Difference between revisions of "IPAC 2012"

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[[File:IPAC_2012_Sadiq.pdf]]
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latex file: [[File:IPAC_2012_Sadiq.txt]]
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= Latex =
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\usepackage{graphicx}
 
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\usepackage{amstext}
 
\usepackage{amstext}
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%\usepackage{hyperref}
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%\usepackage[bottom]{footmisc}
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%\usepackage{tabularx }
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%\usepackage{epsfig}
 
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\begin{document}
 
\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 IDAHO ACCELERATOR CENTER}
 
%\title{TRANSVERSE BEAM EMITTANCE MEASUREMENTS OF A 16 MeV LINAC AT THE IAC\thanks{ Work supported by ...}}
 
%\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\\
+
\author{S. Setiniyaz\thanks{Email: sadik82@gmail.com}, K. Chouffani, T. Forest, and 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\\
 
Idaho State University, Pocatello, ID, 83209, USA\\
 
A. Freyberger, Jefferson Lab, Newport News, Virginia, 23606, USA}
 
A. Freyberger, Jefferson Lab, Newport News, Virginia, 23606, USA}
Line 39: Line 48:
  
 
\begin{abstract}
 
\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.
+
A beam emittance measurement of the 16~MeV S-band High Repetition Rate Linac (HRRL) was performed at Idaho State University's Idaho Accelerator Center (IAC). The HRRL linac structure was upgraded beyond the capabilities of a typical medical linac so it can achieve a repetition rate of 1~kHz. Measurements of the HRRL transverse beam emittance are underway that will be used to optimize the production of positrons using HRRL's intense electron beam on a tungsten converter. In this paper, we describe a beam imaging system using on an OTR screen and a digital CCD camera, a MATLAB tool to extract beamsize and emittance, detailed measurement procedures, and the measured transverse emittances for an arbitrary beam energy of 15~MeV.
 
\end{abstract}
 
\end{abstract}
  
 
\section{Introduction}
 
\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}.
+
The HRRL is an S-band electron linac located in the beam lab of the Physics Department at Idaho State University (ISU). 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 positrons to be used as a secondary beam.   
 
+
%The electron beam characteristics of the 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}
+
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.  Visible radiation is emitted at an angle of 90${^\circ}$ with respect to the incident beam direction~\cite{OTR} when the electron beam intersects the OTR target at a 45${^\circ}$ angle. These backward-emitted photons are observed using a digital camera and can be used to measure the shape and intensity of the electron beam based on the OTR distribution.
  
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.
+
Emittance is a key parameter in accelerator physics that 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} to measure the emittance, Twiss parameters, and beam energy.
  
 +
\section{The Experiment}
 +
\subsection{Quadrupole Scanning Method}
 +
Fig.~\ref{q-scan-layout} illustrates the apparatus used to measure the emittance using the quadrupole scanning method.  A quadrupole is positioned at the exit of the linac to focus or de-focus the beam as observed on a downstream view screen. The 3.1~m distance between the quadrupole and the screen was chosen in order to minimize chromatic effects and to satisfy the thin lens approximation.
 +
%The quadrupole and the screen are located far away to minimize chromatic effects and to increase the veracity of the thin lens approximation used to calculate beam optics.
 
\begin{figure}[htb]
 
\begin{figure}[htb]
 
\centering
 
\centering
 
   \includegraphics[scale=0.40]{quad_scan_setup.eps}
 
   \includegraphics[scale=0.40]{quad_scan_setup.eps}
\caption{Layout for quadrupole scanning method.}
+
\caption{Apparatus used to measure the beam emittance.}
\label{q-scan-layout}  
+
\label{q-scan-layout}
 
\end{figure}
 
\end{figure}
 
+
Assuming the thin lens approximation, $\sqrt{k_1}L << 1$, is satisfied, the transfer matrix of a quadrupole magnet may be expressed as
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
 
% thin lens approximation (sqrt{k1}*L << 1). In our case sqrt{k1}*L =0.07
\begin{equation}  
+
\begin{equation}
\label{quad-trans-matrix}  
+
\label{quad-trans-matrix}
 
\mathrm{\mathbf{Q}}=\Bigl(\begin{array}{cc}
 
\mathrm{\mathbf{Q}}=\Bigl(\begin{array}{cc}
 
1 & 0\\
 
1 & 0\\
Line 96: Line 82:
 
\end{array}\Bigr),
 
\end{array}\Bigr),
 
\end{equation}
 
\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
+
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 the quadrupole and screen is given by
\begin{equation}  
+
\begin{equation}
\label{drift-trans-matrix}  
+
\label{drift-trans-matrix}
 
\mathbf{\mathbf{S}}=\Bigl(\begin{array}{cc}
 
\mathbf{\mathbf{S}}=\Bigl(\begin{array}{cc}
 
1 & l\\
 
1 & l\\
Line 104: Line 90:
 
