Difference between revisions of "Sadiq Proposal Defense"

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= Abstract =
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[[File:sadiq_proposal.pdf]]
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= Introduction =
 
  
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I propose to measure the efficiency of producing positrons using the High Repetition Rate Linac (HRRL) S-band electron linear accelerator.  HRRL cavity is located at the Beam Lab of the Physics Department, at Idaho State University (ISU).
 
  
−
The HRRL facility is divided into two parts by a L-shaped cement wall. The accelerator cell houses the linac and magntic elements needed to transport electrons.   The experimental cell is located in an adjacent room to the accelerator cell.  Previously cavity was located at the center of the accelerator cell, as shown in figure below. To adapt positron project, it was relocated to new position, as shown in same figure.
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= text =
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{| border="0" style="background:transparent;"  align="center"
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\documentclass{article} % essential first line
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|-
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\usepackage{float} % this is to place figures where requested!
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|
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\usepackage{times} % this uses fonts which will look nice in PDF format
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[[image:Sadiq_Pro_HRRL_Move_Plan.png | 300 px |thumb |Fig. Top view of the HRRL cavity room.]]
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\usepackage{graphicx} % needed for the figures
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|}
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\usepackage{url}
  
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\usepackage{rotating}
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\usepackage[none]{hyphenat}
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\usepackage{booktabs}
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\usepackage{epstopdf}
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\usepackage{subfig}
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\usepackage{graphicx}
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\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{subcaption}
  
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%\usepackage{epsfig}
  
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\tolerance=1 % no hyphenation, no zig-zag line.
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Original HRRL beamline was designed by G. Stancari. Based on this designed, it was improved by Dr. Y. Kim, and was finalized by John Ellis. Design is shown on the following figure.
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%\restylefloat{figure}
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{| border="0" style="background:transparent;"  align="center"
 
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[[image:HRRL03242011_dwg.png | 800 px |thumb |Fig. Final HRRL beamline by John Ellis.]]
 
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|}
 
  
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The beam parts were listed in the following table given by John Ellis.
+
%\usepackage{lipsum}% http://ctan.org/pkg/lipsum
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%\usepackage[demo]{graphicx}% http://ctan.org/pkg/graphicx
  
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{| border="1" cellpadding="5" cellspacing="0"
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%% Here I adjust the margins
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| Label || Beam Line Element|| Z location from Gate Valve center of element || Dimensions of Element
 
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|-
 
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|T1||Torroid 1 ||  -0.05 m||
 
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|-
 
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|G1|| Fast Gate Valve || 0.000 m ||
 
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|-
 
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|STXY1|| X-Y steerers 1 ||  || want to locate before Q1!
 
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|-
 
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|Q1 || First Quad|| 0.195 m || (was moved from 0.175 to 0.195)
 
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|-
 
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|Q2 || Second Quad ||0.435 m || (was moved from 0.425 to 0.435)  (24 cm to Q1)
 
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|-
 
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|Q3|| Third Quad || 0.675 m ||(24 cm to Q2)
 
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|-
 
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|STXY2|| X-Y steerers 2 ||  ||
 
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|-
 
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|Targ1 || positron production target || 1.175 m ||
 
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|-
 
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|Q4 || Fourth Quad ||1.635 m  || (was 1.4 now 1.635)
 
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|-
 
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|Q5|| Fifth Quad || 1.659 m  || was 1.650 drawing has 1.899 we want it at 1.659  (want distance to Q4 to be 24 cm)
 
−
|-
 
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|Q6 || Sixth Quad || 1.683||was at 1.8 drawing has it at 2.163 we want it at 1.683 (want distance to Q5 to be 24 cm)
 
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|-
 
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|STXY3|| X-Y steerers 3 ||  ||
 
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|-
 
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|F1 || OTR Flag ||  ||
 
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|-
 
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|FC1 || Faraday Cup 1 || ||
 
−
|-
 
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|D1 || First Kiwi Dipole  || 2.702 m  || was 2.525 now it is 2.702
 
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|-
 
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|S1 || Energy Slits  || 3.076 m || was 2.851 now at 3.076
 
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|-
 
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|STXY4|| X-Y steerers 4 ||  ||
 
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|-
 
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|Q7 || Seventh Quad || 3.317 m || was at 3.026 now at 3.317
 
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|-
 
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|F2 || Yag SCREEN ||  m || attach directly to Dipole D2 and put bellows upstream, drawing has it backwards
 
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|-
 
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|D2 || Second Kiwi Dipole || 4.019 m || was at 3.617 now at 4.019
 
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|-
 
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|Q8 || Eigth Quad ||4.616 m || 
 
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|-
 
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|STXY5|| X-Y steerers 5 ||  ||
 
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|-
 
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|Q9 || Quad || 5.026 m ||
 
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|-
 
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|Q10 || Quad ||5.436 m ||
 
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|-
 
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|T2 || Torroid 2 ||  ||
 
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|-
 
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|F3 || Third Flag || 5.976 m ||
 
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|-
 
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|Targ2 || Brehm target ladder ||  m ||
 
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|-
 
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| || HOLE@WALL || 6.412 m ||
 
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|}
 
  
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Electron beam out of cavity will pass through first set of quadruple triplet magnets, which is going to focus electron beam on the positron target. Positrons created in the target will be collected second set of quadruple triplet, then will be bent 45 degree by first dipole magnet. Positron target can be placed in or removed from beam line, so that we run positron or electron dual mode. Accordingly, we change the polarity of the dipoles to run on e-/e+ modes. The The second dipole will bend beam another 45 degree, thus complete total of 90 degree bend. Third set of quadruple triplet will be used create e-/e+ beam profile that sutable for users' specific need.
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\oddsidemargin -0.25in % Left margin is 1in + this value
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\textwidth 6.75in % Right margin is not set explicitly
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%\topmargin 0in % Top margin is 1in + this value
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\topmargin -1in % Top margin is 0in + this value
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\textheight 9in % Bottom margin is not set explicitly
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\columnsep 0.25in % separation between columns
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%\setlength{\parindent}{15pt}
  
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= Motivation =
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%% Define a macro for inserting postscript images
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%% ==============================================
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%% This is a macro which nominally takes 3 parameters,
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%% it would be used as follows to insert and encapsulated postscript
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%% image at the location where it is used.
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%%
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%% \EPSFIG{epsfilename}{caption}{label}
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%% - epsfilename is the name of the encapsulated postscript file to be
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%%              inserted at this location
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%% - caption is the text to be shown as the figure caption, it will be
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%%          prepended by Figure X.  The number X can be referenced
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%%          using the label parameter.
 +
%% - label is a name given to the figure, it can be referenced using the
 +
%%        \ref{label} command.
  
