\chapter{Conclusions and Suggestions}
A new High Repetition Rate Linac (HRRL) beamline located in ISU's Physics Department beam lab has been successfully reconstructed to produce and transport positrons to the experimental cell. The electron beam energy profile and emittance of the HRRL were measured using a Faraday cup and an OTR based diagnostic system. The positron production rate was measured for positron energies between 1 and 5~MeV.  The results are shown in Figure~\ref{fig:e+2e-exp-sim} along with the prediction made by a GEANT4 simulation of the beamline.

The production of positrons using an electron linac was done in several steps.  First, positrons are emitted from the downstream side of a tungsten target (T1) when electrons impinge on the upstream side and produce photons of sufficient energy to pair produce within the tungsten target. Positrons escaping the downstream side of the target were collected by the quadrupole triplet.  The positrons are then deflected by two dipoles in order to measure the positron rate as a function of the positron energy.  Positrons that traversed the two dipoles would annihilate in a second tungsten target (T2) producing back-to-back 511~keV photons that were measured using two NaI detectors.  The positron rate was measured by requiring a coincidence between both NaI detectors and the electron beam pulse.

The positron beam creation, beam loss in the transportation, and detection process were studied using the simulation package G4beamline and compared to this experiment. 
The simulated e$^+$/e$^-$ ratios are shown in Figure~\ref{fig:e+2e-exp-sim} for the energies measured in this experiment. The simulation includes electron beam generation with the measured electron energy profile, beam losses during transportation, positron annihilation in the tungsten target (T2), and the detection of 511~keV photons in coincidence by the two NaI detectors. While the simulation result agrees with the experiment in that the peak energy distribution is near 3~MeV, it predicts a higher positron to electron ratio as shown in Figure~\ref{fig:e+2e-exp-sim}. 

The simulation was used to study the systematic errors in the experiment.  The simulation predicts that a realistic misalignment of the beamline can reduce the e$^+$/e$^-$ ratios by 20\% to 30\%. In the worst case scenario, the ratios dropped by 60\% to 80\%. The systematic errors in the experiment bring it into agreement with the simulation.


The ratio of the positrons contained within the 90 degree beampipe to the 511~keV photons detected in coincidence mode when the dipoles were set to bend 3~MeV positrons is predicted to be 1655:1 by the simulation. The ratio of the positrons on T2 to the 511~keV photons is 620:1 under the same conditions as above.
The 3~MeV positron rate measured in the experiment was $0.25\pm0.2$~Hz when the HRRL was operated at a 300~Hz repetition rate, 100~mA peak current, and 300~ns (FWHM) RF macro pulse length. 
Based on this simulation, a measured $0.25 \pm 0.02$~Hz coincidence rate by the NaI detectors would correspond to a $155 \pm 12$~Hz positron rate incident on T2.

In the simulation, the number of positrons collected was insensitive to the quadrupole triplet collection field setting (see section 4.5). The ratio of solid angles subtended by the quadrupole (Q4) and dipole (D1) entrance windows approximated the ratios of positron transported.
Quadrupoles focus in one plane and defocus in the other. Thus, one can only collect positrons in one plane while loses occur in the other. Solenoids, on other hand, focus in both planes. A solenoid may be a better option to improve the collection efficiency.
Positioning the target T1 at the entrance of the solenoid may be the optimal choice for capturing positrons. 

%7. Experimental results show quadrupole magnets are not efficient in collecting positrons, since positrons have large angular distribution. Solenoid might be able to improve the collection efficiency of positrons~\cite{kim-bindu-solenoid} and should be placed as close the production target as possible for better efficiency.

\begin{figure}[htbp] 
\includegraphics[scale=0.79]{5-Conclusion/Figures/Overlay_Exp-Sim-Ratio/R.eps}
\caption{Ratio of positrons detected to electrons measured in the experiment (hollow diamond) and simulation (full circle) in coincidence mode. The black solid error bars are statistical and dashed ones are systematic. The systematic errors of experimental measurement are discussed in section 3.4 of Chapter 3 (red dashed lines). The systematics were also studied with simulation (red dashed lines) and described in section 4.6 of Chapter 4.}
\label{fig:e+2e-exp-sim}
\end{figure}
%An OTR based diagnostic tool was designed, constructed, and used to measure the beam emittance of the HRRL. The electron spatial profile measured using the OTR system was not described by a Gaussian distribution but by a super Gaussian or Lorentzian distribution. The unnormalized projected emittances of the HRRL were measured to be less than 0.4~$\mu$m by the OTR based tool using the quadrupole scanning method when accelerating electrons to an energy of 15~MeV. 
%OTR used, Not Gaussian, Changed magnet, measured emittiance