\end{array}\Bigr),
 
\end{array}\Bigr),
 
\end{equation}
 
\end{equation}
where $l$ is the distance between the scanning quadrupole and the screen. The transfer matrix of the scanning region is given by
+
where $l$ is the distance between the scanning quadrupole and the screen. The transfer matrix of the scanning region is given by the matrix product $\mathbf{SQ}$.
\begin{equation}  
+
In the horizontal plane, the beam matrix at the screen ($\mathbf{\sigma_{s}}$) is related to the beam matrix of the quadrupole ($\mathbf{\sigma_{q}}$)  using the similarity transformation
\mathbf{\mathbf{M}}=\mathrm{\mathbf{SQ}}
+
\begin{equation}
=\Bigl(\begin{array}{cc}
+
\mathbf{\mathbf{\sigma_{s}=M\mathrm{\mathbf{\mathbf{\sigma_{q}}}}}M}^{\mathrm{T}}.
m_{11} & m_{12}\\
 
m_{21} & m_{22}
 
\end{array}\Bigr).
 
 
\end{equation}
 
\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
+
where the $\mathbf{\sigma_{s}}$ and $\mathbf{\sigma_{q}}$ are defined as~\cite{SYLee}
\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}
 
\begin{equation}
 
\mathbf{\mathbf{\sigma_{s,\mathnormal{x}}=}}\Bigl(\begin{array}{cc}
 
\mathbf{\mathbf{\sigma_{s,\mathnormal{x}}=}}\Bigl(\begin{array}{cc}
\sigma_{\textnormal{s},x}^{2} & \sigma_{\textnormal{s},xx'}\\
+
\sigma_{\textnormal{s},x}^{2} & \sigma_{\textnormal{s},xx'} \\
 
\sigma_{\textnormal{s},xx'} & \sigma_{\textnormal{s},x'}^{2}
 
\sigma_{\textnormal{s},xx'} & \sigma_{\textnormal{s},x'}^{2}
\end{array}\Bigr),
+
\end{array}\Bigr)
\end{equation}
+
,\;
 
 
\begin{equation}
 
 
\mathbf{\mathbf{\sigma_{q,\mathnormal{x}}}}=\Bigl(\begin{array}{cc}
 
\mathbf{\mathbf{\sigma_{q,\mathnormal{x}}}}=\Bigl(\begin{array}{cc}
 
\sigma_{\textnormal{q},x}^{2} & \sigma_{\textnormal{q},xx'}\\
 
\sigma_{\textnormal{q},x}^{2} & \sigma_{\textnormal{q},xx'}\\
Line 131: Line 107:
 
\end{array}\Bigr).
 
\end{array}\Bigr).
 
\end{equation}
 
\end{equation}
 
 
\noindent
 
\noindent
By defining the new parameters~\cite{quad-scan},
+
%By defining the new parameters~\cite{quad-scan}, $A \equiv \sigma_{11},~B \equiv \frac{\sigma_{12}}{\sigma_{11}},~C \equiv \frac{\epsilon_{x}^{2}}{\sigma_{11}}$
\begin{equation}  
+
By defining the new parameters~\cite{quad-scan}
A \equiv \sigma_{11},~B \equiv \frac{\sigma_{12}}{\sigma_{11}},~C \equiv \frac{\epsilon_{x}^{2}}{\sigma_{11}}
+
\begin{equation}
 +
A \equiv l^2\sigma_{\textnormal{q},x}^{2},~B \equiv \frac{1}{l} + \frac{\sigma_{\textnormal{q},xx'}}{\sigma_{\textnormal{q},x}^{2}},~C \equiv l^2\frac{\epsilon_{x}^{2}}{\sigma_{\textnormal{q},x}^{2}}.
 
\end{equation}
 
\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 $L$
+
the matrix element $\sigma_{\textnormal{s},x}^{2}$, the square of the rms beam size at the screen, may be expressed as a parabolic function of the product of $k_1$ and $L$
\begin{equation}  
+
\begin{equation}
\sigma_{\textnormal{s},x}^{2}=A(k_{1}L)^{2}-2AB(k_{1}L)+(C+AB^{2})
+
\sigma_{\textnormal{s},x}^{2}=A(k_{1}L)^{2}-2AB(k_{1}L)+(C+AB^{2}).
\label{q_scan_layout}
+
\label{par_fit}
 
\end{equation}
 
\end{equation}
 
+
The emittance measurement was performed by changing the quadrupole current, which changes $k_{1}L$, and measuring the  corresponding beam image on the view screen. The measured two-dimensional beam image was projected along the image's abscissa and ordinate axes.  A Gaussian fitting function is used on each projection to determine the  rms value, $\sigma_\textnormal{s}$ in Eq.~(\ref{par_fit}). Measurements of $\sigma_\textnormal{s}$ for several quadrupole currents ($k_{1}L$) is then fit using the parabolic function in Eq.~(\ref{par_fit}) to determine the constants $A$, $B$, and $C$.  The emittance ($\epsilon$)  and the Twiss parameters ($\alpha$ and $\beta$) can be found using Eq.~(\ref{emit-relation}).
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}
\begin{equation}  
+
\epsilon=\frac{\sqrt{AC}}{l^2},~\beta=\sqrt{\frac{A}{C}},~\alpha=\sqrt{\frac{A}{C}}(B+\frac{1}{l}).
\epsilon=\sqrt{AC},~\beta=\sqrt{\frac{A}{C}},~\alpha=-B\sqrt{\frac{A}{C}}
 
