Sadiq Thesis Latex

Chapter 1: Introduction File:Sadiq thesis chapt 1.txt

\chapter{Introduction}

The positron production efficiency using a proposed linac based quadrupole triplet collection system is measured in partnership with the Continuous Electron Beam Accelerator Facility (CEBAF) of Thomas Jefferson National Accelerator Facility (commonly referred to as Jefferson Lab or JLab) and the Idaho Accelerator Center (IAC) of Idaho State University (ISU). There has been substantial interest in developing a polarized positron source for the nuclear physics community~\cite{PolPos}. The main challenge has been increasing the intensity and polarization of the beam. This work investigates a proposed method for collecting positrons using a quadrupole triplet system.

\section{Different Approaches to Produce Positrons} Positrons are used in several disciplines of science, such as chemistry, physics, material science, surface science, biology and nanoscience~\cite{Chemerisov:2009zz}. Positrons may be obtained either from radioactive sources or from pair production of high energy photons. Radioactive sources like Co-58, Na-22, and Cu-64 emit positive beta particles $\beta^{+}$ when they decay. As given in Table~\ref{tab:e+_source}, the positron rate of radioactive sources is about $10^{7} \sim 10^{8}$ e$^{+}$/s because of the source activity limits of 100~mCi~\cite{PosSource1} that are imposed for radiation safety.

Positrons are available for use in experiments at the nuclear reactors~\cite{PosSource2} shown in Table~\ref{tab:e+_source}. Neutrons are used to produce positrons from the photons emitted when neutrons interact with cadmium. Photons pair produce positrons within the tungsten foils positioned in the photon flux. The positron beam created in the nuclear reactor has the intensity shown in Table~\ref{tab:e+_source}.

Another common method used to generate positrons is by using an electron linear accelerator (linac). In this method, electrons, from the linac, incident on a high Z material like tungsten produce positrons by bremsstrahlung and pair production. One of the advantages of the linac based positron beam is its variable energy, intensity, and the ability to pulse the source on and off at specific time intervals as given in Table~\ref{tab:e+_source}.

\begin{table} \centering \caption{Different Positron Sources~\cite{PosSource1,PosSource2}.} \begin{tabular}{llll} \toprule {} & {} & {19:09, 24 December 2013 (MST)$\beta^{+}$ sources} & {} \\ \midrule {Source} & {Activity} & {Rate (e$^{+}$/s)} & {Facility/Source Type} \\ \midrule %{Source} & {Energy Range} & {Intensity} & {Production Method} \\ {Co-58} & {100~mCi} & {$3\times10^{5}$ } & {W-moderator} \\ {Na-22} & {100~mCi} & {$2\times10^{6}$ } & {W-moderator} \\ {Cu-64} & {80~Ci/cm$^2$} &{$10^{7}\sim10^{8}$} & {Brookhaven, reactor beam} \\

\toprule {} & {} & {~~Pair-production} & {} \\ \midrule {Energy } & {} & {Rate (e$^{+}$/s)} & {Facility/Source Type} \\ \midrule {36~MeV} & {} & {$10^{8}$} & {Giessen, LINAC} \\ {100~MeV} & {} & {$10^{10}$} & {Livermore, LINAC} \\ {150~MeV} & {} & {$10^{8}$} & {Oak Ridge, LINAC} \\ {5~keV} & {} & {$5\times10^{6}$} & {NC State University, reactor} \\ \bottomrule \end{tabular} \label{tab:e+_source} \end{table}

\section{Positron Beam Generation from \\ Bremsstrahlung} When a moving charged particle interacts with the electric field of another charged particle, it can be deflected and lose energy in the form of photons, as shown in Figure~\ref{fig:Theo-Brem}. This interaction is known as the bremsstrahlung process. The probability of this interaction increases with the square of the atomic number of the material traversed by the incident charged particle. Figure~\ref{fig:Brems_photon_Ene} shows the photon energy distribution produced when the 12~MeV electron energy distribution from Figure~\ref{fig:Theo-Brems_ele_Ene} interacts with a 1~mm thick tungsten target. As shown in Figure~\ref{fig:Brems_photon_Ene}, the distribution peaks at 0.3~MeV.

\begin{figure}[htbp] \centering \includegraphics[scale=0.40]{1-Introduction/Figures/bremsstrahlung/brems2.eps} \caption{Photon emission from the bremsstrahlung processes.} \label{fig:Theo-Brem} \end{figure}