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= Emittance =
+
\def\EPSFIG[#1]#2#3#4{ % Don't be scared by this monsrosity
−
== What is Emittance ==
+
\begin{figure}[H] % it is a macro to save typing later
−
In accelerator physics, Cartesian coordinate system was used to describe motion of the accelerated particles. Usually the z-axis of Cartesian coordinate system is set to be along the electron beam line as longitudinal beam direction. X-axis is set to be horizontal and perpendicular to the longitudinal direction, as one of the transverse beam direction. Y-axis is set to be vertical and perpendicular to the longitudinal direction, as another transverse beam direction.
+
\begin{center} %
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\includegraphics[#1]{#2} %
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\end{center} %
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\caption{#3} %
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\label{#4} %
 +
\end{figure} %
 +
} %
  
−
For the convenience of representation, we use <math>z</math> to represent our transverse coordinates, while discussing emittance. And we would like to express longitudinal beam direction with <math>s</math>. Our transverse beam profile changes along the beam line, it makes <math>z</math> is function of <math>s</math>, <math>z~(s)</math>. The angle of a accelerated charge regarding the designed orbit can be defined as:
 
  
−
<math>z'=\frac{dz}{ds}</math>
+
%% Define the fields to be displayed by a \maketitle command
  
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If we plot <math>z</math> vs. <math>z'</math>, we will get an ellipse. The area of the ellipse is an invariant, which is called Courant-Snyder invariant. The transverse emittance <math>\epsilon</math> of the beam is defined to be the area of the ellipse, which contains 90% of the particles <ref name="MConte08"> M. Conte and W. W. MacKay, “An Introduction To The Physics Of Particle Accelera
+
\author{Sadiq Setiniyaz (Shadike Saitiniyazi)\thanks{Email: sadik82@gmail.com}}
−
tors”, World Scientifc, Singapore, 2008, 2nd Edition, pp. 257-330. </ref>.
+
%{address={Department of Physics, Idaho State University}}
 +
\title{PROPOSAL FOR POSITRON PRODUCTION EFFICIENCY STUDY USING HIGH REPETITION RATE LINAC AT IAC}
  
 +
%%
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%% Header now finished
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%%
  
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{| border="0" style="background:transparent;"  align="center"
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\begin{document} % Critical
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\twocolumn
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|
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\thispagestyle{empty} % Inhibit the page number on this page
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[[image:sadiq_phd_emittance_phase_space_ellipse.png | 200 px |thumb |Fig.1 Phase space ellipse <ref name="MConte08"></ref>.]]
+
\maketitle % Use the \author, \title and \date info
−
|}
 
  
−
== Measurement of Emittance with Quad Scanning Method ==
+
%% Next comes the abstract, notice the curly-braces surrounding the
 +
%% text.
  
 +
\abstract{
 +
\indent
  
−
In quadrupole scan method, a quadrupole and a Yttrium Aluminum Garnet (YAG ) screen was used to measure emittance. Magnetic field strength of the quadrupole was changed in the process and corresponding beam shapes were observed on the screen.
+
I propose to measure the positron production efficiency for a positron source that uses a quadrupole triplet system to collect positrons from a tungsten target that are produced when the target is impinged by electrons from the High Repetition Rate Linac (HRRL) at Idaho State University's (ISU) Idaho Accelerator Center (IAC). Positrons were observed in May of 2008 at the IAC without the use of a quadrupole triplet collection system. When a 10~MeV electron beam is used on the tungsten target, positrons escaping from the downstream side of the tungsten have a wide momentum spread of 0 to 2~MeV and a large divergence of $\pi$ rad. A quad triplet collection system, after the tungsten target, is used to focus the positron beam and as a result increase our positron collection efficiency. I will install the collection system and associated beam line components and measure the positron production efficiency using the HRRL.}
−
Transfer matrix of a quadrupole magnet under thin lens approximation:
 
  
−
:<math>
+
\section{Introduction}
−
\left( \begin{matrix} 1 & 0 \\ -k_{1}L & 1  \end{matrix} \right)=\left( \begin{matrix} 1 & 0 \\ -\frac{1}{f} & 1  \end{matrix} \right)
+
\indent
−
</math>
 
  
−
Here, <math>k_{1} L</math> is quadrupole strength, <math>L</math> is quadrupole magnet thickness, and f is quadrupole
+
I propose to measure the positron production efficiency for a positron source that uses a quadrupole triplet system to collect positrons from a tungsten target that are produced when the target is impinged by electrons from the HRRL. A polarized positron source, as a new probe to explore nuclear and particle physics at Jefferson Lab, is being studied at the Continuous Electron Beam Accelerator Facility (CEBAF). While their main mission is to optimize polarization, ISU's goal is to optimize positron production efficiency. Additionally, a positron beamline at ISU is also a potential tool for nuclear physics studies. I have measured the emittance of the HRRL electron beam and constructed PMT bases for four NaI detectors. I will install the collection system and associated beam line components to measure the positron production efficiency using the HRRL.
−
focal length. <math> k_{1} L > 0 </math> for x-plane, and <math> k_{1} L < 0 </math> for y-plane. Transfer matrix of a drift
 
−
space between quadrupole and screen:
 
  
−
:<math>  \mathbf{S} = \left( \begin{matrix} S_{11} & S_{12} \\S_{21} & S_{22}  \end{matrix} \right)=\left( \begin{matrix} 1 & l \\ 0 & 1  \end{matrix} \right)
+
\section{Previous Measurements}
−
</math>
+
\indent
  
−
Here,  <math>l</math> (<math>S_{12}</math>) is the distance from the center of the quadrupole to the screen.
+
Earlier positron production measurements were conducted at ISU's IAC in the May of 2008. The setup is shown in Fig.~\ref{fig:2008-pos-beamline} and the beamline elements are described in Table~\ref{tab:2008-pos-beamline-elements}. The accelerator was operated at a 300~Hz repetition rate and 10~MeV energy. Electrons were bent by the first dipole and sent to a 2~mm thick tungsten target. Any positrons produced were focused using two quadrupoles and bent 45 degrees by a second dipole which was set to transport 3~MeV positrons. Positrons were transported to the end of the linac where they annihilated in a Ta target. A HpGe and a NaI detector were used to detect the 511~keV positrons produced as a result of annihilation. Fig.~\ref{fig:2008-spectrum} shows the spectrum taken over a 600 second time interval.
−
Transfer matrix of the scanned region is:
 
  
−
<math>
 
−
\mathbf{M}  =
 
−
\mathbf{SQ}  =
 
−
\begin{pmatrix}
 
−
  m_{11} & m_{12}  \\
 
−
  m_{21} & m_{22}
 
−
\end{pmatrix}=
 
−
\begin{pmatrix}
 
−
  S_{11} & S_{12}  \\
 
−
  S_{21} & S_{22}
 
−
\end{pmatrix}
 
−
\begin{pmatrix}
 
−
  1 & 0  \\
 
−
  -k_1L & 1
 
−
\end{pmatrix}=
 
−
\begin{pmatrix}
 
−
  S_{11} - k_1LS_{12} & S_{12}  \\
 
−
  S_{21} - k_1L S_{22} & S_{22}
 
−
\end{pmatrix}
 
−
</math>
 
  
 +
\begin{figure}[htbp]
 +
\centering
 +
\includegraphics[width=80mm]{2008_positron_measurement_at_IAC.eps}
 +
\caption{The HRRL beamline configured for positron production at IAC in 2008. }
 +
\label{fig:2008-pos-beamline}
 +
\end{figure}
  