 
\label{emit-relation}
 
\label{emit-relation}
 
\end{equation}
 
\end{equation}
 
 
\subsection{The OTR Imaging System}
 
\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}.
+
The OTR target is 10 $\mu$m thick aluminum foil with a 1.25 inch diameter. The OTR is emitted in a cone shape with the maximum intensity at an angle of $1/\gamma$ with respect to the reflecting angle of the electron beam~\cite{OTR}. Three lenses, 2 inches in diameter, are used for the imaging system to avoid optical distortion at lower electron energies. The focal lengths and position of the lenses are shown in Fig.~\ref{image_sys}. The camera used was a JAI CV-A10GE digital camera with a 767 by 576 pixel area. The camera images were taken by triggering the camera synchronously with the electron gun.
 
 
 
\begin{figure}
 
\begin{figure}
\begin{tabular}{lr}
+
\centering
{\scalebox{0.25} [0.25]{\includegraphics{image_sys.eps}}}  
+
{\scalebox{0.16} [0.16]{\includegraphics{image_sys.eps}}} {\scalebox{0.20} [0.20]{\includegraphics{imaging_sys}}}
{\scalebox{0.3} [0.30]{\includegraphics{imaging_sys}}}
+
\caption{The OTR Imaging system.}
\end{tabular}
 
\caption{Square of rms and parabolic fitting for x-projection.}
 
 
\label{image_sys}
 
\label{image_sys}
 
\end{figure}
 
\end{figure}
 
 
\subsection{Quadrupole Scanning}
 
\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 quadrupole current is changed to alter the strength and direction of the quadrupole magnetic field such that a measurable change in the beam shape is seen by the OTR system.  Initially, the beam was steered by the quadrupole indicating that the beam was not entering along the quadrupole's central axis.  Several magnetic elements upstream of this quadrupole were adjusted to align the incident electron beam with the quadrupole's central axis.  First, the beam current observed by a Faraday cup located at the end of beam line was maximized using upstream steering coils within the linac nearest the gun.  Second, the first solenoid nearest the linac gun was used to focus the electron beam on the OTR screen. Steering coils were adjusted to maximize the beam current to the Faraday cup and minimize the deflection of the beam by the solenoid first then by the quadrupole.  A second solenoid and the last steering magnet, both near the exit of the linac, were used in the final step to optimize the beam spot size on the OTR target and maximize the Faraday cup current.  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.
+
The emittance measurement was performed using an electron beam energy of 15~MeV and a 200~ns long, 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 measurements 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{figure}
 
\begin{tabular}{ccc}
 
\begin{tabular}{ccc}
\centerline{\scalebox{0.3} [0.25]{\includegraphics{sg_no_bg_subtraction_0Amp.eps}}} \\
+
\centerline{\scalebox{0.28} [0.22]{\includegraphics{sg_no_bg_subtraction_0Amp.eps}}} \\
\centerline{\scalebox{0.3} [0.25]{\includegraphics{Background.eps}}}\\
+
(a)\\
\centerline{\scalebox{0.3} [0.25]{\includegraphics{bg_subtracted_0Amp.eps}}}
+
\centerline{\scalebox{0.28} [0.22]{\includegraphics{Background.eps}}}\\
 +
(b)\\
 +
\centerline{\scalebox{0.28} [0.22]{\includegraphics{bg_subtracted_0Amp.eps}}}\\
 +
(c)
 
\end{tabular}
 
\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.}
+
\caption{Background subtracted to minimize impact of dark current; (a) a beam with the dark current and background noise, (b) a background image, (c) a beam image when dark background was subtracted.}
\label{bg}
+
\label{bg}
 
\end{figure}
 
\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 dipole, the electron micro-pulse bunch charge  passing through the dipole was measured using a Faraday cup located approximately 50~cm downstream of the OTR screen.  The dipole current was adjusted until a maximum beam current was observed on another Faraday 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 15~$\pm$~1.5~MeV.  Future emittance measurements are planned to cover the entire energy range of the linac.
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}
 
\subsection{Data Analysis and Results}
Images need to be converted from camera pixels to physical length. Diameter of the OTR screen is 31.75~mm. The scaling factor can be obtained by dividing this length with the pixels numbers in the image. Horizontal scaling factor is 0.04327$\pm$0.00016~mm/pixel, and vertical scaling factor is 0.04204$\pm$0.00018~mm/pixel.
+
Images from the JAI camera were calibrated using the OTR target frame.  An LED was used to illuminate the OTR aluminum frame  that has a known inner diameter of 31.75~mm. Image processing software was used to inscribe a circle on the image to measure the circular OTR inner frame in units of pixels.  The scaling factor can be obtained by dividing this length with the number of pixels observed. The result is a horizontal scaling factor of 0.04327~$\pm$~0.00016~mm/pixel and vertical scaling factor of 0.04204~$\pm$~0.00018~mm/pixel.
 