The bremsstrahlung cross section for the energy range of this experiment given is by~\cite{brms-cors} %\begin{equation} %d \sigma = 4 Z^2r_e^2 \alpha \frac{d \nu}{\nu} \left \{ \left (1 + \left( \frac{E}{E_0} \right )^2 \right ) \left [ \frac{\phi_1(\gamma)}{4} - \frac{1}{3} \ln Z -f(Z)\right ] - \frac{2E}{3E_0} \left [ \frac{\phi_2(\gamma)}{4} - \frac{1}{3} \ln Z -f(Z)\right ] \right \}, %\label{eq:Brem-cross} %\end{equation} \begin{equation} \begin{array}{cl} d\sigma= & 4Z^{2}r_{e}^{2}\alpha\frac{d\nu}{\nu}\{\left(1+\left(\frac{E}{E_{0}}\right)^{2}\right)\left[\frac{\phi_{1}(\gamma)}{4}-\frac{1}{3}\ln Z-f(Z)\right]\\

& -\frac{2E}{3E_{0}}\left[\frac{\phi_{2}(\gamma)}{4}-\frac{1}{3}\ln Z-f(Z)\right]\},

\end{array}

\label{eq:Brem}

\end{equation} \noindent where $E_0$ is initial total energy of the electron, $E$ is the final total energy of the electron, $\nu = \frac{E_0-E}{h}$ is frequency of the emitted photon, and $Z$ is atomic number of the target. $\gamma = \frac{100 m_ec^2 h \nu}{E_0 E Z^{1/3}}$ is the charge screening parameter, and $f(Z)$ is given by \begin{equation} f(Z) = (Z \alpha)^2 \sum_1^{\infty} \frac{1}{ n [ n^2 + (Z \alpha)^2]}, \end{equation} \noindent where $\alpha = \frac{1}{137}$ is the fine-structure constant, $\phi_1$ and $\phi_2$ are screening functions that depend on Z. \begin{figure}[htbp] \centering \includegraphics[scale=0.75]{1-Introduction/Figures/En_photon_dnT1_logY_3.eps} \caption{Bremsstrahlung photon energy distribution produced when the 12~MeV electron energy distribution from Figure~\ref{fig:Theo-Brems_ele_Ene} interacts with the simulation's 1~mm thick tungsten target.} \label{fig:Brems_photon_Ene} \end{figure} \begin{figure}[htbp] \centering \includegraphics[scale=0.75]{1-Introduction/Figures/En_e_upT1.eps} \caption{The electron energy distribution incident on a tungsten foil in simulation.} \label{fig:Theo-Brems_ele_Ene} \end{figure}

There are three competing processes that a photon can undergo when interacting with matter. Figure~\ref{fig:Theo-3pro-in-W} illustrates the cross-sections for the different interactions that can occur when a photon traverses tungsten as a function of photon energy. At electron volt (eV) energies, which are comparable to the electron atomic binding energy, the dominant photon interaction is the photoelectric effect. As the photon energy increases up to the kilo electron volt (keV) range, the Compton scattering process starts to be more dominant. Although the photon is totally absorbed during the photoelectric effect, photons merely lose energy when undergoing Compton scattering. As the photon energy reaches twice the rest mass energy of the electron, $i.e.$ 2 \begin{math} \times \end{math} 511~keV, pair production begins to occur. Pair production becomes the dominant interaction process when photon energies are beyond 5~MeV~\cite{Krane}. In this process, a photon interacts with the electric field of the nucleus or the bound electrons and is converted into an electron and positron pair.

\begin{figure}[htbp] \centering \includegraphics[scale=0.5]{1-Introduction/Figures/xcom/10.eps} \caption{The cross-sections for different types of photon interactions with tungsten as a function of photon energy~\cite{nistxcom}.} \label{fig:Theo-3pro-in-W} \end{figure}

Using natural units, where \begin{math}c \equiv 1\end{math}, the differential cross-section for pair production can be expressed as \begin{equation} \begin{array}{l} \frac{d \sigma}{d \epsilon_1 d \theta_1 d \theta_2} = 8 \left ( \frac{\pi a}{\sinh (\pi a)} \right )^2 \frac{a^2}{2 \pi} \frac{e^2}{\hbar c} \left ( \frac{\hbar}{m_e c }\right )^2 \frac{\epsilon_1 \epsilon_2}{k^3} \theta_1 \theta_2 \\ \\ \times \{ \frac{V^2(x)}{q^4} \left [ k^2 (u^2 + v^2) \xi \eta - 2 \epsilon_1 \epsilon_2 (u^2 \xi^2 + v^2 \eta^2 ) + 2 (\epsilon_1^2 + \epsilon_2^2)uv \xi \eta cos(\phi) \right ] \\ \\ \left . + a^2W^2(x) \xi^2 \eta^2 \left [ k^2(1 - (u^2+v^2)\xi \eta - 2 \epsilon_1 \epsilon_2 (u^2 \xi^2 + v^2 \eta^2) \right . \right .\\ \\ \left . \left .- 2 (\epsilon_1^2 + \epsilon_2^2) u v \xi \eta \cos(\phi)\right ]\right \}, \\ \end{array} \end{equation}