−
<math>\mathbf{M}</math> is related with the beam matrix <math>\mathbf{\sigma}</math> as:
+
\begin{table}[htbp]
 +
\caption{Beamline elements for positron production at IAC in 2008.}
  
 +
\begin{tabular}{ll}
 +
\hline
 +
      \textbf{Item} & {$\textbf {Description}$} \\
 +
\hline
 +
          Tantalum foil  &  6 mm thick 20 mm x 20 mm area  \\
 +
          Tungsten foil  &  2 mm thick 20 mm x 20 mm area    \\
 +
          Phosphorus flag  & 1 mil aluminum backing            \\
 +
          HpGe detector & 81.3mm Diameter, 55.5mm Length \\
 +
          %NaI detector &
 +
\hline
 +
\end{tabular}
 +
\label{tab:2008-pos-beamline-elements}
 +
\end{table}
  
−
<math>
+
\begin{figure}[htbp]
−
\mathbf{ \sigma_{screen}}  =
+
\centering
−
\mathbf{M \sigma_{quad} M^T}  =
+
   \includegraphics*[scale=0.45]{2008_Run60_HpGe-NaI}
−
\begin{pmatrix}
+
\caption{Spectrum from HpGe Detector and NaI detecotrs.}
−
  m_{11} & m_{12}  \\
+
\label{fig:2008-spectrum}
−
   m_{21} & m_{22}
+
\end{figure}
−
\end{pmatrix}
 
−
\begin{pmatrix}
 
−
  \sigma_{quad, 11} &  \sigma_{quad, 12}  \\
 
−
  \sigma_{quad, 21} &  \sigma_{quad, 22}
 
−
\end{pmatrix}
 
−
\begin{pmatrix}
 
−
  m_{11} & m_{12}  \\
 
−
  m_{21} & m_{22}
 
−
\end{pmatrix}
 
−
</math>
 
  
−
Since:  
+
%\begin{figure}[htbp]
 +
%\centering
 +
%  \includegraphics[scale=0.45]{2008_PositronYield_SweeperMagnet_run60-61}
 +
%\caption{Spectrum.}
 +
%\label{fig:2008-spectrum-zoom}
 +
%\end{figure}
  
−
<math>
 
−
\sigma_{x}=\sqrt{\epsilon_x\beta},~\sigma_{x'}=\sqrt{\epsilon_x\gamma},~\sigma_{xx'}={-\epsilon_x\alpha}
 
−
</math>
 
  
−
<math>
+
\section{Proposed Beamline}
−
\mathbf{ \sigma} =
+
\indent
−
\begin{pmatrix}
 
−
  \sigma_{11} &  \sigma_{12}  \\
 
−
  \sigma_{21} &  \sigma_{22}
 
−
\end{pmatrix} =
 
−
\begin{pmatrix}
 
−
  \sigma_{x}^2 &  \sigma_{xx'}  \\
 
−
  \sigma_{xx'} &  \sigma_{x'}^2
 
−
\end{pmatrix}
 
−
</math>
 
  
  
−
So, <math>\mathbf{\sigma}</math> matrix can be written as:
+
I propose a measurement of the positron production efficiency using the HRRL. The HRRL can provide electron beams with energies between 3~MeV and 16~MeV, and a maximum repetition rate of 300~Hz. The HRRL beamline has recently been reconfigured to generate and collect positrons, see Fig.~\ref{fig:HRRL-e+-line} and Table~\ref{tab:hrrl}.
−
<math>
 
−
\mathbf{\sigma}_{quad}  =
 
−
\begin{pmatrix}
 
−
  \sigma_{quad, x} &  \sigma_{quad, xx'}  \\
 
−
  \sigma_{quad, xx'} &  \sigma_{quad, x,}
 
−
\end{pmatrix} =
 
−
\epsilon_{rms, x}
 
−
\begin{pmatrix}
 
−
  \beta    & -\alpha    \\
 
−
  -\alpha  &  \gamma
 
−
\end{pmatrix}
 
−
</math>
 
  
−
Substituting this give:
+
\begin{table}[hbt]
 +
  \centering
 +
  \caption{Operational Parameters of The 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      &  300  \\
 +
        \midrule
 +
        macro-pulse pulse length (FWHM)          &  ns      &  250    \\
 +
        \midrule
 +
        rms energy spread                                &  \%      &  4.23  \\
 +
  \bottomrule
 +
\end{tabular}
 +
\label{tab:hrrl}
 +
\end{table}
  
−
<math>
+
The new beamline was first designed by Dr. G. Stancari to use a quadrupole triplet system to collect positrons~\cite{stancari}. The design was further optimized by Dr. Y Kim. The final design of the beamline is shown in Fig.~\ref{fig:HRRL-e+-line}. The HRRL accelerator room is divided into two parts by an L-shaped cement wall. The accelerator cell houses the cavity and other elements needed to transport electrons to an experimental cell. The experimental cell is located in a room adjacent to the accelerator cell. The HRRL beamline was reconfigured into an achromat by moving the accelerator cavity to accommodate two dipoles and a system of quadrupole magnets optimized for collecting positrons.
−
\mathbf{ \sigma_{screen}}  =
 
−
\mathbf{M \sigma_{quad} M^T}  =
 
−
\begin{pmatrix}
 
−
  m_{11} & m_{12}  \\
 
−
  m_{21} & m_{22}
 
−
\end{pmatrix}
 
−
\epsilon_{rms, x}
 
−
\begin{pmatrix}
 
−
  \beta    & -\alpha    \\
 
−
  -\alpha  &  \gamma
 
−
\end{pmatrix}
 
−
\begin{pmatrix}
 
−
  m_{11} & m_{12}  \\
 
−
  m_{21} & m_{22}
 
−
\end{pmatrix}
 
−
</math>
 
  
 +
In the new beamline, shown in Fig.~\ref{fig:HRRL-e+-line}, the electron beam exits the cavity and passes through a quadruple triplet  that will focus the electron beam onto the positron target. Positrons produced from the positron target will be collected by the second quadruple triplet that will be optimized to collect positrons. The first dipole magnet bends the positrons/electrons, depending on the magnet polarity, by 45 degrees towards the second dipole magnet. The second dipole will bend the beam another 45 degrees, thus completing a 90 degree bend. A third quadruple triplet will focus the e-/e+ beam, as users desire. All beam elements are described in Table~\ref{tab:new-hrrl-line-elements}.
  