+
Digital images from the JAI camera were extracted in a matrix format in order to take projections on both axes and perform a Gaussian fit. The 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 the best option~\cite{sup-Gau}, because rms values may be directly extracted.
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. The image size was calibrated using images of the OTR screen holder that is illuminated by an LED.  In the data analysis, the beam image was projected to a single axis and fitted it with Gaussian function. The beam projection is sharper than Gaussian distribution, it is more like Lorentzian. However, the rms of the Lorentzian function is not defined. Fitting it with the super Gaussian function seems to be best option~\cite{sup-Gau}, since rms values can be extracted.  
 
 
 
Two plots were generated with square of rms ($\sigma^2$) $vs$ $k_1L$ for $x$ (horizontal) and $y$ (vertical) projections of beam profiles, as shown in Fig.~\ref{par-fit} along with parabolic fits. Emittances and Twiss parameters from fits summarized in Table.~\ref{results}. All these were done using MATLAB. For details, please look at~\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}
 
 
 
  
 +
Fig.~\ref{par-fit}  shows the square of the rms ($\sigma^2_\textnormal{s}$) $vs$ $k_1L$ for $x$ (horizontal) and $y$ (vertical) beam projections along with the parabolic fits using Eq.~\ref{par_fit} . The emittances and Twiss parameters from these fits are summarized in Table.~\ref{results}.  Further details of the fitting procedures are described in reference~\cite{emit-mat}.
 
\begin{figure}
 
\begin{figure}
 
\begin{tabular}{cc}
 
\begin{tabular}{cc}
{\scalebox{0.21} [0.20]{\includegraphics{par_fit_x.eps}}}  
+
{\scalebox{0.21} [0.20]{\includegraphics{par_fit_x.eps}}}
 
{\scalebox{0.21} [0.20]{\includegraphics{par_fit_y.eps}}}
 
{\scalebox{0.21} [0.20]{\includegraphics{par_fit_y.eps}}}
 
\end{tabular}
 
\end{tabular}
 
\caption{Square of rms values and parabolic fittings.}
 
\caption{Square of rms values and parabolic fittings.}
\label{par-fit}  
+
\label{par-fit}
 
\end{figure}
 
\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]
 
\begin{table}[hbt]
 
   \centering
 
   \centering
Line 240: Line 167:
 
   \begin{tabular}{lcc}
 
   \begin{tabular}{lcc}
 
       \toprule
 
       \toprule
         {Parameter}        & {Unit}    &    {Value}    \\  
+
         {Parameter}        & {Unit}    &    {Value}    \\
 
       \midrule
 
       \midrule
 
         projected emittance $\epsilon_x$        &  $\mu$m    &    $0.37 \pm 0.02$    \\
 
         projected emittance $\epsilon_x$        &  $\mu$m    &    $0.37 \pm 0.02$    \\
 
           projected emittance $\epsilon_y$            &  $\mu$m    &    $0.30 \pm 0.04$    \\
 
           projected emittance $\epsilon_y$            &  $\mu$m    &    $0.30 \pm 0.04$    \\
  normalized emittance $\epsilon_{n,x}$  &  $\mu$m    &  $10.10 \pm 0.51$        \\
+
%   normalized \footnote{normalization procedure assumes appropriate beam chromaticity.} emittance $\epsilon_{n,x}$  &  $\mu$m    &  $10.10 \pm 0.51$        \\
  normalized emittance $\epsilon_{n,y}$      &  $\mu$m    &  $8.06 \pm 1.1$          \\
+
  %normalized emittance $\epsilon_{n,y}$      &  $\mu$m    &  $8.06 \pm 1.1$          \\
 
         $\beta_x$-function                            &  m                          &  $1.40  \pm  0.06$          \\
 
         $\beta_x$-function                            &  m                          &  $1.40  \pm  0.06$          \\
 
         $\beta_y$-function                                &  m                          &  $1.17  \pm 0.13$        \\
 
         $\beta_y$-function                                &  m                          &  $1.17  \pm 0.13$        \\
 
  $\alpha_x$-function                          &  rad                        &  $0.97  \pm  0.06$          \\
 
  $\alpha_x$-function                          &  rad                        &  $0.97  \pm  0.06$          \\
 
  $\alpha_y$-function                              &  rad                        &  $0.24  \pm 0.07$        \\
 
