IPAC 2012

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\begin{document} \title{TRANSVERSE BEAM EMITTANCE MEASUREMENTS OF\\A 16 MeV LINAC AT THE IDAHO ACCELERATOR CENTER (IAC)} %\title{TRANSVERSE BEAM EMITTANCE MEASUREMENTS OF A 16 MeV LINAC AT THE IAC\thanks{ Work supported by ...}}

\author{S. Setiniyaz, K. Chouffani, T. Forest, Y. Kim\\ 

move the names C. O'Neill, C. F. Eckman, and D. Wells to an acknowledgement section

Idaho State University, Pocatello, ID, 83209, USA\\ A. Freyberger, Jefferson Lab, Newport News, Virginia, 23606, USA}

\maketitle

\begin{abstract} A beam emittance measurement of a 16 MeV S-band High Repetition Rate Linac (HRRL) was performed at Idaho State University's Idaho Accelerator Center (IAC). The HRRL is one of several low energy accelerators operating at the IAC. Originally, the linac structure of the HRRL was similar to that used by a typical medical linac. Its RF system was upgraded to facilitate a maximum repetition rate of 1 kHz. The transverse beam emittance of the HRRL is currently underway to optimize the production of positrons using an intense electron beam on a tungsten converter. In this paper we describe a beam imaging system based on an OTR screen and a digital CCD camera, a MATLAB tool to extract beamsize and emittance, detailed measurement procedures, and the results of measured transverse emittances for an arbitrary beam energy. The HRRL beam line is being reconfigured into an achromat to be used as a positron source. \end{abstract}

\section{Introduction}

The HRRL is an S-band electron linac located in the Beam Lab of the Physics Department at Idaho State University (ISU). It is one of the fifteen low energy linacs operated by the IAC. The HRRL accelerates electrons to energies between 3 and 16~MeV with a maximum repetition rate of 1 kHz. The HRRL beamline has recently been reconfigured to generate and collect positrons. More detailed operational parameters on HRRL are summarized in Table~\ref{tab:hrrl}.

An Optical Transition Radiation (OTR) based viewer was installed to allow measurements at the high electron currents available using the HRRL. The visible light from the OTR based viewer is produced when a relativistic electron beam crosses the boundary of two mediums with different dielectric constants. Photons are emitted along the direction of the incident electron beam and in the opposite direction~\cite{OTR}. When the electron beam intersects the OTR target at a 45${^\circ}$ angle, visible radiation is emitted at an angle of 90${^\circ}$ with respect to the incident beam direction~\cite{OTR2}. These backward-emitted photons are observed using a digital camera and can measure the shape and intensity of the beam based on the OTR image distribution.

Emittance is a key parameter in accelerator physics which is used to quantify the quality of an electron beam produced by an accelerator. An emittance measurement can be performed in a several ways~\cite{emit-ways, sole-scan-Kim}. This work used the Quadrupole scanning method~\cite{quad-scan} was used to measure emittance, Twiss parameters, and energy of the beam.

\begin{table}[hbt] 

  \centering
  \caption{Operational Parameters of HRRL Linac.}
  \begin{tabular}{lccc}
      \toprule
      Parameter     & Unit   & Value \\ 
      \midrule
       maximum electron beam energy $E$   &  MeV     &  16   \\
       \midrule
       electron beam peak current $I_{\textnormal{peak}}$ &  mA      &  80     \\
       \midrule
       macro-pulse repetition rate                   &   Hz       &  1000  \\
       \midrule
       macro-pulse pulse length (FWHM)          &   ns       &  250    \\
       \midrule
       rms energy spread                                &  \%      &   4.23   \\
 \bottomrule

\end{tabular} \label{tab:hrrl} \end{table}

\section{The experiment}

\subsection{Theory of Quadrupole Scanning Method}

As shown in Fig.~\ref{q-scan-layout} illustrates the basic components used to measure the emittance with the quadrupole scanning method. The quadrupole is positioned at the exit of the linac in order focusing or de-focusing the beam observed to a view screen located downstream. The quadrupole and the screen are located far away to minimize chromatic effects and the veracity of the thin lens approximation used to cacluate beam optics.

\begin{figure}[htb] \centering 

 \includegraphics[scale=0.40]{quad_scan_setup.eps}

\caption{Layout for quadrupole scanning method.} \label{q-scan-layout} \end{figure}