\noindent where $k$ is photon energy, $\theta_{1}$ and $\theta_2$ are the scattering angle of $e^+$ and $e^-$ respectively, $ \phi = \phi_1 - \phi_2$ is the angle between the $e^+$ and $e^-$ pair, $\epsilon_1$ and $\epsilon_2$ are the energy of the positron and electron respectively. Other constants are $u = \epsilon_1 \theta_1$, $v=\epsilon_2 \theta_2$, $\xi = \frac{1}{1+u^2}$, $\eta= \frac{1}{1+v^2}$, $q^2 = u^2 + v^2 + 2 u v \cos(\phi)$, $x= 1-q^2 \xi \eta$, $a = \frac{Ze^2}{\hbar c}$, $V(x) = 1 + \frac{a^2}{(1!)^2} + \frac{a^2 (1+a^2) x^2}{(2!)^2} + \frac{a^2 (1+a^2)(2^2+a^2)x^4 x^2}{(3!)^2} + \cdots$, and $W(x) = \frac{1}{a^2} \frac{d V(x)}{d x}$.

In pair production, positron and electron pairs are created back to back in the center of mass frame as given by \begin{equation} \gamma \rightarrow e^{+}+e^{-}. \label{eq:pair} \end{equation} In the lab frame, electrons and positrons tend to move in the direction of the photon, as shown in Figure~\ref{fig:Theo-pair-pro}. The positron and electron carry away the energy from the photon that is in excess of 1.022~MeV. In the center of mass frame, the kinetic energy is equally shared. Photons with an energy above 1.022~MeV in the bremsstrahlung spectrum of Figure~\ref{fig:Brems_photon_Ene} have the potential to create electron and positron pairs. Figure~\ref{fig:Theo-brem} is the simulation of 10 million 12~MeV mono energetic electrons impinging on a 1.016~mm thick tungsten target. Turning on the annihilation process resulted in a 511~keV peak on top of the bremsstrahlung spectrum. This 511~keV peak represents photons produced when the created positrons from the pair production annihilate with atomic electrons inside the tungsten target.

\begin{figure}[htbp] \centering \includegraphics[scale=0.40]{1-Introduction/Figures/Pair_Production/Pair_Production.eps} \caption{Pair production.} \label{fig:Theo-pair-pro} \end{figure} \begin{figure}[htbp] \centering \includegraphics[scale=0.7]{1-Introduction/Figures/pair/on/Eng3.eps} \\ \caption{Photon spectrum created by one million 12~MeV mono energy electrons impinging on a 1.016~mm thick tungsten target.} \label{fig:Theo-brem} \end{figure}

\section{Generation of Electron Beam Using a \\ Linac} Electrons need to be accelerated, using a linac (linear particle accelerator), up to at lest few mega electron volts (MeV) in order to generate bremsstrahlung photons with enough energy to produce electron and positron pairs. A linac is a device that accelerates charged particles to nearly the speed of light using an electromagnetic wave. The HRRL (High Repetition Rate Linac), located in the Beam Lab of ISU's Physics Department, can accelerate electrons up to 16~MeV peak energy, which is sufficient energy for positron production.

To optimize positron production, one needs to know the beam size and divergence of the electrons impinging the production target. The emittance and the Twiss parameters ($\alpha$, $\beta$, and $\gamma$) quantify these beam properties and are used as the input parameters for accelerator simulation tools. These tools can study beam transport and predict beam properties (beam size and divergence) along the beam line.