−
Dropping off subscript "rms" on emittance <math>\epsilon_{rms, x}</math>:
 
−
<math>
 
−
\sigma_{screen, 11}=\sigma_{screen, x}^2=\epsilon_x (m_{11}^2\beta - 2m_{12}m_{11}\alpha+m_{12}^2\gamma)
 
−
</math>
 
  
  
 +
%\begin{figure*}[htbp]
 +
\begin{sidewaysfigure*}[htbp]
  
−
Using <math>\mathbf{\sigma}</math> matrix relations:
+
\centering
 +
%\includegraphics[scale=0.28]{HRRL_Pos_and_Ele_Go}
 +
\includegraphics[scale=0.35]{HRRL_Pos_and_Ele_Go.eps}
 +
\caption{The new HRRL beamline cofiguration for positron generation.}
 +
\label{fig:HRRL-e+-line}
 +
\end{sidewaysfigure*}
  
−
<math>
+
%\end{figure*}
−
\sigma_{x}={\epsilon_x\beta},~\sigma_{12}={-\epsilon_x\alpha},~{\epsilon_x\gamma}=\epsilon_x \frac{1+\alpha^2}{\beta}=\frac{\epsilon_x^2+\sigma_{12}^2}{\sigma_{11}}
 
−
</math>
 
  
−
Here <math>\sigma_{x}</math> is <math>\sigma_{screen, x}</math>.  We got:
 
  
−
<math>
 
−
\sigma_{x}^2=m_{11}^2 \sigma_{11}  + 2m_{12}m_{11} \sigma_{12} + m_{12}^2 \frac{\epsilon_x^2+\sigma_{12}^2}{\sigma_{11}} 
 
−
</math>
 
  
−
<math>
+
\begin{table}[hbt]
−
\sigma_{x}^2=\sigma_{11} \left(m_{11}^2 + 2m_{11}m_{12}\frac{\sigma_{12}}{\sigma_{11} }+ m_{12}^2\frac{\sigma_{12}^2}{\sigma_{11}^2}\right) + m_{12}\frac{\epsilon_x^2}{\sigma_{11}} 
+
  \centering
−
</math>
+
  \caption{The new HRRL positron beamline elements.}
 +
  \begin{tabular}{lccc}
 +
      \toprule
 +
        Item  &  Description \\
 +
      \midrule
 +
        T1    & Positron target \\
 +
      \midrule
 +
        T2    &  Annihilation target \\
 +
        \midrule
 +
        EnS    & Energy Slit  \\
 +
        \midrule
 +
        FC1, FC2& Faraday Cups \\
 +
        \midrule
 +
        Q1,...Q10     & Quadrupoles \\
 +
        \midrule
 +
          D1, D2     & Dipoles \\
 +
        \midrule
 +
        NaI    &  NaI Detecotrs \\
 +
        \midrule
 +
        OTR    & Optical Transition Radiaiton screen\\
 +
        \midrule
 +
        YAG    & Yttrium Aluminium Garnet screen\\
 +
  \bottomrule
 +
\end{tabular}
 +
\label{tab:new-hrrl-line-elements}
 +
\end{table}
  
−
<math>
+
%00000000000000000000000000000000000000000000000000000000000
−
\sigma_{x}^2=\sigma_{11}\left(m_{11} + m_{12}\frac{\sigma_{12}}{\sigma_{11} }\right)^2  + m_{12}\frac{\epsilon_x^2}{\sigma_{11}} 
+
\section{Preparation for the Positron \\ Production Experiment}
−
</math>
+
\subsection{HRRL Emittance measurements}
 +
\indent
  
−
Recall:
 
  
−
<math>
+
Emittance, a key parameter in accelerator physics, is used to quantify the quality of an electron beam produced by an accelerator. The beam size and divergence at any point in the beamline can be described using emittance and Twiss parameters.
−
m_{11} = S_{11}-kLS_{12}~~~~~~m_{12}=S_{12}
 
−
</math>
 
  
−
Substituting and reorganizing result in:
+
An Optical Transition Radiation (OTR) based viewer was installed to allow measurements at the high electron currents available from 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 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.
  
−
<math>
+
The emittance of the HRRL was measured to be less than 0.4~$\mu$m using the OTR based tool at an energy of 15~MeV.  The details of this emittance measurement using the quadrupole scanning method were described in the IPAC12 proceedings~\cite{setiniyaz-q-scan}. The results are summarized in Table~\ref{results}.
−
\sigma_{x}^2=\sigma_{11} {S_{12}^2}\left(kL - \left( \frac{S_{11}}{S_{12}} + \frac{\sigma_{12}}{\sigma_{11}} \right) \right)^2 + S_{12}^2\frac{\epsilon_x^2}{\sigma_{11}} 
 
−
</math>
 
  
−
Introducing constants <math>A</math>,<math>B</math>, and <math>C</math>
+
\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                          &  35          \\
 +
  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}
  
−
<math>
+
\subsection{Positron Detection using NaI crystals}
−
A = \sigma_{11} {S_{12}^2},~~B =  \frac{S_{11}}{S_{12}} + \frac{\sigma_{12}}{\sigma_{11}},~~C = S_{12}^2\frac{\epsilon_x^2}{\sigma_{11}}
+
\indent
−
</math>
 
  
−
This will simplify equation to:
+
A tungsten target will be placed at the end of the 90 degree beamline to annihilate positrons. I want to use two NaI detectors to detect the 511~keV photons created when positrons annihilate. I acquired some NaI crystals from Idaho Accelerator Center (IAC). Since their original bases used a slow post-amplifier, I built new PMT bases. I modified the design of model PA-14 from Saint-Gobain Crystals \& Detectors Ltd. These detectors are tested, calibrated, and ready to be used for the measurement. Fig.~\ref{fig:IAC-dets} shows the crystals and the bases I built. Fig.~\ref{fig:IAC-dets-Co60-Na22-spec} shows the spectrum taken by the detector using button sources.
 +
%I expect by doing coincidence, the resolution of 511~keV peak in the spectrum will be improved.
  