  $\alpha_y$-function                              &  rad                        &  $0.24  \pm 0.07$        \\
  single bunch charge                                    &  pC                          &  11        \\
+
    micro-pulse charge                                    &  pC                          &  11        \\
  energy of the beam $E$                                &  MeV                        &  14         \\
+
    micro-pulse length                                    &  ps                          &  350.16          \\
 +
  energy of the beam $E$                                &  MeV                        &  15    $\pm$ 1.6    \\
 +
  relative energy spread $\Delta E/E$                                &  \%                        &  10.4         \\
  
 
   \bottomrule
 
   \bottomrule
Line 259: Line 188:
  
 
\section{Conclusions}
 
\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.
+
A diagnostic tool was developed and used to measure the beam emittance of the High Rep Rate Linac at the Idaho Accelerator Center. The tool relied on measuring the images generated by the optical transition radiation of the electron beam on a polished thin aluminum target. The electron beam profile was not described well using a single Gaussian distribution but rather by a super Gaussian or Lorentzian distribution. The larger uncertainties observed for $\sigma^2_y$ are still under investigation. The projected emittance of the High Rep Rate Linac, similar to medical linacs, at ISU was measured to be less than 0.4~$\mu$m as measured by the OTR based tool described above when accelerating electrons to an energy of 15~MeV. The normalized emittance may be obtained by multiplying the projected emittance by the average relativistic factor $\gamma$ and $\beta$ of the electron beam. We plan to perform similar measurements over the energy range of the linac in the near future.
 
 
%\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{}
 
% }
 
  
 +
\section{ACKNOWLEDGMENT}
 +
We would like to acknowledge the outstanding efforts of Idaho Accelerator Center.  This work was supported by DOE award \# DE-SC0002600.
 +
%Thanks to C. F. Eckman, C. O'Neill, and Dr. D. Wells.
 
\begin{thebibliography}{9}  % Use for  1-9  references
 
\begin{thebibliography}{9}  % Use for  1-9  references
%\begin{thebibliography}{99} % Use for 10-99 references
 
 
%\bibitem{emit-ways}
 
%A. Jim and B. Mark, ``some paper on methods of emittance measurement,'' EPAC'96, Sitges, June 1996, MOPCH31, p. 7984 (1996),
 
%
 
%
 
%\bibitem{quad-scan}
 
%A. Jim and B. Mark, ``some paper on methods of quad scan,'' EPAC'96, Sitges, June 1996, MOPCH31, p. 7984 (1996),
 
%\texttt{http://www.JACoW.org}  \{no period after URL\}
 
%
 
%\bibitem{sup-Gau}
 
%C. Petit-Jean-Genaz and J. Poole, ``JACoW, A service to the Accelerator Community,''
 
%EPAC'04, Lucerne, July 2004, THZCH03,  p.~249, \texttt{http://www.JACoW.org}
 
%
 
%\bibitem{jacow-help} A. Name and D. Person, Phys. Rev. Lett. 25 (1997) 56.
 
%
 
%\bibitem{exampl-ref}
 
%A.N. Other, ``A Very Interesting Paper,'' EPAC'96, Sitges, June 1996, MOPCH31, p. 7984 (1996),
 
%\texttt{http://www.JACoW.org}  \{no period after URL\}
 
%
 
%
 
%\bibitem{exampl-ref2}
 
%F.E.~Black et al., {\it This is a Very Interesting Book}, (New York: Knopf, 2007), 52.
 
%
 
%\bibitem{exampl-ref3}
 
%G.B.~Smith et al., ``Title of Paper,'' MOXAP07, these proceedings.
 
  
 
%000000000000000000000000000000000000000000000000000000000000
 
%000000000000000000000000000000000000000000000000000000000000
 
%@article{Murokh_Rosenzweig_Yakimenko_Johnson_Wang_2000, title={Limitations on the Resolution of Yag:Ce Beam Profile Monitor for High Brightness Electron Beam}, url={http://eproceedings.worldscinet.com/9789812792181/9789812792181_0038.html}, journal={The Physics of High Brightness Beams Proceedings of the 2nd ICFA Advanced Accelerator Workshop}, publisher={World Scientific Publishing Co. Pte. Ltd.}, author={Murokh, A and Rosenzweig, J and Yakimenko, V and Johnson, E and Wang, X J}, year={2000}, pages={564--580}}
 
%@article{Murokh_Rosenzweig_Yakimenko_Johnson_Wang_2000, title={Limitations on the Resolution of Yag:Ce Beam Profile Monitor for High Brightness Electron Beam}, url={http://eproceedings.worldscinet.com/9789812792181/9789812792181_0038.html}, journal={The Physics of High Brightness Beams Proceedings of the 2nd ICFA Advanced Accelerator Workshop}, publisher={World Scientific Publishing Co. Pte. Ltd.}, author={Murokh, A and Rosenzweig, J and Yakimenko, V and Johnson, E and Wang, X J}, year={2000}, pages={564--580}}
  
\bibitem{otr-yag}
+
%\bibitem{otr-yag}
A. Murokh $et$ $al$., {\it The Physics of High Brightness Beams}, (Singapore: World Scientific, 2000), 564.
+
%A. Murokh $et$ $al$., {\it The Physics of High Brightness Beams}, (Singapore: World Scientific, 2000), 564.
 