Assuming thin lens approximation, $\sqrt{k_1}L << 1$, is satisfied, the transfer matrix of a quadrupole magnet may be expressed as % thin lens approximation (sqrt{k1}*L << 1). In our case sqrt{k1}*L =0.07 \begin{equation} \label{quad-trans-matrix} \mathrm{\mathbf{Q}}=\Bigl(\begin{array}{cc} 1 & 0\\ -k_{1}L & 1 \end{array}\Bigr)=\Bigl(\begin{array}{cc} 1 & 0\\ -\frac{1}{f} & 1 \end{array}\Bigr), \end{equation} where $k_{1}$ is the quadrupole strength, $L$ is the length of quadrupole, and $f$ is the focal length. A matrix representing the drift space between quadrupole and screen is given by \begin{equation} \label{drift-trans-matrix} \mathbf{\mathbf{S}}=\Bigl(\begin{array}{cc} 1 & l\\ 0 & 1 \end{array}\Bigr), \end{equation} where $l$ is the distance between the scanning quadrupole and the screen. The transfer matrix of the scanning region is given by \begin{equation} \mathbf{\mathbf{M}}=\mathrm{\mathbf{SQ}} =\Bigl(\begin{array}{cc} m_{11} & m_{12}\\ m_{21} & m_{22} \end{array}\Bigr). \end{equation} For a horizontal plane, the beam matrix at the screen ($\mathbf{\sigma_{s}}$) is related to the beam matrix of the quadrupole ($\mathbf{\sigma_{q}}$) a similarity transformation \begin{equation} \mathbf{\mathbf{\sigma_{s}=M\mathrm{\mathbf{\mathbf{\sigma_{q}}}}}M}^{\mathrm{T}} \end{equation} where the $\mathbf{\sigma_{s}}$ is defined as~\cite{SYLee}\\

\begin{equation} \mathbf{\mathbf{\sigma_{s,\mathnormal{x}}=}}\Bigl(\begin{array}{cc} \sigma_{\textnormal{s},x}^{2} & \sigma_{\textnormal{s},xx'}\\ \sigma_{\textnormal{s},xx'} & \sigma_{\textnormal{s},x'}^{2} \end{array}\Bigr), \end{equation}

\begin{equation} \mathbf{\mathbf{\sigma_{q,\mathnormal{x}}}}=\Bigl(\begin{array}{cc} \sigma_{\textnormal{q},x}^{2} & \sigma_{\textnormal{q},xx'}\\ \sigma_{\textnormal{q},xx'} & \sigma_{\textnormal{q},x'}^{2} \end{array}\Bigr). \end{equation}

\noindent By defining the new parameters~\cite{quad-scan}, \begin{equation} A \equiv \sigma_{11},~B \equiv \frac{\sigma_{12}}{\sigma_{11}},~C \equiv \frac{\epsilon_{x}^{2}}{\sigma_{11}} \end{equation} the matrix element will describe the square of the beam size at the screen. As a result, $\sigma_{\textnormal{s},x}^{2}$ becomes a parabolic function of the product of $k_1$ and $L$ \begin{equation} \sigma_{\textnormal{s},x}^{2}=A(k_{1}L)^{2}-2AB(k_{1}L)+(C+AB^{2}) \label{q_scan_layout} \end{equation}

The emittance measurement was performed by changing the quadrupole current, $k_{1}L$, and measureing the corresponding beam image on the view screen. The measured two-dimensional beam image was projected along the images abscissa and ordinate axes. A Gaussian fitting function is used on each projection to determine the rms value, $\sigma_{s,x}$ in Eq.~(\ref{q_scan_layout}), of the image along each axis. Measurements of $\sigma_{s,x}$ for several quadrupole current ($k_{1}L$) is then fit using the parabolic funct in Eq.~(\ref{q_scan_layout} to determinethe constants $A$, $B$, and $C$. The emittance ($\epsilon$) and the Twiss parameters ($\alpha$ and $\beta$) can be found using Eq.~(\ref{emit-relation}). \begin{equation} \epsilon=\sqrt{AC},~\beta=\sqrt{\frac{A}{C}},~\alpha=-B\sqrt{\frac{A}{C}} \label{emit-relation} \end{equation}

\subsection{The OTR Imaging System} The OTR target is a 10 $\mu$m thick aluminum circular disk with a 1.25 inch diameter. The OTR is emitted in a cone with the maximum intensity at the angle $1/\gamma$ with respect to the reflecting angle of the electron beam~\cite{OTR}. Three 2 inches diameter lenses are used to focus the OTR onto a digital camera. Focal lengths and position of the lenses are shown in Fig.~\ref{image_sys}.