−
<math>
+
\begin{figure}[htbp]
−
\sigma_{x}^2=A(kL - B)^2 + C = A(kL)^2 - 2AB(kL)+(C+AB^2)
+
\centering
−
</math>
+
\includegraphics[scale=0.08]{IAC_NaI_Detectors}
 +
\caption{The NaI detector and base built.}
 +
\label{fig:IAC-dets}
 +
\end{figure}
  
−
It is easy to see that:
+
\begin{figure}[htbp]
 +
\centering
 +
\includegraphics[scale=0.18]{Na22_Co60Spectrum_by_IAC_Detectors}
 +
\caption{Detector 3 calibrated Spectrum.}
 +
\label{fig:IAC-dets-Co60-Na22-spec}
 +
\end{figure}
  
−
<math>
+
%\subsection{Positron Target Installation}
−
\epsilon = \frac{\sqrt{AC}}{S_{12}^2}
+
%\indent
−
</math>
+
%
 +
%A step motor is ready to be installed once the vacuum chamber is ready. The step motor, shown in the Fig.~\ref{fig:step-motor}, will hold 8 tungsten targets.
 +
%
 +
%\begin{figure}[htbp]
 +
%\centering
 +
%\includegraphics[scale=0.08]{setep_motor}
 +
%\caption{Step motor for holding W targets.}
 +
%\label{fig:step-motor}
 +
%\end{figure}
  
−
By changing quadrupole magnetic field strength <math>k</math>, we can change beam sizes <math>\sigma_{x,y}</math> on the screen. We make projection to the x, y axes, then fit them with Gaussian fittings to extract rms beam sizes, then plot vs <math>\sigma_{x,y}</math> vs <math>k_{1}L</math>. By Fitting a parabola we can find constants
+
\section{Future Plan}
−
<math>A</math>,<math>B</math>, and <math>C</math>, and get emittances.
+
\indent
  
−
== First Emittance Measurement Experiment ==
+
We want to produce positrons using the HRRL beam line. We can improve positron collection efficiency by applying following methods:
−
In July 2010y, Emittance measurement of HRRL was conducted at Beam Lab, at Physics Department of ISU. We installed a YAG crystal on the HRRL beam line to see electron beam. A quadrupole magnet was installed between HRRL gun and the YAG screen. We changed current on the quadrupole to control magnetic field strength of the quadrupole magnet, thus we changed electron beam shape on the YAG screen.
 
  
−
=== Experimental Setup ===
+
1. By using a quadrupole triplet before tungsten a target, we will have control over the beam size and divergence at the target.
  
−
We did quadrupole scan to measure emittance of the electron beam in HRRL. In quadrupole scan method, the strength of the quadrupole magnet was changed by changing the current go through quadrupole coils. The electron beam were coming out of the gun went through quadrupole, then beam would enter a 3-way cross. Two end of the 3-way cross was installed on the beam line. The third end of the 3-way cross was placed upward and there was a actuator installed to it.  The YAG crystal was mounted in the actuator, which can put the YAG in the beam line or take it out of the beam line. A camera was placed inside the actuator to look through vacuum a window and to capture the image on the YAG crystal created by electron beam. A Faraday cup was mounted at the end of the beam line to measure the transmission of the charge.
+
2. Cryogenically cooled converter will be installed, and these targets will be able to take on more beam power and increase positron yield.
  
−
Setup and beam line and are shown in figures 1.2 and 1.3:
+
3. Positrons will be collected by the quadrupole triplet system, which will improve collection efficiency.
  
−
{| border="0" style="background:transparent;"  align="center"
+
4. Simulations will optimize beam elements for positron collection.
−
|-
 
−
|
 
−
[[image:sadiq_phd_emittance_HRRL_July_Emit_Lay_Out.png | 470 px |thumb|Fig.2 Experiment set up of HRRL 2010 July emittance test.]]
 
−
|
 
−
[[image:Constructed Beam Line for Emittance Test 1.jpg | 300 px |thumb|Fig.3 Beam Line of HRRL 2010 July emittance test.]]
 
−
|}
 
  
 +
%\bibliographystyle{unsrt} % Order by citation
 +
%\bibliography{report}
  
−
Figures 4, 5, and 6 show Faraday cup, Quadrupole Magnet, and YAG Chrystal used in the test:
+
\begin{thebibliography}{9}
 +
%{stancari}
 +
%@techreport{stancari,
 +
% title      ={{stancari's proposal-------}},
 +
% month      ={Nov.},
 +
% year = {2005},
 +
% author      ={J. Stancari},
 +
% address    ={Frascati, Italy},
 +
% number      ={},
 +
% institution ={DAFNE Technical Note}
 +
\bibitem{stancari}
 +
G. Stancari and T. Forest "Design of a new beamline for electrons, positrons and photons at the HRRL lab", Pocatello, ID, USA (2009).
  
−
{| border="0" style="background:transparent;"  align="center"
 
−
|-
 
−
|
 
−
[[image:Beam_Line_Parts_HRRL_Emittance_Test_FC.jpg | 280 px |thumb|Fig.4 Faraday cup used for HRRL 2010 July emittance test.]]
 
−
|
 
−
[[image:Beam_Line_Parts_HRRL_Emittance_Test_QuadT1.jpg | 200 px |thumb|Fig.5 Quadrupole Magnet used for HRRL 2010 July emittance test.]]
 
−
|
 
−
[[image:Beam_Line_Parts_HRRL_Emittance_Test_YAG.jpg | 240 px |thumb|Fig.6 YAG Christal used for HRRL 2010 July emittance test.]]
 
−
|}
 
  
−
=== Experiment ===
+
%@techreport{OTR,
 +
% title      ={{Optical Transition Radiation}},
 +
% month      ={},
 +
% year = {1992},
 +
% author      ={B. Gitter},
 +
% address    ={Los Angeles, CA 90024},
 +
% institution ={Particle Beam Physics Lab, Center for Advanced Accelerators, UCLA Department of Physics}
 +
%}
  
−
Emittance measurement was carried out on HRRL on July of 2010 under the experimental setup discussed in previous section. In this measurement we used analog camera to take images.  
+
\bibitem{OTR}
 +
B. Gitter, Tech. Rep., Los Angeles, USA (1992).
  
−
When relativistic electron beam pass through YAG target, Opitcal Transition Radiation (OTR) is produced. OTR are taken for different quadrupole coil current (0-20 A).
+
%\bibitem{setiniyaz-q-scan}
 +
%@InProceedings{setiniyaz-q-scan,
 +
%  author = {S. Setiniyaz, K. Chouffani, T. Forest, and Y. Kim},
 +
%  title = {TRANSVERSE BEAM EMITTANCE MEASUREMENTS OF A 16 MeV LINAC AT THE IDAHO ACCELERATOR CENTER},
 +
% booktitle = {IPAC2012},%pages = {151--158},
 +
% year = 2012,
 +
% address = {New Orleans, USA}
 +
%}
 +
\bibitem{setiniyaz-q-scan}
 +
S. Setiniyaz, K. Chouffani, T. Forest, and Y. Kim, in $Proc$. $IPAC2012$, New Orleans, USA.
  
 +
%\bibitem{emit-mat}
 +
%C.F. Eckman $et$ $al$., in $Proc$. $IPAC2012$, New Orleans, USA.
  
−
{|  border="0" style="background:transparent;"  align="center"
 
−
|-
 
−
| [[image:HRRL_Emit_test_Quad_Scan_First_0Amp.jpg | 300 px |thumb|Fig. OTR image of 0 Amp quadrupole coil current.]] ||[[image:HRRL_Emit_test_Quad_Scan_First_5Amp.jpg | 300 px |thumb|Fig. OTR image of 5 Amp quadrupole coil current.]] ||[[image:HRRL_Emit_test_Quad_Scan_First_10Amp.jpg | 300 px |thumb|Fig. OTR image of 10 Amp quadrupole coil current.]]
 