\subsection{Emittance and Twiss Parameters} In accelerator physics, a Cartesian coordinate system is used to describe the motion of the accelerated particles. As shown in Figure~\ref{fig:coordinates}, the $s$-axis of the Cartesian coordinate system is defined as the natural coordinate that is oriented along the same direction as the beam momentum. The $x$-axis and $y$-axis are horizontal and vertical coordinates which constitute the transverse beam profile. The transverse beam profiles are described as a function of the longitudinal coordinates, $x(s)$ and $y(s)$.

\begin{figure}[htbp] \centering \includegraphics[scale=0.7]{1-Introduction/Figures/coordinates.eps} \caption{Coordinated system and reference orbit (dashed line)~\cite{Conte}.} \label{fig:coordinates} \end{figure}

The horizontal phase space $x'$ vs. $x$ (similar for $y$ projection), shown in Figure~\ref{fig:phase-space}, of the beam is an ellipse with invariant area along the beamline (under conditions that space charge effects, coherent synchrotron radiation, and wakefield are ignorable)~\cite{Conte}. Here $x'$ is defined as \begin{equation} x'=\frac{dx}{ds}. \label{eq:divergence} \end{equation} \noindent The area of the ellipse is \begin{equation} A = \pi w = \pi (\gamma z^2 + 2\alpha z z^{\prime} + \beta z^{\prime 2}). \label{eq:el-area} \end{equation} \noindent Here $w$ is called the Courant-Snyder invariant~\cite{Conte} and $\alpha$, $\beta$, and $\gamma$ are called Twiss parameters. The transverse emittance $\epsilon$ of the beam is defined to be the area of the ellipse that contains fraction of the particles. The units for the emittance are m$\cdot$rad and mm$\cdot$mrad. Conventionally used unit for emittance is $\mu$m, which is similar as mm$\cdot$mrad (1 $\mu$m = 1 mm$\cdot$mrad = $10^{-6}$ m$\cdot$rad). Twiss parameters are useful because they are related to the beam size and divergence by \begin{equation} \sigma_{x}(s)=\sqrt{\epsilon _x (s) \beta _x (s)},~ \sigma_{x'}(s)=\sqrt{\epsilon _x (s) \gamma _x (s)}, \label{eq:twiss-emit} \end{equation} \noindent where $\epsilon_{x}$ is beam's horizontal emittance, $\sigma_{x}$ is the horizontal rms beamsize, $\sigma_{x'}$ is the horizontal rms beam divergence, and $\beta _x $ and $\gamma _x$ are two of the three Twiss parameters (same for vertical projection). The Twiss parameters are related by \begin{equation} \gamma = \frac{1 + \alpha^2}{\beta}. %\text{ or } \beta _x (s) \gamma _x (s) - \alpha _x (s)^2 = 1. \label{eq:twiss} \end{equation} \begin{figure}[htbp] \centering \includegraphics[scale=0.5]{1-Introduction/Figures/Emttance_Ellipse.eps} \caption{Phase space ellipse and its relation to the emittance and the Twiss parameters $\alpha$,$\beta$, and $\gamma$~\cite{Conte}.} \label{fig:phase-space} \end{figure} The beam emittance is inversely proportional to the beam energy. As the electron beam gains energy during acceleration, the divergence of the beam decreases because the momentum increases in forward direction. This emittance decrease due to the energy gain is called adiabatic damping. Thus, it is more practical to use normalized emittance which is defined as \begin{equation} \epsilon_{\text{n}} = \beta\gamma\epsilon, \label{eq:nor_emi} \end{equation} where $\beta$ is $c/v$, $\gamma$ is relativistic (Lorentz) factor, and $\epsilon$ unnormalized emittance.

In this chapter, the possible ways to generate positrons were described. Positrons from radioactive sources have lower intensities due to safety limits placed on the source activity. Positrons from reactors have intensities comparable to radioactive sources but are low in energy. Generating positrons using a linac can produce higher energy positrons at higher fluxes than reactors.

Chapter 2 discusses the hardware used in this experiment and the tools used to measure emittance, Twiss parameter, and energy of the HRRL. The measured emittance, Twiss parameter and energy, as well as the positron production efficiency are discussed in the Chapter 3. The simulation of the positron production efficiency and transportation process are compared with measurement in Chapter 4. The conclusion from this work is presented in Chapter 5.

Chapter 2: Apparatus File:Sadiq thesis chapt 2.txt

\chapter{Apparatus} This chapter describes the apparatus and associated hardware used in the experiment to produce positrons as described in Chapter 1. The new HRRL beamline was constructed using two dipoles as well as ten quadrupoles to optimize the beam transportation. Beamline elements were aligned using a laser alignment system. Additional beamline elements such as an energy slit, beam viewers, and Faraday cups were added. Two NaI detectors were installed at the end of the beamline and were used to detect 511~keV photons emitted when positrons annihilate in a second tungsten target.