%000000000000000000000000000000000000000000000000000000000000
 
%000000000000000000000000000000000000000000000000000000000000
  
Line 414: Line 208:
 
%journal = "Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment",
 
%journal = "Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment",
 
%volume = "357",
 
%volume = "357",
%number = "2–3",
+
%number = "2–3",
 
%pages = "231 - 237",
 
%pages = "231 - 237",
 
%year = "1995",
 
%year = "1995",
Line 423: Line 217:
 
%url = "http://www.sciencedirect.com/science/article/pii/0168900294015333",
 
%url = "http://www.sciencedirect.com/science/article/pii/0168900294015333",
 
%}
 
%}
\bibitem{OTR}
+
%\bibitem{OTR2}
M. Castellano, $et$ $al$., Nucl.
+
%M. Castellano, $et$ $al$., Nucl.
Instr. and Meth. A \textbf{357}, (1995) 231.
+
%Instr. and Meth. A \textbf{357}, (1995) 231.
  
 
%000000000000000000000000000000000000000000000000000000000000
 
%000000000000000000000000000000000000000000000000000000000000
  
%@techreport{OTR2,
+
%@techreport{OTR,
 
% title      ={{Optical Transition Radiation}},
 
% title      ={{Optical Transition Radiation}},
% month      ={},  
+
% month      ={},
 
% year = {1992},
 
% year = {1992},
 
% author      ={B. Gitter},
 
% author      ={B. Gitter},
 
% address    ={Los Angeles, CA 90024},
 
% address    ={Los Angeles, CA 90024},
% institution ={Particle Beam Physics Lab, Center for Advanced Accelerators, UCLA Department of Physics}  
+
% institution ={Particle Beam Physics Lab, Center for Advanced Accelerators, UCLA Department of Physics}
 
%}
 
%}
\bibitem{OTR2}
+
\bibitem{OTR}
 
B. Gitter, Tech. Rep., Los Angeles, USA (1992).
 
B. Gitter, Tech. Rep., Los Angeles, USA (1992).
  
 
%000000000000000000000000000000000000000000000000000000000000
 
%000000000000000000000000000000000000000000000000000000000000
%@article{emit-ways,  
+
%@article{emit-ways,
%title={Methods of Emittance Measurement},  
+
%title={Methods of Emittance Measurement},
%volume={08544},  
+
%volume={08544},
 
% journal={Frontiers of Particle Beams Observation Diagnosis and Correction},
 
% journal={Frontiers of Particle Beams Observation Diagnosis and Correction},
% publisher={Springer-Verlag},  
+
% publisher={Springer-Verlag},
 
% author={Mcdonald, K T and Russell, D P},
 
% author={Mcdonald, K T and Russell, D P},
% editor={Month, M and Turner, SEditors},  
+
% editor={Month, M and Turner, SEditors},
%year={1988},  
+
%year={1988},
 
%pages={1--12},
 
%pages={1--12},
 
%url={http://www.springerlink.com/index/M04123462V02P745.pdf}
 
%url={http://www.springerlink.com/index/M04123462V02P745.pdf}
Line 464: Line 258:
 
%@techreport{quad-scan,
 
%@techreport{quad-scan,
 
% title      ={{Emittance Measurement of The DAFNE Linac Electron Beam}},
 
% title      ={{Emittance Measurement of The DAFNE Linac Electron Beam}},
% month      ={Nov.},  
+
% month      ={Nov.},
 
% year = {2005},
 
% year = {2005},
 
% author      ={G. Benedetti, B. Buonomo, D. Filippetto},
 
% author      ={G. Benedetti, B. Buonomo, D. Filippetto},
 
% address    ={Frascati, Italy},
 
% address    ={Frascati, Italy},
 
% number      ={},
 
% number      ={},
% institution ={DAFNE Technical Note}  
+
% institution ={DAFNE Technical Note}
 
%}
 
%}
 
\bibitem{quad-scan}
 
\bibitem{quad-scan}
D.F.G. Benedetti, $et$ $al$., Tech. Rep., DAFNE Tech.
+
D.F.G. Benedetti, $et$ $al$., Tech. Rep., DAFNE Tech. Not., Frascati, Italy (2005).
Not., Frascati, Italy (2005).
 
  
 
%000000000000000000000000000000000000000000000000000000000000
 
%000000000000000000000000000000000000000000000000000000000000
Line 513: Line 306:
 
C.F. Eckman $et$ $al$., in $Proc$. $IPAC2012$, New Orleans, USA.
 
C.F. Eckman $et$ $al$., in $Proc$. $IPAC2012$, New Orleans, USA.
 