−
|-
 
−
|[[image:HRRL_Emit_test_Quad_Scan_First_15Amp.jpg | 300 px |thumb|Fig. OTR image of 15 Amp quadrupole coil current.]] ||[[image:HRRL_Emit_test_Quad_Scan_First_20Amp.jpg | 300 px |thumb|Fig. OTR image of 20 Amp quadrupole coil current.]] ||
 
−
[[image:HRRL_Emit_test_Quad_Scan_Second_10Amp_2.jpg | 300 px |thumb|Fig. OTR image of -10 Amp quadrupole coil current.]]
 
−
|}
 
  
−
=== Data Analysis ===
+
\end{thebibliography}
  
−
In the mages we can see a bright spot at the center. This spot did not change by changing quad coil current. So, this is image of hot filament. The bigger spot at the right side of the filament was changing by changing quad coil current, hence it is OTR. We also see 10 mm circle mounted on the OTR target, as well as beam hallow.
+
\end{document}
−
 
 
−
We did Guassian fits to beam image to extract x, y RMS values for different quad currents. We discovered that the camera was rotated slightly. To compensate for images were rotated, so that we have beam image upright. To reduce back ground, we just focused on OTR beam image and took out the filament spot from data, as shown in image below.
 
−
 
 
−
{|  border="0" style="background:transparent;"  align="center"
 
−
|-
 
−
| [[image:Fit_Rotated_HRRL_Emit_test_Quad_Scan_Second_2Amp.jpg | 400 px |thumb|Fig. Gaussian fits for OTR images.]]
 
−
|}
 
−
 
 
−
Each image was fitted 7 times, and RMS values are extracted and listed below.
 
−
 
 
−
Positive quad coil current
 
−
 
 
−
{| border="1"  |cellpadding="20" cellspacing="0 ;"  align="center"
 
−
|-
 
−
| Coild Current (Amps) ||  Mean and Error
 
−
|-
 
−
 
 
−
| 0  ||  <math>{\sigma}_{x,y}=  25.3\pm2.2  , 25.2 \pm1.9    </math>
 
−
|-
 
−
 
 
−
| 1  ||  <math>{\sigma}_{x,y}=  27.5\pm4.6  , 24.8 \pm 2.7  </math>
 
−
|-
 
−
 
 
−
| 2  ||  <math>{\sigma}_{x,y}= 31.4 \pm 6.9 , 23.8 \pm 2.8  </math>
 
−
|-
 
−
 
 
−
| 3  ||  <math>{\sigma}_{x,y}= 35.3 \pm 5.0 , 21.8 \pm 4.7  </math>
 
−
|-
 
−
 
 
−
| 4  ||  <math>{\sigma}_{x,y}= 35.4 \pm 5.5 , 20.0 \pm 4.1  </math>
 
−
|-
 
−
 
 
−
| 5  ||  <math>{\sigma}_{x,y}= 37.0 \pm 4.2 , 17.6 \pm 0.6  </math>
 
−
|-
 
−
 
 
−
| 6  ||  <math>{\sigma}_{x,y}= 38.6 \pm 4.8 , 16.1 \pm  0.4  </math>
 
−
|-
 
−
 
 
−
| 7  ||  <math>{\sigma}_{x,y}= 42.4 \pm 3.8 , 15.4 \pm 0.5  </math>
 
−
|-
 
−
 
 
−
| 8  ||  <math>{\sigma}_{x,y}= 42.4 \pm 2.3 , 15.0 \pm  0.5  </math>
 
−
|-
 
−
 
 
−
| 9  ||  <math>{\sigma}_{x,y}= 42.8 \pm 2.4 , 14.1 \pm 1.2  </math>
 
−
|-
 
−
 
 
−
| 10  ||  <math>{\sigma}_{x,y}= 44.6 \pm 2.2 , 14.4 \pm  0.3  </math>
 
−
|-
 
−
 
 
−
| 11  ||  <math>{\sigma}_{x,y}= 46.6 \pm 0.6 , 13.5 \pm 1.0  </math>
 
−
|-
 
−
 
 
−
| 12  ||  <math>{\sigma}_{x,y}= 47.3 \pm 2.0 , 12.1 \pm 0.5  </math>
 
−
|-
 
−
 
 
−
| 13  ||  <math>{\sigma}_{x,y}= 49.9 \pm 1.0 , 11.6 \pm 0.4  </math>
 
−
|-
 
−
 
 
−
| 14  ||  <math>{\sigma}_{x,y}= 51.5 \pm 0.7 , 11.5 \pm 0.2  </math>
 
−
|-
 
−
 
 
−
| 15  ||  <math>{\sigma}_{x,y}= 51.8 \pm 1.2 , 11.7 \pm 0.3  </math>
 
−
|-
 
−
 
 
−
| 16  ||  <math>{\sigma}_{x,y}= 53.4 \pm 1.1 , 12.3 \pm 0.5  </math>
 
−
|-
 
−
 
 
−
| 17  ||  <math>{\sigma}_{x,y}= 56.5 \pm 0.9 , 13.1 \pm 0.7  </math>
 
−
|-
 
−
 
 
−
| 18  ||  <math>{\sigma}_{x,y}= 56.4 \pm 1.9 , 13.6 \pm 0.4  </math>
 
−
|-
 
−
 
 
−
| 19  ||  <math>{\sigma}_{x,y}= 56.5 \pm 3.0 , 15.0 \pm 0.7  </math>
 
−
|-
 
−
 
 
−
| 20  ||  <math>{\sigma}_{x,y}= 57.8 \pm 2.4 , 18.0 \pm 1.0  </math>
 
−
|-
 
−
 
 
−
|}
 
−
 
 
−
 
 
−
Negative quad coil current
 
−
 
 
−
{| border="1"  |cellpadding="20" cellspacing="0 ; "  align="center"
 