\section{HRRL Beamline} A 16~MeV S-band (2856~MHz RF frequency) standing-wave High Repetition Rate Linac (HRRL) located in the Department of Physics Beam Lab at Idaho State University was used to impinge a 12~MeV electron beam onto a tungsten foil. The energy of the HRRL is tunable between 3 to 16~MeV and its repetition rate is variable from 1 to 300~Hz. The operating parameters of the HRRL is given in Table~\ref{tab:hrrl-par}. As shown in Figure~\ref{fig:app-hrrl-cavity}, the HRRL has a thermionic gun, vertical and horizontal steering magnet sets on two ends, and two solenoid magnets. The startup, shutdown, and beam optimization procedure of the HRRL is given in the Appendix C.

\begin{table} \centering \caption{The Basic Parameters of the HRRL.} \begin{tabular}{lcc} \toprule {Parameter} & {Unit} & {Value} \\ \midrule maximum energy & MeV & 16 \\ peak current & mA & 100 \\ repetition rate & Hz & 300 \\ absolute energy spread & MeV & 25\% \\ macro pulse length & ns & $>$50 \\ RF Frequency & MHz & 2856 \\ \bottomrule \end{tabular} \label{tab:hrrl-par} \end{table}

\begin{figure}[htbp] \centering \includegraphics[scale=0.74]{2-Apparatus/Figures/HRRL_Cavity4.png} \caption{The configuration of the HRRL cavity.} \label{fig:app-hrrl-cavity} \end{figure}

The accelerator's cavity was relocated to the position shown in Figure~\ref{fig:app-hrrl-line} to provide enough space for a beam line that can transport either positrons or electrons. The beam elements are described in Table~\ref{tab:app-hrrl-coordinates}. Quadrupole and dipole magnets were added to the new beam line as well as diagnostic tools like an OTR and YAG screens (see Appendix D for magnetic field map of dipoles and quadrupoles and for more details). Faraday cups and toroids were installed to measure the electron beam size and the current. Energy slits were installed to control the energy/momentum spread of the beam after the first dipole.

A 1.016~mm thick retractable tungsten (99.95\%) foil target (T1) was placed between the 1st and 2nd quadrupole triplets and used to produce positrons when the electron beam interacts with it. The room where the HRRL is located is divided by a wall into two parts; the accelerator side and the experimental cell. A beam pipe at the end of the 90 degree beamline goes through a hole in the wall and delivers the beam from the accelerator side to the experimental cell. The positron detection system consisting of two NaI detectors was placed at the end of the beamline in the experimental cell side as shown in Figure~\ref{fig:app-hrrl-line}.

\begin{sidewaysfigure} \centering \includegraphics[scale=0.265]{2-Apparatus/Figures/HRRL_line2.eps} \caption{The HRRL beamline layout and parts.} \label{fig:app-hrrl-line} \end{sidewaysfigure}

\begin{table} \centering \caption{The HRRL Beamline Parts and Coordinates.} \begin{tabular}{llll} \toprule {Label} & {Beamline Element} & {Distance from} & {} \\ {} & {} & {Linac Exit (mm)} & \\ \midrule Q1 & quadrupole & 335 & \\ Q2 & quadrupole & 575 & \\ Q3 & quadrupole & 813 & \\ T1 & e$^+$ production target & 1204 & \\ Q4 & quadrupole & 1763 & \\ Q5 & quadrupole & 2013 & \\ Q6 & quadrupole & 2250 & \\ D1 & dipole & 2680 & \\ S1 & OTR screen & 3570 & \\ FC1 & Faraday cup & 3740 & \\ EnS & energy slit & 3050 & \\ S2 & YAG screen & 3410 & \\ Q7 & quadrupole & 3275 & \\ D2 & dipole & 3842 & \\ FC2 & Faraday cup & 4142 & \\ Q8 & quadrupole & 4044 & \\ Q9 & quadrupole & 4281 & \\ Q10 & quadrupole & 4571 & \\ T2 & annihilation target & 7381 & \\ \bottomrule \end{tabular} \label{tab:app-hrrl-coordinates} \end{table} The positron production target, T1 were shielded with 8 inches of Fe bricks and 4 inches of Pb bricks to lower photon and electron background. The two dipoles were also shielded with Pb bricks because the beam is scraping the dipoles when they were bent. There were also 8 inches of Pb bricks on the both side of the wall to shield the background from the accelerator side. The NaI detectors were placed at the experimental cell side would lower the background because of the larger distance from T1. The NaI detectors were shielded with Pb brick house, to lower background, which took big space that wasn't available in the experimental cell side. However, lowering background by distancing the NaI detectors from T1 would also decrease positron rates detectable as well. The signal to noise ratio should increase, because the most photons and electrons were shielded from the detection system while positrons were collected and transported to T2.

