim File on 27th, Jul. 2010:

## Beam Line Parts

Length of the pole face of Quad2Tin z direction is 8 cm.

## Constructed Beam Line for Emittance Test

Vacuum pressure on the beam line is less than torr (on 2010-July-7th).

# Leveling Survey

Downstream of the beam up by 2.6 mm.

# How to do Leveling Survey and Alignment with Theodolite on e- Beam Line

## A. Leveling Beam Pipe

1. Put the theodolite as high as the center of the beam line at upstream. Turn theodolite up and down. If the up angle is equal to down angle from the center of the pipe, theodolite is exactly as high as beam pipe. If not, adjust theodolite, until up and down angles are equal.

2. Once first step finished, then rotate theodolite horizontally to down stream. Turn it up and down, if up and down angles are not equal, adjust the stand till they are equal.

## B. How to Make Sure the Quad is Perpendicular to the Beam Line

If the distances between quads and end of cavity at any given points are equal, then quad and end of cavity are parallel. Pipe is perpendicular to the end of the cavity, thus, magnet would also be perpendicular to the pipe.

I will find at lest three random points quads and three corresponding points at the end of the cavity, make sure they are equal, then I can say, magnet is perpendicular to the beam line.

I am planning to stick a metal ruler two, so two faces are parallel.

## C. Centering the Quad Magnet with Theodolite

### Vertical Centering

1. Finish the step 1 in A.

2. Then turn up the theodolite from the upper edge of the pipe to the magnet hole, call this angle upper angle. Do the same at lower part, call it lower angle. If the this two angles are not equal adjust the stand till they are equal.

### Horizantal Centering

We know the diameter of the pipe . So, we can calculate from the pipe to the edge of the quad as:

We need to make sure this distance is same when measure it horizontally, so that our quad is centered on the pipe. I am going to use a ruler to ...(thinking)

# July 2010 Run

Initial Accelerator Settings

E = 10 MeV Control Voltage= 4.09 V

Pulse Width <= 50 ns

Average Beam Current = least amount needed to light up YaG crystal, start at 1 mA and Rep rate of 100 Hz.

At the same time we want to do radiation test on HRRL. This is for predicting the radiation after shifting cavity to new position. Radiation test run plan is at: 

## 7/26/10

### Alignment check

1.) Survey the Quad to be sure it is centered on the beam pipe

2.) survey the flag to determine if target is centered on the beam pipe

### Transmission tuning

1.) Using the quads and accelerator coils, focus the beam on the YaG crystal to as fine a spot as possible. Monitor the FC during the focusing.

changed control Voltage from

Control Voltage= 4.9 V E = 16 MeV

to

4.09 V E = 10 MeV

Tune the 4 accelerator coils for max transmission.

We want to maximize the current reach the Farady Cup. This can be determined by the ratio on Channels of FC and Gun Current.

Gun current is the current on the pick up coil, which is input current for cavity. Current on Farady cup is the current reach the end of the beam line (FC is at the end of the beam line). We want to maximize the the ratio of Farady cup current to Gun current (FCC/GC), so there are more electrons will make it to the target. Thus, we enlarge our positron yield.

Basic principle: Fix three coils, change one till it maximized.

 Coil 1 upstream left/right (mA) Coil 2 upstream UP/down (mA) Coil 3 downstream up/down Coil 4 downstream left right Scope Picture Gun Current FC current Transmission Gun / FC 10 15 +/- 0.65 nV s -5.41.8 nV s 36 12 %

The HRRL went down after 2 hours of operation.

## 7/27/10

No HRRL beam time today. Chad tested the Thermatron module and believes it is not the problem. Chad will continue debugging tomorrow.

### Filament

BMP format:

Wiki won't allow me to upload with bmp extension. So, I used png extension to upload. After download files, you will find they are still with bmp extension.

## 7/28/10

The HRRL came back around 3pm today. A capacitor in the bank was found to be the problem.

### Maximize Transmission

Maximized setup according to the accelerator operator.