%000000000000000000000000000000000000000000000000000000000000
 
%000000000000000000000000000000000000000000000000000000000000
 
  
 
\end{thebibliography}
 
\end{thebibliography}
  
 
\end{document}
 
\end{document}

Latest revision as of 00:16, 17 May 2012

File:IPAC 2012 Sadiq.pdf

latex file: File:IPAC 2012 Sadiq.txt

Latex

\documentclass[acus]{JAC2003}

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\usepackage{graphicx} \usepackage{booktabs} \usepackage{epstopdf} \usepackage{subfig} \usepackage{graphicx} \usepackage{amstext} %\usepackage{hyperref} %\usepackage[bottom]{footmisc} %\usepackage{tabularx } %\usepackage{footnote} %\usepackage{caption} %\usepackage{subcaption}

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

\author{S. Setiniyaz\thanks{Email: sadik82@gmail.com}, K. Chouffani, T. Forest, and Y. Kim\\ Idaho State University, Pocatello, ID, 83209, USA\\ A. Freyberger, Jefferson Lab, Newport News, Virginia, 23606, USA}

\maketitle

\begin{abstract} A beam emittance measurement of the 16~MeV S-band High Repetition Rate Linac (HRRL) was performed at Idaho State University's Idaho Accelerator Center (IAC). The HRRL linac structure was upgraded beyond the capabilities of a typical medical linac so it can achieve a repetition rate of 1~kHz. Measurements of the HRRL transverse beam emittance are underway that will be used to optimize the production of positrons using HRRL's intense electron beam on a tungsten converter. In this paper, we describe a beam imaging system using on an OTR screen and a digital CCD camera, a MATLAB tool to extract beamsize and emittance, detailed measurement procedures, and the measured transverse emittances for an arbitrary beam energy of 15~MeV. \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). 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 positrons to be used as a secondary beam. %The electron beam characteristics of the 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. Visible radiation is emitted at an angle of 90${^\circ}$ with respect to the incident beam direction~\cite{OTR} when the electron beam intersects the OTR target at a 45${^\circ}$ angle. These backward-emitted photons are observed using a digital camera and can be used to measure the shape and intensity of the electron beam based on the OTR distribution.

Emittance is a key parameter in accelerator physics that 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} to measure the emittance, Twiss parameters, and beam energy.

\section{The Experiment} \subsection{Quadrupole Scanning Method} Fig.~\ref{q-scan-layout} illustrates the apparatus used to measure the emittance using the quadrupole scanning method. A quadrupole is positioned at the exit of the linac to focus or de-focus the beam as observed on a downstream view screen. The 3.1~m distance between the quadrupole and the screen was chosen in order to minimize chromatic effects and to satisfy the thin lens approximation. %The quadrupole and the screen are located far away to minimize chromatic effects and to increase the veracity of the thin lens approximation used to calculate beam optics. \begin{figure}[htb] \centering

