Sadiq Thesis

Introduction

Positron

Positron is the antimatter of electron. Positrons have same mass as electron ( [math]511~\frac{keV}{c^2}[/math]), carries positive charge, and it is noted as "[math]e^+[/math]".

Positrons predicted by Paul Dirac in 1928, <ref name="Dirac1928"> The Quantum Theory of the Electron, P. A. M. Dirac, Proc. R. Soc. Lond. A February 1, 1928 117 778 610-624;</ref>, and experimentally observed by Dmitri Skobeltsyn in 1929 and by Carl D. Anderson in 1932 <ref name="e+_discover"> General Chemistry, Taylor and Francis. p. 660. </ref>. Anderson also coined the term positron and he won the Nobel Prize for Physics in 1936.

<ref name="name"> BOOK_Gernal, Auther, Month_Year,issue,page </ref>

Apparatus

HRRL Positron Beamline

HRRL beamline layout is given in the figure below, and the item descriptions are given in the table below.

HRRL beamline layout.

Item	Description
T1	Positron target
T2	Annihilation target
EnS	Energy Slit
FC1, FC2	Faraday Cups
Q1,...Q10	Quadrupoles
D1, D2	Dipoles
NaI	NaI Detecotrs
OTR	Optical Transition Radiaiton screen
YAG	Yttrium Aluminium Garnet screen

Som parameters of HRRL is given by:

Parameter	Unit	Value
maximum energy	MeV	16
peak current	mA	100
repetition rate	Hz	300
absolute energy spread	MeV	2-4
macro pulse length	ns	>50

Beam properties

Emittance Measurement

Emittance is an important parameter in accelerator physics. If emittance with twiss parameters are given at the exit of the gun, we will be able to calculate beam size and divergence any point after the exit of the gun. Knowing the beam size and beam divergence on the positron target will greatly help us study the process of creating positron. Emittance with twiss parameters are also key parameters for any accelerator simulations. Also, energy and energy spread of the beam will be measured in the emittance measurement.

What is Emittance

Fig.1 Phase space ellipse <ref name="MConte08"></ref>.

In accelerator physics, Cartesian coordinate system was used to describe motion of the accelerated particles. Usually the z-axis of Cartesian coordinate system is set to be along the electron beam line as longitudinal beam direction. X-axis is set to be horizontal and perpendicular to the longitudinal direction, as one of the transverse beam direction. Y-axis is set to be vertical and perpendicular to the longitudinal direction, as another transverse beam direction.

For the convenience of representation, we use [math]z[/math] to represent our transverse coordinates, while discussing emittance. And we would like to express longitudinal beam direction with [math]s[/math]. Our transverse beam profile changes along the beam line, it makes [math]z[/math] is function of [math]s[/math], [math]z~(s)[/math]. The angle of a accelerated charge regarding the designed orbit can be defined as:

[math]z'=\frac{dz}{ds}[/math]

If we plot [math]z[/math] vs. [math]z'[/math], we will get an ellipse. The area of the ellipse is an invariant, which is called Courant-Snyder invariant. The transverse emittance [math]\epsilon[/math] of the beam is defined to be the area of the ellipse, which contains 90% of the particles <ref name="MConte08"> M. Conte and W. W. MacKay, “An Introduction To The Physics Of Particle Accelera tors”, World Scientifc, Singapore, 2008, 2nd Edition, pp. 257-330. </ref>.

By changing quadrupole magnetic field strength [math]k[/math], we can change beam sizes [math]\sigma_{x,y}[/math] on the screen. We make projection to the x, y axes, then fit them with Gaussian fittings to extract rms beam sizes, then plot vs [math]\sigma_{x,y}[/math] vs [math]k_{1}L[/math]. By Fitting a parabola we can find constants [math]A[/math],[math]B[/math], and [math]C[/math], and get emittances.

Emittance Measurement Using a YaG crystal

In July 2010y, Emittance measurement of HRRL was conducted at Beam Lab, at Physics Department of ISU. I installed a YAG crystal on the HRRL beam line to see electron beam shape. A quadrupole magnet was installed between HRRL gun and the YAG screen. I changed current on the quadrupole to control magnetic field strength of the quadrupole magnet, this changed electron beam shape on the YAG screen.

Experimental Setup

I did quadrupole scan to measure emittance of the electron beam in HRRL. In quadrupole scan method, the strength of the quadrupole magnet was changed by changing the current go through quadrupole coils. The electron beam were coming out of the gun went through quadrupole, then beam would enter a 3-way cross. Two end of the 3-way cross was installed on the beam line. The third end of the 3-way cross was placed upward and there was a actuator installed to it. The YAG crystal was mounted in the actuator, which can put the YAG in the beam line or take it out of the beam line. A camera was placed inside the actuator to look through vacuum a window and to capture the image on the YAG crystal created by electron beam. A Faraday cup was mounted at the end of the beam line to measure the transmission of the charge.