−
|-
 
−
| Coild Current (Amps) || Mean and Error
 
−
|-
 
−
 
 
−
| 0  ||  <math>{\sigma}_{x,y}=31.1 \pm 3.1,34.9\pm3.8  </math>
 
−
|-
 
−
| 1  ||  <math>{\sigma}_{x,y}= 25.5 \pm 1.9 , 35.5 \pm 5.1  </math>
 
−
|-
 
−
| 2  ||  <math>{\sigma}_{x,y}= 25.2 \pm 1.5 , 40.1 \pm 6.0  </math>
 
−
|-
 
−
| 3  ||  <math>{\sigma}_{x,y}=23.5 \pm 1.1 , 39.6\pm 2.5  </math>
 
−
|-
 
−
| 4  ||  <math>{\sigma}_{x,y}= 20.4\pm 0.8 , 41.1\pm 2.2  </math>
 
−
|-
 
−
| 5  ||  <math>{\sigma}_{x,y}= 18.0 \pm 0.4 , 46.1 \pm 2.7  </math>
 
−
|-
 
−
| 6  ||  <math>{\sigma}_{x,y}= 16.2 \pm 0.3 , 49.2\pm 1.6  </math>
 
−
|-
 
−
| 7  ||  <math>{\sigma}_{x,y}= 13.3\pm0.4 , 47.8\pm 2.1  </math>
 
−
|-
 
−
| 8  ||  <math>{\sigma}_{x,y}= 12.3\pm 0.5 , 48.4 \pm 1.7  </math>
 
−
|-
 
−
| 9  ||  <math>{\sigma}_{x,y}= 13.3 \pm 0.1 ,53.0 \pm 2.0  </math>
 
−
|-
 
−
| 10  ||  <math>{\sigma}_{x,y}= 12.6 \pm 0.3 , 55.6 \pm 1.9  </math>
 
−
|-
 
−
| 11  ||  <math>{\sigma}_{x,y}= 10.1 \pm 0.4 ,54.4 \pm 2.4  </math>
 
−
|-
 
−
| 12  ||  <math>{\sigma}_{x,y}= 10.8\pm 0.9, 57.3\pm1.8  </math>
 
−
|-
 
−
| 13  ||  <math>{\sigma}_{x,y}= 8.9 \pm 0.2 , 56.8 \pm 2.3  </math>
 
−
|-
 
−
| 14  ||  <math>{\sigma}_{x,y}= 10.7 \pm 0.2 , 58.5\pm 2.3  </math>
 
−
|-
 
−
|  15 ||  <math>{\sigma}_{x,y}= 10.5 \pm 0.3 , 57.5 \pm 1.8  </math>
 
−
|-
 
−
|  16 ||  <math>{\sigma}_{x,y}= 11.3 \pm 0.4 , 59.4 \pm 2.9  </math>
 
−
|-
 
−
|  17 ||  <math>{\sigma}_{x,y}= 12.2 \pm 0.7 , 59.6 \pm 2.6  </math>
 
−
|-
 
−
|  18 || <math>{\sigma}_{x,y}= 12.4 \pm 0.6 , 59.0\pm 1.7  </math>
 
−
|-
 
−
|  19 || <math>{\sigma}_{x,y}= 13.5 \pm 2.7 , 57.8 \pm 2.9  </math>
 
−
|-
 
−
| 20 ||  <math>{\sigma}_{x,y}= 13.8 \pm 1.5 , 60.3 \pm 2.0  </math>
 
−
|-
 
−
| 22 ||  <math>{\sigma}_{x,y}= 13.3 \pm 2.4 , 59.8 \pm 2.1  </math>
 
−
|-
 
−
|}
 
−
 
 
−
Now, we need to convert pixels to physical length. Diameter of circle inside YAG crystal is 10 mm. Dividing 10 mm by the pixel numbers of the circle will give us conversion factor.
 
−
 
 
−
 
 
−
{| border="1"  |cellpadding="20" cellspacing="0 ;"  align="center"
 
−
|-
 
−
|      Average Horizontal Diameter (pixels)  ||  Average Vertical Diameter (pixels) 
 
−
|-
 
−
|      <math> 90.29 \pm 0.49 </math> ||  <math> 59.43 \pm 0.53 </math>
 
−
|-
 
−
|      Horizontal mm/pixels  ||  Vertical mm/pixels
 
−
|-
 
−
|      <math> 0.1108 \pm 0.0006 </math> ||  <math> (0.1683 \pm 0.0015)*cos45^{o} </math> = <math> 0.1190\pm 0.0011 </math> 
 
−
|-
 
−
|}
 
−
 
 
−
Magnetic coil current relation to the B-filed at the center of the quad was measured to be:
 
−
 
 
−
<math>  B(I) = (3.6 \pm 1.3) \times 10^{-3} + (1945 \pm 2) \times 10^{-5} I [kG] = (3.6 \pm 1.3) \times 10^{-4} + (1945 \pm 2) \times 10^{-6} I [T]  </math>
 
−
 
 
−
Quadrupole Strength is defined as:
 
−
 
 
−
<math>  k = 0.2998  \frac{g[T/m]}{p[GeV]}  </math>
 
−
 
 
−
g here is the gradient of the qudrupole. p is the momentum of the e- beam. In our case, energy of the beam is 0.01 GeV and gap between dipole center and pole face is 1 inch.
 
−
 
 
−
<math>  k = 0.2998  \frac{\frac{B(I)}{(1 inch)\times\frac{1 m}{1 inch}}[T/m]}{0.01 GeV}  </math>
 
−
 
 
−
Subsituting <math> B(I) </math> with current. So,
 
−
 
 
−
<math>  k = 0.2998  \frac{ (3.6 \pm 1.3) \times 10^{-4} + (1945 \pm 2) \times 10^{-6} I [T] }{0.01 \times 0.0254 [GeV][m]}  </math>
 
−
 
 
−
<math>  k =  (0.42 \pm 0.16) + (2.2956 \pm 0.0024) \times I</math>
 
−
 
 
−
 
 
−
 
 
−
 
 
−
=== Results ===
 
−
 
 
−
==== X Projection ====
 
−
 
 
−
[[File:HRRL_Emitt_2010_Jul_Refit_After_Correcting_Calibration_Projection_X.png | 300 px]]
 
−
 
 
−
<math> \sigma_x^2= (8.05  \pm 0.25) + (4.18 \pm 0.19)k_1L + (0.64 \pm 0.034)(k_1L)^2 </math>
 
−
 
 
−
<math> \epsilon_x = 2.2 \pm 1.3~mm*mrad ~\Rightarrow~ \epsilon_{n,x} = 42.4 \pm 25.4~mm*mrad</math>
 
−
 
 
−
<math> \beta_x=0.72 \pm 0.31, \alpha_x=-1.23 \pm 0.56 </math>
 
−
 
 
−
 
 
−
 
 
−
==== Y Projection ====
 
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[[File:HRRL_Emitt_2010_Jul_Refit_After_Correcting_Calibration_Projection_Y.png | 300 px]]
 
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<math>\sigma_y^2 = (8.52 \pm 0.40) + (-3.88 \pm 0.28)k_1L + (0.57 \pm 0.048)(k_1L)^2 </math>
 
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<math> \epsilon_y = 2.6 \pm 2.0~mm*mrad  ~\Rightarrow~  \epsilon_{n,y} = 50.5 \pm 38.3~mm*mrad</math>
 
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<math> \beta_y=0.54 \pm 0.22, \alpha_y=2.68 \pm 1.13 </math>
 
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Effective length
 
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== Second Emittance Measurement Experiment ==
 
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During first emittance measurement we realized that YAG crystal is too sensitive for charge, and our beam charge is too big to be measurement with it. So, We did out second emittance measurement with 10<math>\mu m</math>
 
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=== Results ===
 
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=== Results===
 
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= Future Plan =
 
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== Energy Scan ==
 
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== Positron Target ==
 
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== Positron Yield ==
 
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= References =
 
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<references/>
 
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[[File:Emittance.tex]]
 
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Go back: [[Positrons]]
 

Latest revision as of 23:38, 21 August 2012

File:Sadiq proposal.pdf


text

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\author{Sadiq Setiniyaz (Shadike Saitiniyazi)\thanks{Email: sadik82@gmail.com}} %{address={Department of Physics, Idaho State University}} \title{PROPOSAL FOR POSITRON PRODUCTION EFFICIENCY STUDY USING HIGH REPETITION RATE LINAC AT IAC}

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%% Next comes the abstract, notice the curly-braces surrounding the %% text.