\section{HRRL Beamline Alignment Using Laser} The HRRL beamline was aligned using a laser beam as shown in Figure~\ref{fig:alignment}. The gun of the HRRL was removed so that the laser beam from a laser placed on a table in the experimental side of the HRRL cell would be directed into the cavity. The mirrors were mounted to the holders with horizontal and vertical adjustments. The laser was first adjust with two mirrors on the laser table and focused two focusing lenses. Two mirrors one in the experimental side one at the side of the linac reflected beam to the center of the linac.

\begin{figure}[htbp] \centering \includegraphics[scale=0.24]{2-Apparatus/Figures/HRRL_Alignment.png} \caption{HRRL beamline alignment using laser.} \label{fig:alignment} \end{figure}

The laser beam was shot through the center of the HRRL cavity and the geometrical center of the 0 degree beamline magnets (quadrupoles Q1$\sim$Q6, first dipole D1) downstream were aligned according to the laser beam. The laser beam was reflected by a mirror mounted on a rotator that reflected the beam by 90$^{\circ}$ to the 90 degree beamline and the quadrupole magnets in the 90 degree beamline was aligned according to it.

Two irises were placed at the end of the 90 degree beamline and aligned to the reflected 90 degree laser beam. Second laser was mounted on the wall in the experimental cell side. The laser on the wall tuned to pass through the center of the two irises placed at the end of the 90 degree beamline. Thus, the laser on the wall was aligned to the center of the 90 degree beamline and can be used as a reference as shown in Figure~\ref{fig:laser}. \begin{figure}[htbp] \centering \includegraphics[scale=0.23]{2-Apparatus/Figures/BeamlineParts/laser.jpg} \caption{The laser mounted on the wall in experimental cell side. This laser was aligned to the center of the 90 degree beamline.} \label{fig:laser} \end{figure}

At last, the second dipole, D2, was connected to the 90 degree beampipe and beamline elements between D1 and D2 (energy slits, Q7, and 5-way cross holds YAG screen) were placed one after another.

\section{Energy Slit and Flag Controller} A controller box was built to open or close the energy slit and to control three flags as shown Figure~\ref{fig:controller}. The slit control is on the right side of the box and the maximum width of the slit is 3.47~cm as shown in Figure~\ref{fig:controller}. On the left of the controller are the switches for three flags. Power supplies were installed inside the box and controlled by these switches to remove the targets from the beamline, turn on/off the cameras of the flags, and turn on/off the lights of the flag.

\subsection{Energy Slit Controller} The controller was built to open or close the energy slit (Danfysik water cooled slit model 563 system 5000) based on the design from Danfysik~\cite{Danfysik} as shown in Figure~\ref{fig:controller} (on right side). The wiring diagram of the controller is shown in Figure~\ref{fig:controllerConnection}. When the energy slit is fully open, the width between slits is 3.47~cm as indicated by the LED number display. When the slit is fully open/closed, one of the two LED light will light up and the motor will stop.

The power source of the energy slit provides 12~VDC, 1.8~A max current, 20~W power, and takes 85$\sim$264~VAC input. The motor and the relay switch both takes 12~VDC. The LED indicating lights take 12~V/50~mA current and the 57~$\Omega$ resistors take 0.5~W power.

A potentiometer is placed inside the energy slit and the resistance of the potentiometer changes as the width of the slit. A 370~mV voltage is applied to the potentiometer. The LED number display is connected to the potentiometer so that the voltage change in the potentiometer is indicated by the LED display. The slit width is indicated by the potentiometer resistance in the circuit.The potentiometer resistance in the circuit is indicated by the voltage across the resistor in the circuit which displayed on the LED number display. For example, when the width of the energy slit is 3.24~cm, the voltage on the potentiometer read by the LED display is 324~mV, and the LED number display indicates 3.24. The cm unit is labeled on the right of LED display. \begin{figure}[htbp] \centering \includegraphics[scale=0.29]{2-Apparatus/Figures/BeamlineParts/controller.jpg} \caption{Front panel of the energy slit controller (on the right) and flag controllers (on the left). } \label{fig:controller} \end{figure} \begin{figure}[htbp] \centering \includegraphics[scale=0.43]{2-Apparatus/Figures/controllerConnection.png} \caption{Controller wiring diagram of energy slit controller (modified from the design given in the Danfysik water cooled slit model 563 system 5000 manual)~\cite{Danfysik}.} \label{fig:controllerConnection} \end{figure}

\subsection{Flag Controller} On the left of the controller box are the switches for three flags (0 degree/OTR flag, 45 degree/YAG flag, and 90 degree/annihilation target flag) as shown in Figure~\ref{fig:controller}. Fours power supplies (one back up) were installed inside the box and controlled by these switches. The switches in the top row insert or remove the targets from the beamline and the ones in the middle turn on/off the cameras of the flags. The bottom row switches turn on/off the lights of the flag which lights up the target.