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

\caption{Apparatus used to measure the beam emittance.} \label{q-scan-layout} \end{figure} Assuming the 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 the 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 the matrix product $\mathbf{SQ}$. In the horizontal plane, the beam matrix at the screen ($\mathbf{\sigma_{s}}$) is related to the beam matrix of the quadrupole ($\mathbf{\sigma_{q}}$) using the similarity transformation \begin{equation} \mathbf{\mathbf{\sigma_{s}=M\mathrm{\mathbf{\mathbf{\sigma_{q}}}}}M}^{\mathrm{T}}. \end{equation} where the $\mathbf{\sigma_{s}}$ and $\mathbf{\sigma_{q}}$ are 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) ,\; \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}, $A \equiv \sigma_{11},~B \equiv \frac{\sigma_{12}}{\sigma_{11}},~C \equiv \frac{\epsilon_{x}^{2}}{\sigma_{11}}$ By defining the new parameters~\cite{quad-scan} \begin{equation} A \equiv l^2\sigma_{\textnormal{q},x}^{2},~B \equiv \frac{1}{l} + \frac{\sigma_{\textnormal{q},xx'}}{\sigma_{\textnormal{q},x}^{2}},~C \equiv l^2\frac{\epsilon_{x}^{2}}{\sigma_{\textnormal{q},x}^{2}}. \end{equation} the matrix element $\sigma_{\textnormal{s},x}^{2}$, the square of the rms beam size at the screen, may be expressed as 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{par_fit} \end{equation} The emittance measurement was performed by changing the quadrupole current, which changes $k_{1}L$, and measuring the corresponding beam image on the view screen. The measured two-dimensional beam image was projected along the image's abscissa and ordinate axes. A Gaussian fitting function is used on each projection to determine the rms value, $\sigma_\textnormal{s}$ in Eq.~(\ref{par_fit}). Measurements of $\sigma_\textnormal{s}$ for several quadrupole currents ($k_{1}L$) is then fit using the parabolic function in Eq.~(\ref{par_fit}) to determine the 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=\frac{\sqrt{AC}}{l^2},~\beta=\sqrt{\frac{A}{C}},~\alpha=\sqrt{\frac{A}{C}}(B+\frac{1}{l}). \label{emit-relation} \end{equation} \subsection{The OTR Imaging System} The OTR target is 10 $\mu$m thick aluminum foil with a 1.25 inch diameter. The OTR is emitted in a cone shape with the maximum intensity at an angle of $1/\gamma$ with respect to the reflecting angle of the electron beam~\cite{OTR}. Three lenses, 2 inches in diameter, are used for the imaging system to avoid optical distortion at lower electron energies. The focal lengths and position of the lenses are shown in Fig.~\ref{image_sys}. The camera used was a JAI CV-A10GE digital camera with a 767 by 576 pixel area. The camera images were taken by triggering the camera synchronously with the electron gun. \begin{figure} \centering {\scalebox{0.16} [0.16]{\includegraphics{image_sys.eps}}} {\scalebox{0.20} [0.20]{\includegraphics{imaging_sys}}} \caption{The OTR Imaging system.} \label{image_sys} \end{figure} \subsection{Quadrupole Scanning} The quadrupole current is changed to alter the strength and direction of the quadrupole magnetic field such that a measurable change in the beam shape is seen by the OTR system. Initially, the beam was steered by the quadrupole indicating that the beam was not entering along the quadrupole's central axis. Several magnetic elements upstream of this quadrupole were adjusted to align the incident electron beam with the quadrupole's central axis. First, the beam current observed by a Faraday cup located at the end of beam line was maximized using upstream steering coils within the linac nearest the gun. Second, the first solenoid nearest the linac gun was used to focus the electron beam on the OTR screen. Steering coils were adjusted to maximize the beam current to the Faraday cup and minimize the deflection of the beam by the solenoid first then by the quadrupole. A second solenoid and the last steering magnet, both near the exit of the linac, were used in the final step to optimize the beam spot size on the OTR target and maximize the Faraday cup current. 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 15~MeV and a 200~ns long, 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 measurements 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{0.28} [0.22]{\includegraphics{sg_no_bg_subtraction_0Amp.eps}}} \\ (a)\\ \centerline{\scalebox{0.28} [0.22]{\includegraphics{Background.eps}}}\\ (b)\\ \centerline{\scalebox{0.28} [0.22]{\includegraphics{bg_subtracted_0Amp.eps}}}\\ (c) \end{tabular} \caption{Background subtracted to minimize impact of dark current; (a) a beam with the dark current and background noise, (b) a background image, (c) 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 dipole, the electron micro-pulse bunch charge passing through the dipole was measured using a Faraday cup located approximately 50~cm downstream of the OTR screen. The dipole current was adjusted until a maximum beam current was observed on another Faraday 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 15~$\pm$~1.5~MeV. Future emittance measurements are planned to cover the entire energy range of the linac. \subsection{Data Analysis and Results} Images from the JAI 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 of 0.04327~$\pm$~0.00016~mm/pixel and vertical scaling factor of 0.04204~$\pm$~0.00018~mm/pixel. Digital images from the JAI camera were extracted in a matrix format in order to take projections on both axes and perform a Gaussian fit. The 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 the best option~\cite{sup-Gau}, because rms values may be directly extracted.

Fig.~\ref{par-fit} shows the square of the rms ($\sigma^2_\textnormal{s}$) $vs$ $k_1L$ for $x$ (horizontal) and $y$ (vertical) beam projections along with the parabolic fits using Eq.~\ref{par_fit} . The emittances and Twiss parameters from these fits are summarized in Table.~\ref{results}. Further details of the fitting procedures are described in reference~\cite{emit-mat}. \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{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 \footnote{normalization procedure assumes appropriate beam chromaticity.} 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 & $0.24 \pm 0.07$ \\ micro-pulse charge & pC & 11 \\ micro-pulse length & ps & 350.16 \\ energy of the beam $E$ & MeV & 15 $\pm$ 1.6 \\ relative energy spread $\Delta E/E$ & \% & 10.4 \\

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

\end{table}

\section{Conclusions} A diagnostic tool was developed and used to measure the beam emittance of the High Rep Rate Linac at the Idaho Accelerator Center. The tool relied on measuring the images generated by the optical transition radiation of the electron beam on a polished thin aluminum target. The electron beam profile was not described well using a single Gaussian distribution but rather by a super Gaussian or Lorentzian distribution. The larger uncertainties observed for $\sigma^2_y$ are still under investigation. The projected emittance of the High Rep Rate Linac, similar to medical linacs, at ISU was measured to be less than 0.4~$\mu$m as measured by the OTR based tool described above when accelerating electrons to an energy of 15~MeV. The normalized emittance may be obtained by multiplying the projected emittance by the average relativistic factor $\gamma$ and $\beta$ of the electron beam. We plan to perform similar measurements over the energy range of the linac in the near future.

\section{ACKNOWLEDGMENT} We would like to acknowledge the outstanding efforts of Idaho Accelerator Center. This work was supported by DOE award \# DE-SC0002600. %Thanks to C. F. Eckman, C. O'Neill, and Dr. D. Wells. \begin{thebibliography}{9} % Use for 1-9 references

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