\begin{figure} \begin{tabular}{lr} {\scalebox{0.25} [0.25]{\includegraphics{image_sys.eps}}} {\scalebox{0.3} [0.30]{\includegraphics{imaging_sys}}} \end{tabular} \caption{Square of rms and parabolic fitting for x-projection.} \label{image_sys} \end{figure}

\subsection{Quadrupole Scanning} The current for one of the beam line quadrupoles is changed to alter the strength and direction of the quadrupole magnetic field over a finite range to produce measurable change in the beam shape as seen by the OTR system. Initially, the beam was steered by the quadrupole indicating that the beam was entering along the quadrupoles central axis. Several magnetic elements upstream of this quadrupole were adjusted to align the incident electron beam with the quadrupoles central axis. First, the beam current observed by a Faraday cup located at the end of beam line was maximized using steering coils within the linac. Second, the first solenoid nearest the linac gun was used to focus the electron beam on the OTR screen. Steering coils were adjusted to maximum the beam current to the FC and minimize the deflection of the beam by the quadrupole. A second solenoid and the last steering magnets, both near the exit of the linac, were used in the final step to optimize the beam spot size on the OTR target and maximum current the Faraday cup. A configuration was found that minimized the electron beam deflection when the quadrupole current was altered during the emittance measurements.

The emittance measurement was performed using an electron beam energy of approximately 14~MeV beam and a 40~mA macro pulse peak current. The current in the first quadrupole after the exit of the linac was changed from -5~A to 5~A with an increment of 0.2~A. Seven measurement were taken at each current step in order to determine the average beam width and the variance. Background measurements were taken by turning the linac's electron gun off while keep the RF on. Background image and beam images before and after background subtraction are shown in Fig.~\ref{bg}. A small dark current is visible in Fig.~\ref{bg}b that is known to be generated when electrons are pulled off the cavity wall and accelerated.

\begin{figure} \begin{tabular}{ccc} \centerline{\scalebox{0.3} [0.25]{\includegraphics{sg_no_bg_subtraction_0Amp.eps}}} \\ \centerline{\scalebox{0.3} [0.25]{\includegraphics{Background.eps}}}\\ \centerline{\scalebox{0.3} [0.25]{\includegraphics{bg_subtracted_0Amp.eps}}} \end{tabular} \caption{Background subtracted to minimize impact of dark current; (top) a beam with the dark current and background noises, (middle) a background image, (bottom) a beam image when dark background was subtracted.} \label{bg} \end{figure}

The electron beam energy was measured using a dipole magnet downstream of the quadrupole used for the emittance measurements. Prior to energizing the diople, the single electron bunch charge passing through the dipole was measured using a Faraday cup located approximately 50 cm downstream. The dipole current was adjusted until a maximum single electron bunch charge was observed on another Farady cup located just after the 45 degree exit port of the dipole. A magnetic field map of the dipole suggests that the electron beam energy was approximately 14 MeV. Future emittance measurements are planned to cover the entire energy range of the linac.

%${^\circ}$ \subsection{Data Analysis and Results}


Images from the (insert camera model here) digital camera were calibrated using the OTR target frame. An LED was used to illuminate the OTR aluminum frame that has a known inner diameter of 31.75~mm. Image processing software was used to inscribe a circle on the image to measure the circular OTR inner frame in units of pixels. The scaling factor can be obtained by dividing this length with the number of pixels observed. The result is a horizontal scaling factor is 0.04327$\pm$0.00016~mm/pixel and vertical scaling factor is 0.04204$\pm$0.00018~mm/pixel.

Digital images from the (specify camera used here) were extracted in a matrix format (used common terminology here) in order to take projections on both axes and perform a multi-gaussian or Lorentzian fit. A observed image profiles were not well described by a single Gaussian distribution. The profiles may be described using a Lorentzian distribution however, the rms of the Lorentzian function is not defined. The super Gaussian distribution seems to be best option~\cite{sup-Gau}, since rms values can be extracted.

Fig.~\ref{par-fit} show the square of rms ($\sigma^2$) $vs$ $k_1L$ for $x$ (horizontal) and $y$ (vertical) projections of beam profiles along with the parabolic fits using Equation 9. The emittances and Twiss parameters from these fits are summarized in Table.~\ref{results}. Further details describing the fitting procedures using are described in reference~\cite{emit-mat}.