Setup and beam line and are shown in figures 1.2 and 1.3:

Fig.2 Experiment set up of HRRL 2010 July emittance test.

Fig.3 Beam Line of HRRL 2010 July emittance test.

Figures 4, 5, and 6 show Faraday cup, Quadrupole Magnet, and YAG Chrystal used in the test:

Fig.4 Faraday cup used for HRRL 2010 July emittance test.

Fig.5 Quadrupole Magnet used for HRRL 2010 July emittance test.

Fig.6 YAG Christal used for HRRL 2010 July emittance test.

Emittance measurement was carried out on HRRL on July of 2010 under the experimental setup discussed in previous section. In this measurement I used analog camera to take images.

When relativistic electron beam pass through YAG target, Opitcal Transition Radiation (OTR) is produced. OTR are taken for different quadrupole coil current (0-20 A).

Fig. OTR image of 0 Amp quadrupole coil current.	Fig. OTR image of 5 Amp quadrupole coil current.	Fig. OTR image of 10 Amp quadrupole coil current.
Fig. OTR image of 15 Amp quadrupole coil current.	Fig. OTR image of 20 Amp quadrupole coil current.	Fig. OTR image of -10 Amp quadrupole coil current.

Data Analysis

Fig. Gaussian fits for OTR images.

In the mages we can see a bright spot at the center. This spot did not change by changing quad coil current. So, this is image of hot filament. The bigger spot at the right side of the filament was changing by changing quad coil current, hence it is OTR. We also see 10 mm circle mounted on the OTR target, as well as beam hallow.

I did Guassian fits to beam image to extract x, y RMS values for different quad currents. I found out that the camera was rotated slightly. To compensate for it, images were rotated back, and I had beam image upright. To reduce back ground, I just focused on OTR beam image and took out the filament spot from data, as shown in image below.

Results

Fig. Square of RMS beam size [math] \sigma_x^2 [/math] vs. quad strength times quad pole length [math] k_1L [/math] for x projection of electron beam profile

Fig. Square of RMS beam size [math] \sigma_x^2 [/math] vs. quad strength times quad pole length [math] k_1L [/math] for y projection of electron beam profile

[math] \sigma_x^2= (8.05 \pm 0.25) + (4.18 \pm 0.19)k_1L + (0.64 \pm 0.034)(k_1L)^2 [/math]

[math] \epsilon_x = 2.2 \pm 1.3~mm*mrad ~\Rightarrow~ \epsilon_{n,x} = 42.4 \pm 25.4~mm*mrad[/math]

[math] \beta_x=0.72 \pm 0.31, \alpha_x=-1.23 \pm 0.56 [/math]

[math]\sigma_y^2 = (8.52 \pm 0.40) + (-3.88 \pm 0.28)k_1L + (0.57 \pm 0.048)(k_1L)^2 [/math]

[math] \epsilon_y = 2.6 \pm 2.0~mm*mrad ~\Rightarrow~ \epsilon_{n,y} = 50.5 \pm 38.3~mm*mrad[/math]

[math] \beta_y=0.54 \pm 0.22, \alpha_y=2.68 \pm 1.13 [/math]

Emittance Measurements with an OTR

During first emittance measurement, we see our electron beam image at YAG crystal is much bigger than expected. Comparison study shows that for same beam YAG screen shows bigger beam size than Optical Transition Radiation (OTR) screen. Yag is good for low charge beam. Electron beam from HRRL has a big charge in a single pulse and beam size is big.

I did second emittance measurement with 10 [math]\mu m[/math] thick aluminium OTR screen. I also improved our optical imaging system by using better digital camera that can be triggered by the same pulse trigger electron gun. Also I used three 2-inch diameter lenses to focus the lights from OTR to the CCD of the camera.

Experimental Setup

Fig. Simplified setup configuration for HRRL beamline at 2011 March measurement.

The cavity was moved the new location and beam line was built by the design of Dr. Yujong Kim, as shown in figure

Experimental setup is shown in the following figure

I chose one of the quad at a time to do the scan and turned off all the other quads. Optical transition radiation was observed at OTR target. At the end of 0 degree beamline I had a Faraday cup to measure the charge of the beam. Camera cage system was located below the OTR target. There are 3 lenses used to focus lights from target to the CCD camera. Target can be pushed into or taken out of the beamline by the actuator at the top.

OTR Target can be pushed into or taken out of the beamline vertically by the actuator at the top, which is attached to the 6-way cross. This actuator controlled remotely at the control desk.

Camera cage system was located below the OTR target. Cage system attached to the bottom of the 6-way cross. Lower end of cross is a transparent window. There are 3 lenses used to focus lights from target to the CCD camera. They have focal length of 100 mm, 500 mm, and 50 mm.

The lens closest to the OTR target is 10 cm away from the target, an it has 100 mm focal length. This lens was located as close to the target as possible, so that we might collect as much OTR light as possible, and it was thus called collector lens. The lens in the middle has focal length of 500 mm. Moving this lens will change total focal length in a small amount, and this allow us to do fine tuning. Thus, we called this lens fine tuning lens. The last lens, which is furthest from target, and closed to the CCD camera has the shortest focal length of 5o mm. Its short focal length allow us to focus the light on the very small sensing area of the CCD camera.