\section{The OTR Imaging System} The OTR target is a 10~$\mu$m thick aluminum foil with a 1.25 inch diameter. Moving charged particle carries the electromagnetic fields that are dependent on the dielectric constant of the media. When a moving charge particle cross the boundary of two medium (vacuum and aluminum in this case), the electromagnetic radiation is emitted to reorganize the fields in the new media. The radiation is emitted in both forward (beam direction) and backward (image charge direction) as shown in Figure~\ref{fig:otr}. \begin{figure}[htbp] \centering \includegraphics[scale=0.6]{2-Apparatus/Figures/OTR.eps} \caption{OTR pattern when the incident beam is at $45^{\circ}$ angle with respect to the foil~\cite{OTR-Gitter}.} \label{fig:otr} \end{figure}

Three two inch diameter lenses were used for the imaging system to avoid optical distortion at lower electron energies. The focal lengths and positions of the lenses, shown in Figure~\ref{image_sys}, were calculated with thin lens equation and magnification of the image. The lenses, assembly rods, and lens holder plates for the camera cage system were purchased from Thorlabs, Inc.~\cite{thorlabs}.

The camera used is a JAI CV-A10GE digital 1/2" progressive scan camera with a 767 (horizontal) by 576 (vertical) pixel area and 6.49 (horizontal) by 4.83 (vertical) mm sensing area. It has high speed shutter from 1/60 to 1/300,000 second, edge pre-select, pulse width trigger modes, auto shutter, and smear-less mode. The images were taken by triggering the camera (in edge pre-select mode) synchronously with the electron gun. \begin{figure}[htbp] \centering {\scalebox{0.46} [0.46]{\includegraphics{2-Apparatus/image_sys2.eps}}} {\scalebox{0.5} [0.5]{\includegraphics{2-Apparatus/MOPPR087f3}}} \caption{The OTR imaging system.} \label{image_sys} \end{figure}

\section{Positron Detection} When the electron beam is incident on T1, photons and secondary electrons are created along with positrons. These particles are the main source of noise in the experiment. The positrons were transported to the second tungsten target (T2) which was shielded from this background by the concrete wall and Pb bricks. The setup is shown in Figure~\ref{fig:HRRL-pos-det-setup}. A 6-way cross was placed at the end of the beamline to hold T2. The 6-way cross has three 1~mil (0.0254 millimeters) thick stainless steel windows. The two horizontal windows perpendicular to the beamline allowed the 511~keV photons created from the positron annihilation to escape the beamline with a limited attenuation. A third window at the end of the 90 degree beamline was used as the beam exit. Two NaI detectors were placed facing the two exit windows to detect the photons produced in T2. A 2 inch thick lead brick collimator with a 2 inch diameter hole was placed between the exit window and NaI detector. A scintillator (Scint) and a Faraday cup (FC3) were placed at the end of the beamline and were used to tune the electron and positron beam. When positrons reach T2, they can thermalize and annihilate inside T2. During thermalization, a positron loses its kinetic energy. When it annihilates with an electron, two 511~keV photons are emitted back to back. A triplet coincidence is required between the accelerator RF pulse and the detection of a photon in each NaI detector.

\begin{figure}[htbp] \centering \includegraphics[scale=0.50]{2-Apparatus/HRRL_Pos_detection2.eps} \caption{The positron detection system: T2 was placed with 45$^\circ$ angle to the horizontal plane first, then rotated 45$^\circ$ along the vertical axis.} \label{fig:HRRL-pos-det-setup} \end{figure}

\subsection{NaI Detectors}

NaI crystals, shown in Figure~\ref{fig:PMT}, were used to detect 511~keV photons from positron annihilation. Originally, the detectors had pulse signal lengths around 400~$\mu$s. New PMT base were built to use the HV divider shown in Figure~\ref{fig:PMT_base}. A picture of the constructed bases is shown in Figure~\ref{fig:new_base_made}. The pulse length of the new PMT base is about 1~$\mu$s. The NaI crystal is from Saint-Gobain Crystal \& Detectors (Mod. 3M3/3) with a dimension of $3 \times 3$. Operating high voltage of -1150~V would position the 511~keV photons within the range of the charge sensing ADC (CAEN Mod. V792).