%\subsection{Measured Results} %Parabolic fits are plotted in Fig.~\ref{par-fit}.

%Parabolic fits for x and y projections are given by Eq.~(\ref{eq:x-fit-eq}) and ~(\ref{eq:y-fit-eq}), which are plotted in Fig.~\ref{par-fit-x} and Fig.~\ref{par-fit-y}. %\begin{equation} %\sigma_x^2 = (3.68 \pm 0.02) + (-4.2 \pm 0.2)k_{1}L + (5.6 \pm 0.4)(k_{1}L)^2 %\label{eq:x-fit-eq} %\end{equation} %\begin{equation} %\sigma_y^2 = (2.84 \pm 0.04) + (1.0 \pm 0.5)k_{1}L + (3.8 \pm 1.2)(k_{1}L)^2 %\label{eq:y-fit-eq} %\end{equation}


\begin{figure} \begin{tabular}{cc} {\scalebox{0.21} [0.20]{\includegraphics{par_fit_x.eps}}} {\scalebox{0.21} [0.20]{\includegraphics{par_fit_y.eps}}} \end{tabular} \caption{Square of rms values and parabolic fittings.} \label{par-fit} \end{figure}

%\begin{figure} %\begin{tabular}{cc} %\centerline{\scalebox{0.20} [0.20]{\includegraphics{par_fit_x.eps}}} \\ %\centerline{\scalebox{0.20} [0.20]{\includegraphics{par_fit_y.eps}}} %\end{tabular} %\caption{Square of rms values and parabolic fittings.} %\label{par-fit} %\end{figure}

%Projected emittance $\epsilon$, normalized emittance $\epsilon_n$, and Twiss parameters are shown in Table~\ref{results}. %\begin{table}[hbt] % \centering % \caption{Emittance Measurement Results.} % \begin{tabular}{llll} % \toprule % \textbf{} & \textbf Unit & Horizontal Plane & Vertical Plane\\ % \midrule % $\epsilon$ &$\mu$m & $0.369 \pm 0.019$ & $0.294 \pm 0.038$ \\ % $\epsilon_n$ &$\mu$m & $10.10 \pm 0.51$ & $8.06 \pm 1.1 $ \\ % $\beta$ &m & $1.40 \pm 0.06$ & $1.17 \pm 0.13$ m \\ % $\alpha$ &rad & $0.97 \pm 0.06$ & $0.24 \pm 0.07$ rad \\ % \bottomrule % \end{tabular} % \label{results} %\end{table}

\begin{table}[hbt] 

  \centering
  \caption{Emittance Measurement Results.}
  \begin{tabular}{lcc}
      \toprule
       {Parameter}         & {Unit}     &    {Value}    \\ 
      \midrule
        projected emittance $\epsilon_x$        &   $\mu$m    &    $0.37 \pm 0.02$     \\
         projected emittance $\epsilon_y$            &   $\mu$m    &    $0.30 \pm 0.04$     \\

normalized emittance $\epsilon_{n,x}$ & $\mu$m & $10.10 \pm 0.51$ \\ normalized emittance $\epsilon_{n,y}$ & $\mu$m & $8.06 \pm 1.1$ \\ 

        $\beta_x$-function                            &  m                           &   $1.40  \pm  0.06$          \\
        $\beta_y$-function                                &  m                           &   $1.17   \pm 0.13$         \\

$\alpha_x$-function & rad & $0.97 \pm 0.06$ \\ $\alpha_y$-function & rad & $0.24 \pm 0.07$ \\ single bunch charge & pC & 11 \\ energy of the beam $E$ & MeV & 14 \\ 

 \bottomrule
  \end{tabular}
  \label{results}

\end{table}

\section{Conclusions} Diagnostic tools to measure the beam emittance at the HRRL was established. Electron beam profiles from HRRL are not Gaussian, but rather super Gaussian or Lorentzian. When beam was projected to a single plane, due to more pixel numbers of horizontal plane, projection to vertical plane has bigger signal to noise ratio. Thus rms beam sizes measured in vertical plane have bigger error bars, which also lead to bigger estimated errors on the results of vertical beam profile.

%\section{ACKNOWLEDGMENT} %Thanks to A, B, and C.