Beam Energy: 16 MeV

Rep Rate: 95 Hz

Pulse Width: 100 ns

 Coil 1 upstream left/right (A) Coil 2 upstream UP/down (A) Coil 3 downstream up/down (A) Coil 4 downstream left right (A) Scope Picture Gun Current FC current Ratio Spot Size 0.1 0.5 3.1 0.7 Reversed the polarities on coil # 3 and coil # 4. Rep rate: 3Hz

 Coil 1 upstream left/right (A) Coil 2 upstream UP/down (A) Coil 3 downstream up/down (A) Coil 4 downstream left right (A) Scope Picture Gun Current FC current Ratio Spot Size 1.2 1.2 0.0 3 After image manipulation in GIMP to remove spot from the filament, Arne obtained reasonable projections for horizontal and vertical beam sizes ( < 2 mm). The quad was off, low rep rate to avoid saturation, 10MeV. This was the spot for the initial setup on Wednesday. #### Electron beam deflection due to Earth's B-field.

It appears the the image from electrons hitting the YaG crystal is offset (to the right) compare to the image from the filament which appears near the center of the cross hairs.

Is the earths Magnetic field causing the electrons to move this far beam right?

= 0.00005 Tesla ( ) = 0.5 Gauss

E_{electron} = 10 MeV = Pc P = 10 MeV/c

Estimation using Classical Lorentz Force (forget about angle of B and V)

assuming and are orthogonal then we get the cyclotron radius

Now some Geometry.

Assuming the orbit is a circle with a 700 m radius, then the question becomes how far does the electron move to maintain the orbit if it travels 1 m in a straight line.

let

= distance along the beam line

= deflection due to gravity

Note
is a tangent to the orbit

one can construct a right angle triangle with side of length d, the as the base and as the hypotenuse.

Then Pythagorean's theorem gives

Giving

since l/r is very small (1/700) we can approximate this as

for 10 MeV and a 1 m long beam pipe

where is in units of m

Spent the remaining beam time doing radiation footprint measurements.

## 7/29/10

Today we first tune up the beam for max transmission.

If the above calculation is correct we can expect the electron beam to move at least 2 mm away from the center of the FC. We could test it the Earth's B-field is the cause of the deflection by watch the deflection as a function of the beam energy. If we had enough -metal we could wrap the beam pipe in it and see if the deflection goes away.

Beam current

#### PS Output Current to Shunt Resistance Current Conversion

PS negative connected to Quad positive.

Shunt resistance: 50 AMP, 50 MV. (PR 0050, QECO)

 PS Reading (Amps) Shunt Resistance Voltage (mV) Shunt Resistance Current (Amps) (Calculated) 0 0 0 1 1 1 2 2.1 2.1 3 3.2 3.2 4 4.3 4.3 5 5.4 5.4 6 6.4 6.4 7 7.4 7.4 8 8.5 8.5 9 9.6 9.6 10 10.7 10.7 11 11.7 11.7 12 12.8 12.8 13 13.9 13.9 14 14.9 14.9 15 16 16 16 17 17 17 18.1 18.1 18 19.2 19.2 19 20.3 20.3 20 21.3 21.3 21 22.4 22.4 22 23.5 23.5

spent noon to 3pm on radiation measurements below

### Earth's B-field effect

It the above calculation on the effects of the Earth's Magnetic field on a the electron beam is correct then we should see the amount of deflection depend inversely on the electron's momentum (1/P).

So lets take a few pictures at the energy exterma to see how far the electron spot moves away from the filament image on the crystal.

 E beam (V gun) YaG picture Beam Spot posiiton (arb offset) 5 100 px 10 (4.09 V) -31.8 .1 mm 16 (4.9 V) -32.0 0.1 mm

We did not see the beam spot move when the energy was changed from 10 MeV to 16 MeV, but going to lower energy definitely moved the beam spot farther away from the center filament image that is located on the YaG crystal cross hairs.

### Maximize Transmission

Change the linac coils to determine a setting which delivers the maximum current to the FC and has a reasonable spot size on the YaG viewer.