\begin{table} \centering \caption{The Radioactive Sources and Corresponding Photon Peaks.} \begin{tabular}{lccc} \toprule {Radioactive Sources} & Unit & First Peak & Second Peak \\ \midrule Co-60 & keV & 1173 & 1332 \\ Na-22 & keV & 511 & 1275 \\ \bottomrule \end{tabular} \label{tab:Na22_Co60} \end{table}

\begin{figure}[htbp] 
\centering
\includegraphics[scale=0.52]{2-Apparatus/SAINT-GOBAIN_3M33.png}
\caption{The NaI crystal dimension.}
\label{fig:PMT}
\end{figure}

\begin{figure}[htbp] \centering \includegraphics[scale=0.75]{2-Apparatus/Modified_PMT.png} \caption{The modified PMT base design.} \label{fig:PMT_base} \end{figure}

\begin{figure}[htbp] \centering \includegraphics[scale=0.13]{2-Apparatus/IAC_NaI.png} \caption{The NaI crystals and new bases.} \label{fig:new_base_made} \end{figure}

The NaI detectors were calibrated using a Na-22 and a Co-60 source with the photon peaks indicated in Table~\ref{tab:Na22_Co60}. Figure~\ref{fig:NaI_Co60_Scope} is the oscilloscope image of several Co-60 photon pulses observed by the detector with the new PMT. The calibrated NaI detector spectrum from the Na-22 and Co-60 sources is shown in Figure~\ref{fig:NaI-Calb}. The rms values of the fits on the four peaks shown in Figure~\ref{fig:NaI-Calb} are $\sigma_{Na, 511}=18.28\pm0.04$~keV, $\sigma_{Na, 1275}=44.51\pm0.27$~keV, $\sigma_{Co, 1173}=42.49\pm0.24$~keV, and $\sigma_{Co, 1332}=50.30\pm0.39$~keV.

\begin{figure}[htbp] \centering \includegraphics[scale=0.5]{2-Apparatus/NaI_Co60_Scope.png} \caption{Detector output pulses using the Co-60 source and new PMT. The amplitude of the pulse is about 60~mV. The rise time of the pulse is larger than 50~ns, and the fall time is larger than 700~ns.} \label{fig:NaI_Co60_Scope} \end{figure}

\begin{figure}[htbp] \centering \includegraphics[scale=0.77]{2-Apparatus/Figures/NaI_Calbration/NaI_Calb8.eps} \caption{The calibrated NaI spectrum of Na-22 and Co-60 sources.} \label{fig:NaI-Calb} \end{figure}

\subsection{The DAQ Setup}

The data acquisition (DAQ) setup and timing diagram is shown in Figure~\ref{fig:daq-setup}. The last dynode signals from left and right NaI detectors were inverted using a ORTEC 474 inverting amplifier and sent to a CAEN Mod. N842 constant fraction discriminator (CFD). An electron gun pulse generated a VETO sent to the CFD which prevented the RF noise from triggering the CFD, otherwise the CFD would generate multiple digital pulses for a single signal received. A GG~8000-01 octal gate generator was used to create a single 1~$\mu$s wide pulse from the first pulse in order to ignore the multiple CFD pulses produced by a single analog output pulse from the detector. A triple coincidence was formed between the gun pulse and the 1~$\mu$s wide pulse from each detector using a LeCroy model 622 logic module. %\begin{equation} %\text{NaI~Left~\&\&~NaI~Right~\&\&~Gun~Trigger}. %\end{equation}

The ADC requires 5.7~$\mu$s to convert the analog signal to a digital signal. The logic module output was delayed 6~$\mu$s by a dual timer (CAEN Mod. N93B) to accommodate the ADC's conversion time and trigger the DAQ. The ADC (CAEN Mod. V792) converted the NaI detector's analog signals to digital when a 1~$\mu$s gate, created by the gun pulse using a dual timer, was present as shown in the lower part of Figure~\ref{fig:daq-setup}. The ADC was fast cleared unless it received a veto signal from the inverted output of logic module created using a dual timer.

\begin{sidewaysfigure}[htbp] \centering \includegraphics[scale=0.8]{2-Apparatus/Figures/DAQ_Logic_all.eps} \caption{The DAQ setup and timing diagram.} \label{fig:daq-setup} \end{sidewaysfigure}

Chapter 5: Conclusion File:Sadiq thesis chapt 5.txt

pdf file: File:Sadiq hesis Latex.pdf