\chapter{Apparatus} This chapter describes the apparatus and hardwares 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. The beamline elements like 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. \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} %When there is a trigger in the ADC, the data in the ADC is read