 Coil 1 upstream left/right (A) Coil 2 upstream UP/down (A) Coil 3 downstream up/down Coil 4 downstream left right Scope Picture Gun Current FC current Ratio YaG Image 0 0.6 1.8 2.7

 Coil 1 upstream left/right (A) Coil 2 upstream UP/down (A) Coil 3 downstream up/down Coil 4 downstream left right Scope Picture Gun Current FC current Ratio YaG Image 0 0.6 1.8 2.7 100px 100px

a.) Does a small beam spot size on the crystal give maximum FC signal?

b.) Is there a point where the spot size changes and you can't resolve a change in the FC output?

c.) Remove the YaG target and determine if above observations are unchanged.

### Pickup Coil Calibration

2.) After tuning the beam to deliver the Maximum beam current to the FC, measure the FC and green pickup coil output as a function of current by integrating the pulse with an oscilloscope.

a.) does the FC output change with rep rate? It should not but maybe there is loss at high rates?

Tune the beam so a change in the quad B-field does not cause a deflection.

First attempt to measure the spot size change as a function of Quad current

 Quad Current Beam Spot RMS (0 degrees= Left/right) Beam Spot RMS (90 degrees= Up/Down) (Amps) (mm) (mm)

Shall we do both polarities?

Imaging

### Background subtraction

The filament produces at least a 2 mm diameter spot on the YaG crystal. Beam dominates the image.

## 7/30/10

At 4pm yesterday we attempted to measure the emittance at high currents of 10 mA, previous measurements were at 0.3 mA. The beam spot became larger than the 1" YaG target holder. This would make emittance measurements impossible.

In order to measure the emittance above 1 mA we will need to insert a doublet as close to the accelerator entrance as possible. Since this would not be done by today we decided to cancel today's beam time and work on the next emittance measurement.

The YaG camera saturated at about 0.6 mA of beam current (our measurements were made at about 0.3 mA). Perhaps we should use a thin Aluminum target instead of the YaG crystal for high current measurements.

We were able to Trigger the GigE camera. We should use this next time.

## Imaging scratch area

After image manipulation in GIMP to remove spot from filament. Obtained reasonable projections for horizontal and vertical beam sizes. The quad was off, low rep rate to avoid saturation, 10MeV. This was the spot for the initial setup on Wednesday. # Data Analysis

Root Code: File:Pixle.C

The cut is changed from circular to elliptical on Sep. 23rd, 2010.

## Rotating the Image

Images need to be rotated -6 degree, so cross at center of the crystal is perpendicular to the image. Here are the rotated images

### 2nd Scan

Polarity was switched from 1st scan.

## Coil Current vs Beam Spot Projection Gaussian Fit's Sigma

### 1st Scan

 Coil Current Reading on PS (Amps) Coil Current Reading From Shunt Resistance (Amps) X Projection Sigma (pixels) Y Projection Sigma (pixels) 0 0 30.28 30.69 1 1 31.6 29.81 1.4 32.3 29.37 2 2.1 32.93 2864 3 3.2 34.45 27.85 4 4.3 35.51 27.3 5 5.4 36.28 27.06 6 6.4 37.22 26.52 7 7.4 38.14 26.8 8 8.5 38.89 26.97 9 9.6 38.59 28.29 10 10.7 39.97 27.44 11 11.7 39.8 27.72 12 12.8 40.35 27.67 13 13.9 40.06 27.67 14 14.9 40.2 27.76 15 16 40.26 27.96 16 17 40.84 27.81 17 18.1 41.41 27.93 18 19.2 41.55 28.12 19 20.3 41.41 28.18 20 21.3 42.25 28.58