Fig. HRRL beamline: Optical cage system to focus OTR lights on CCD camera.

Fig. HRRL beamline: Optical lenses lay out for optical cage system.

Experiment with OTR

Optical Transition Radiation (OTR): Transition radiation is emitted when a charge moving at a constant velocity cross a boundary between two materials with different dielectric constant.

Emittance measurement was carried out on HRRL on March of 2011 under the experimental setup discussed in previous section. In this measurement I used JAI digital camera.

When relativistic electron beam pass through Aluminum target OTR is produced. OTR are taken for different quadrupole coil currents.

Fig. OTR image of 0 Amp Q1 coil current.

Fig. OTR image of +1 Amp Q1 coil current.

Fig. OTR image of +2 Amp Q1 coil current.

Data Analysis and Results

The projection of the beam is not Gaussian distribution. So, I fit Super Gaussian fitting <ref name="BeamDisBeyondRMS"> F.-J Decker, “Beam Distributions Beyond RMS”, BIW94, Vancouver,CA,Sep 1994, . </ref>.

I used the MATLAB to analyze the data. The results shows that:

[math] \sigma_x^2= (3.678 \pm 0.022) + (-4.17 \pm 0.22)k_1L + (5.55 \pm 0.42)(k_1L)^2 [/math]

[math] \epsilon_x = 0.417 \pm 0.023~mm*mrad ~\Rightarrow~ \epsilon_{n,x} = 11.43 \pm 0.64~mm*mrad[/math]

[math] \beta_x=1.385 \pm 0.065, \alpha_x=0.97 \pm 0.07 [/math]

[math]\sigma_y^2 = (2.843 \pm 0.044) + (1.02 \pm 0.52)k_1L + (3.8 \pm 1.2)(k_1L)^2 [/math]

[math] \epsilon_y = 0.338 \pm 0.065~mm*mrad ~\Rightarrow~ \epsilon_{n,y} = 9.3 \pm 1.8~mm*mrad[/math]

[math] \beta_y=1.17 \pm 0.19, \alpha_y=0.22 \pm 0.10 [/math]

Data Analysis

Signal extraction

For 3 MeV and on detector show all the steps

1. Raw counts target in and out (calibrated energy)
2. Normalized counts
3. background subtracted
4. Integral (zoomed in and with error)

Example of error propagation for the above

Raw counts target in and out

The ingeral shown in read is from the background is subtracted spectrum.

run in

run out

NaI Left: image with cut

NaI Right: image with cut

3735

3736

Reprate = 300 Hz

Run time = 1002 s

Pulses = 301462

Events = 9045 (Hz)

e+ rate NaI Left = 256 +- 16 (Hz).

Normalized counts

The ingeral shown in read is from the background is subtracted spectrum.

3735 and 3736

Reprate = 300 Hz

Run time = 1002 s

Pulses = 301462

Events = 9045

Total number of electrons in this run = 3.91669e+016 +- 2.25412e+015

Total charge of electrons in this run = 0.00627523 +- 0.000361151 C

e- rate = 3.90887e+013 +- 2.24963e+012 (Hz)

e- current:I_e- =6.26271e-006+-3.6043e-007 (A).

e+ rate = 0.254997 +- 0.0159527 (Hz).

Ne+/Ne-=6.52353e-015+-5.54538e-016.

Ne+/I_e-=0.255 Hz e+ / 6.2627 [math]\mu[/math]A e-

hand calculation of error

[math]R = \frac{N_{e^+}}{N_{e^-}} = \frac{ 0.25 \pm 0.015 Hz}{ (3.90887 \pm 0.224963) \times 10^{13} Hz} = 0.06395 \times 10^{-13} = 6.4 \times 10^{-15}[/math]

[math]R = 18.3 \times 10^{-16}[/math]

[math]\Delta R = \sqrt{\frac { \Delta N_p^{2} }{ N_e^{2} } + (- \frac{ N_p }{ N_e^{2} })^2 \Delta N_e^{2} } = \frac{\sqrt{ \Delta N_p^{2} + \frac{ N_p^{2} }{ N_e^{2} } \Delta N_e^{2} }}{ N_e}[/math]

[math]\Delta R = \frac{\sqrt{ 0.016^{2} + (\frac{ 0.25 }{ 3.909\times 10^{13} } 0.225 \times 10^{13})^{2} }}{ 3.909\times 10^{13}} = \frac{\sqrt{ 0.000256 + 0.000207 }}{ 3.909\times 10^{13}} = \frac{\sqrt{ 0.000463 }}{ 3.909\times 10^{13}} = \frac{0.0215}{ 3.909\times 10^{13}} = 0.0055 \times 10^{-13} = 5.5 \times 10^{-16}[/math]

References

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