%\begin{figure} %\begin{tabular}{cc} %\centerline{\includegraphics[width=60mm]{par_fit_x.eps}} \\ %\centerline{\includegraphics[width=60mm]{par_fit_y.eps}} %\end{tabular} %\caption{Square of rms and parabolic fitting for x-projection.} %\end{figure} % %\begin{figure}[htb] %\centerline %\scalebox{0.21} [0.3]{{\includegraphics{sg_no_bg_subtraction_0Amp.png}}}\\ %\scalebox{0.21} [0.3]{{\includegraphics{Background.png}}}\\ %\scalebox{0.21} [0.3]{{\includegraphics{bg_subtracted_0Amp.png}}} %\caption{\small Background subtraction.} %\label{par-fit} %\end{figure} % %\begin{figure}[htb] %\centerline{ %%\scalebox{0.21} [0.28]{{\includegraphics{par_fit_x.png}}}\\ %%\scalebox{0.21} [0.28]{\includegraphics{par_fit_y.png}}} %\scalebox{0.21} [0.3]{{\includegraphics{par_fit_x.eps}}}\\ %\scalebox{0.21} [0.3]{\includegraphics{par_fit_y.eps}}} %\caption{\small $\sigma^2$ from super Gaussian and parabolic fittings.} %\label{par-fit} %\end{figure} %\begin{figure}[htb] % \centering % \includegraphics*[width=80mm]{image_sys} % \caption{Imaging system.} % \label{image_sys} %\end{figure} % %\begin{figure}[htb] % \centering % \includegraphics*[width=40mm]{imaging_sys} % \caption{Imaging system.} % \label{imaging_sys} %\end{figure}

%\begin{figure} % \centering % \subfloat[X-projection.]{\label{par-fit-x}\includegraphics[width=0.25\textwidth]{par_fit_x.eps}} % ~ %add desired spacing between images, e. g. ~, \quad, \qquad etc. (or a blank line to force the subfig onto a new line) % \subfloat[Y-projection.]{\label{par-fit-y}\includegraphics[width=0.25\textwidth]{par_fit_y.eps}} % ~ %add desired spacing between images, e. g. ~, \quad, \qquad etc. (or a blank line to force the subfig onto a new line) % \caption{Square of rms and parabolic fittings.} % \label{par-fit} % \label{fig:animals} %\end{figure}


%\begin{figure}[htb] % \centering % \includegraphics[width=60mm]{par_fit_x.eps} % \caption{Square of rms and parabolic fitting for x-projection.} % \label{par-fit-x} %\end{figure} %\begin{figure}[htb] % \centering % \includegraphics[width=60mm]{par_fit_y.eps} % \caption{Square of rms and parabolic fitting for y-projection.} % \label{par-fit-y} %\end{figure}

%\begin{figure} %\centering %\begin{tabular}{cc} %\epsfig{file=par_fit_x.eps,width=0.5\linewidth,clip=a} & %\epsfig{file=par_fit_y.eps,width=0.5\linewidth,clip=b} \\ %\epsfig{file=par_fit_x.eps,width=0.5\linewidth,clip=} & %\epsfig{file=par_fit_y.eps,width=0.5\linewidth,clip=} %\end{tabular} %\end{figure}

%\begin{table}[hbt] % \centering % \caption{HRRL Parameters.} % \begin{tabular}{lccc} % \toprule % \textbf{En} & {$\textbf I_{peak}$} & \textbf{Rep Rate} & \textbf{Pulse Length}\\ % \midrule % 16 MeV & 80 mA & 1 kHz & 250 ns (FWHM) \\ % \bottomrule %\end{tabular} %\label{tab:hrrl} %\end{table}

%\begin{figure*}[htb] % \centering % %\includegraphics*[width=168mm]{HRRL_BeamLine} % \includegraphics*[width=160mm]{HRRL_Pos_and_Ele_Go.pdf} % \caption{HRRL beamline for positron production. } % \label{hrrl-beamline} %\end{figure*}

%\bibliographystyle{aipproc} %\bibliography{bibtex} % %\IfFileExists{\jobname.bbl}{} % {\typeout{} % \typeout{******************************************} % \typeout{** Please run "bibtex \jobname" to optain} % \typeout{** the bibliography and then re-run LaTeX} % \typeout{** twice to fix the references!} % \typeout{******************************************} % \typeout{} % }

\begin{thebibliography}{9} % Use for 1-9 references %\begin{thebibliography}{99} % Use for 10-99 references

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%000000000000000000000000000000000000000000000000000000000000 \bibitem{emit-mat} C.F. Eckman $et$ $al$., in $Proc$. $IPAC2012$, New Orleans, USA. %000000000000000000000000000000000000000000000000000000000000


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