### 2nd Scan

 Coil Current Reading on PS (Amps) Coil Current Reading From Shunt Resistance (Amps) X Projection Sigma (pixels) Y Projection Sigma (pixels) 0 0 31.68 33.79 1 1 30.51 34.77 2 2.1 29.72 36.33 3 3.2 28.81 37.6 4 4.3 28.11 38.3 5 5.4 27.99 38.45 6 6.4 27.78 39.73 7 7.4 28.07 39.32 8 8.5 27.91 39.31 9 9.6 28.38 41.08 10 10.7 28.62 41.87 11 11.7 28.66 41.52 12 12.8 28.91 42.31 13 13.9 28.8 42.16 14 14.9 28.95 42.41 15 16 29.06 42.58 16 17 29.27 42.95 17 18.1 29.15 43.26 18 19.2 29.01 42.98 19 20.3 29.05 42.61 20 21.3 28.93 43.63 22 23.5 29.08 44.39

## Multi-Fits for Beam Spot Projection

### Multi-Fits 1st Scan

Naming the photos: Rotated_HRRL_Emit_Test_Quad_Scan_First_20Amp_Multi_Fit7 -> RHETQSF20AMF7

### Multi-Fits 2nd Scan

Naming the photos: Rotated_HRRL_Emit_Test_Quad_Scan_Second_22Amp_Multi_Fit7 -> RHETQSS22AMF7

### Current -vs- Sigma Data Files

First Scan:

Second Scan:

Current vs Sigma:

X projections:

Fit:

P-value of this fit is less than 0.000001.

Y projections:

Fit:

P-value of this fit is less than 0.000001.

Next step:
calibrate: mm/pxiel
Parabola: All the x projections makeup one parabola, and y projections makeup one parabola. Put them in together.


### Converting pixels to length

Diameter of circle inside crystal is 10 mm.

Convert the pictures to a histogram and measure pixels that way

### Sigma (in mm) vs Dipole Coil Current (on Shunt Resistance)

#### X Projection

The fit is:

p-value is less than 0.000001

For a parabola , the corresponding to the minimum is:

.

So,

and

.

.

.

So,

#### Y Projection

The fit is:

p-value is less than 0.000001

.

So,

.

.

So,

#### Conclusions

For X projection: , and

For X projection: , and

## Emittance

g here is the gradient of the qudrupole. p is the momentum of the e- beam.

In our case, energy of the beam is 0.01 GeV and gap between dipole center and pole face is 1 inch.

So,

According to File:Emit Meas DAFNE Linac e Beam.pdf, for the case of quadruple scanning one quadrupole and screen, the emittance related to the quadrupole strength.

Transfer Matrix for 1uaruople \tilde{Q} and screen (drift space?) \tilde{S} consist the transfer matrix of the whole system as:

is the distance between quadrupole and screen.

If I have a fit:

Then,

Two fits are:

### Dr. Kim's Suggestion in his email

from	Yujong Kim <yjkim@isu.edu>
cc	Dr Forest <tforest@athena.physics.isu.edu>
date	Fri, Oct 8, 2010 at 6:44 AM

Dear Sadiq,

Many thanks,

I re-checked your QM scan fitting plot (final plots on emittance mewasurement).

Your fitting range too wide (-20 < k < 50).

Please fit again with a narrower range (+10 < k < 50).
Then, you can get much beautiful results.
Normally, we fit for only one k sign (positive or negative).
Yujong Kim


Here are results after doing Dr. Kim's suggested fit.

Note: I also corrected the distance S12 to the distance between quad center and screen (I originally did from the end of the quad to the screen, this is wrong).


#### For X projection

Minimum ChiSqrd is: 129.749

The fit is:

sig^2 = (7.82463e-06+-2e-08) + (4.23945e-07+-1e-09)*k + (6.82167e-09+-1e-10)*k*k

Probability of obtaining data at least as incompatible with distribution as the data actually observed is 0.000000 A = 7.82463e-06, B = -0.0270904, C = 1.07925e-09, S12=0.64. Geometrical Emittance: 2.24354e-07 (m*rad), Normalized Emittance: 4.39048e-06 (m*rad).

Data file contains: Number-of-points B-Field-Strength Error-on-B-Field-Strength Sigma^2 Error-on-Sigma^2

#### For Y projection

Minimum ChiSqrd is: 25.3174

The fit is:

sig^2 = (1.71755e-05+-8e-08) + (-8.38108e-07+-3e-09)*k + (1.3229e-08+-1e-10)*k*k

Probability of obtaining data at least as incompatible with distribution as the data actually observed is 0.000000 A = 1.71755e-05, B = 0.0243983, C = 3.00479e-09, S12=0.64. Geometrical Emittance: 5.54629e-07 (m*rad), Normalized Emittance: 1.08538e-05 (m*rad).

Data file contains: Number-of-points B-Field-Strength Error-on-B-Field-Strength Sigma Error-on-Sigma

## Emittance Results for HRRL at 10 MeV and 102 micro Amp peak Measurements of the beam spot size as a function of the quadrupole magnetic field used to calculate the beam emittance. The fits are and with a of 8.1 and 1.7 respectively. The respective P-values for this fit are 0.05 and 10^{-20}.

# Automatic Script to plot RMS

## ROOT

How does the fit look when using the script below.

Working on it.

You should do background subtraction instead of cutting out the spot.

2 bugs remain till Spe 24th. 1. entries; 2. Sub->Draw();


Running Parabola_Fit_for_AutoRMS.C will run AutoRMS.C and do the fits.

This 2 programs and pictures for data can be downloaded at: 

## MATLAB

These MATLAB scripts will do Gaussian fits for beam spots and get rms beam size on x and projections (by Gauss_Fit.m). These rms values will be passed on (to Emit_Parabola_Fit_kl_YProjection.m and Emit_Parabola_Fit_kl_YProjection.m) to fit parabola. Parabola fit will be plotted,and emittances, normalized emittances, beta functions, alpha functions will given at the end.

# New Fits with K1L

## No Fringe Field Effect

We want to do new fits with K1L. K1 is quadrupole strength and L is the thickness of the quadrupole. We will do it for the data we got previously. They are the following two data sets.

At this step, we will ignore fringe field effect, we want to consider it later.

need uncertainties in plots below

The uncertainties are difficult to believe because they are so small (< 0.1% !)

Redo you plots so they look like the ones below in terms of line boldness and quality.  Identify the fit parameters and their error as well as a measurement of the goodness of fit.

https://wiki.iac.isu.edu/index.php/File:Emittance_HRRL_1mA.png


Data files contains:

Number-of-points B-Field-Strength Error-on-B-Field-Strength Sigma^2 Error-on-Sigma^2

X-Projection:
Fit Parameters by MATLAB:
y = 0.00000784 + (0.00000288)*x + 0.00000031*x*x
Fit Parameters by Matrix Inversion:
y = (0.00000781+-0.00000027) + (0.00000282+-0.00000014)*x + (0.00000030+-0.00000002)*x*x
P-value = 7.6238e-21

Y-Projection:
Fit Parameters by MATLAB:
y = 0.00001766 + (-0.00000599)*x + 0.00000066*x*x
Fit Parameters by Matrix Inversion:
y = (0.00001717+-0.00000084) + (-0.00000558+-0.00000041)*x + (0.00000059+-0.00000005)*x*x
P-value =  0.020964

geometrical emittance:
normalized emittance:



X Projection:

Y Projection:

# Corrections for vertical calibration

We made error when we are doing vertical calibration. When we calculate vertical calibration, we need to multiply the diameter of the circle by .

This is the reason that we got dramatically different results in vertical and horizontal emittances.

## Errors in Converting pixels to length for Vertical

 Average Horizontal Diameter (pixels) Average Vertical Diameter (pixels) Horizontal mm/pixels Vertical mm/pixels need to be multiplied by

## New Fits with K1L

### Considering fringe field effect with "Cheap and Dirty" way

#### X Projection

x-projection:

beta=0.72 +- 0.31, alpha=-1.23 +-0.56

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


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

y = (8.05126 +-0.24983) + (4.18341+-0.18968)*x + (0.64143+-0.03472)*x.*x

Data created from parabola fit

#### Y Projection

y-projection:

beta=0.54 +- 0.22, alpha=2.68 +-1.13

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


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

y = (8.51813 +-0.40098) + (-3.88142+-0.28132)*x + (0.57350+-0.04792)*x.*x

Data created from parabola fit

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