\abstract{ \indent

I propose to measure the positron production efficiency for a positron source that uses a quadrupole triplet system to collect positrons from a tungsten target that are produced when the target is impinged by electrons from the High Repetition Rate Linac (HRRL) at Idaho State University's (ISU) Idaho Accelerator Center (IAC). Positrons were observed in May of 2008 at the IAC without the use of a quadrupole triplet collection system. When a 10~MeV electron beam is used on the tungsten target, positrons escaping from the downstream side of the tungsten have a wide momentum spread of 0 to 2~MeV and a large divergence of $\pi$ rad. A quad triplet collection system, after the tungsten target, is used to focus the positron beam and as a result increase our positron collection efficiency. I will install the collection system and associated beam line components and measure the positron production efficiency using the HRRL.}

\section{Introduction} \indent

I propose to measure the positron production efficiency for a positron source that uses a quadrupole triplet system to collect positrons from a tungsten target that are produced when the target is impinged by electrons from the HRRL. A polarized positron source, as a new probe to explore nuclear and particle physics at Jefferson Lab, is being studied at the Continuous Electron Beam Accelerator Facility (CEBAF). While their main mission is to optimize polarization, ISU's goal is to optimize positron production efficiency. Additionally, a positron beamline at ISU is also a potential tool for nuclear physics studies. I have measured the emittance of the HRRL electron beam and constructed PMT bases for four NaI detectors. I will install the collection system and associated beam line components to measure the positron production efficiency using the HRRL.

\section{Previous Measurements} \indent

Earlier positron production measurements were conducted at ISU's IAC in the May of 2008. The setup is shown in Fig.~\ref{fig:2008-pos-beamline} and the beamline elements are described in Table~\ref{tab:2008-pos-beamline-elements}. The accelerator was operated at a 300~Hz repetition rate and 10~MeV energy. Electrons were bent by the first dipole and sent to a 2~mm thick tungsten target. Any positrons produced were focused using two quadrupoles and bent 45 degrees by a second dipole which was set to transport 3~MeV positrons. Positrons were transported to the end of the linac where they annihilated in a Ta target. A HpGe and a NaI detector were used to detect the 511~keV positrons produced as a result of annihilation. Fig.~\ref{fig:2008-spectrum} shows the spectrum taken over a 600 second time interval.


\begin{figure}[htbp] \centering \includegraphics[width=80mm]{2008_positron_measurement_at_IAC.eps} \caption{The HRRL beamline configured for positron production at IAC in 2008. } \label{fig:2008-pos-beamline} \end{figure}

\begin{table}[htbp] \caption{Beamline elements for positron production at IAC in 2008.}

\begin{tabular}{ll} \hline 

      \textbf{Item} & {$\textbf {Description}$} \\

\hline 

          Tantalum foil   &  6 mm thick 20 mm x 20 mm area   \\
          Tungsten foil   &  2 mm thick 20 mm x 20 mm area    \\
          Phosphorus flag  & 1 mil aluminum backing             \\
          HpGe detector & 81.3mm Diameter, 55.5mm Length \\
          %NaI detector	&

\hline \end{tabular} \label{tab:2008-pos-beamline-elements} \end{table}

\begin{figure}[htbp] \centering 

 \includegraphics*[scale=0.45]{2008_Run60_HpGe-NaI}

\caption{Spectrum from HpGe Detector and NaI detecotrs.} \label{fig:2008-spectrum} \end{figure}

%\begin{figure}[htbp] %\centering % \includegraphics[scale=0.45]{2008_PositronYield_SweeperMagnet_run60-61} %\caption{Spectrum.} %\label{fig:2008-spectrum-zoom} %\end{figure}


\section{Proposed Beamline} \indent


I propose a measurement of the positron production efficiency using the HRRL. The HRRL can provide electron beams with energies between 3~MeV and 16~MeV, and a maximum repetition rate of 300~Hz. The HRRL beamline has recently been reconfigured to generate and collect positrons, see Fig.~\ref{fig:HRRL-e+-line} and Table~\ref{tab:hrrl}.

\begin{table}[hbt] 

  \centering
  \caption{Operational Parameters of The 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       &  300  \\
       \midrule
       macro-pulse pulse length (FWHM)          &   ns       &  250    \\
       \midrule
       rms energy spread                                &  \%      &   4.23   \\
 \bottomrule

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

The new beamline was first designed by Dr. G. Stancari to use a quadrupole triplet system to collect positrons~\cite{stancari}. The design was further optimized by Dr. Y Kim. The final design of the beamline is shown in Fig.~\ref{fig:HRRL-e+-line}. The HRRL accelerator room is divided into two parts by an L-shaped cement wall. The accelerator cell houses the cavity and other elements needed to transport electrons to an experimental cell. The experimental cell is located in a room adjacent to the accelerator cell. The HRRL beamline was reconfigured into an achromat by moving the accelerator cavity to accommodate two dipoles and a system of quadrupole magnets optimized for collecting positrons.

In the new beamline, shown in Fig.~\ref{fig:HRRL-e+-line}, the electron beam exits the cavity and passes through a quadruple triplet that will focus the electron beam onto the positron target. Positrons produced from the positron target will be collected by the second quadruple triplet that will be optimized to collect positrons. The first dipole magnet bends the positrons/electrons, depending on the magnet polarity, by 45 degrees towards the second dipole magnet. The second dipole will bend the beam another 45 degrees, thus completing a 90 degree bend. A third quadruple triplet will focus the e-/e+ beam, as users desire. All beam elements are described in Table~\ref{tab:new-hrrl-line-elements}.


%\begin{figure*}[htbp] \begin{sidewaysfigure*}[htbp]

\centering %\includegraphics[scale=0.28]{HRRL_Pos_and_Ele_Go} \includegraphics[scale=0.35]{HRRL_Pos_and_Ele_Go.eps} \caption{The new HRRL beamline cofiguration for positron generation.} \label{fig:HRRL-e+-line} \end{sidewaysfigure*}

%\end{figure*}


\begin{table}[hbt] 

  \centering
  \caption{The new HRRL positron beamline elements.}
  \begin{tabular}{lccc}
      \toprule
        Item   &  Description \\
      \midrule
        T1    & Positron target \\
      \midrule
        T2    &  Annihilation target \\
       \midrule
        EnS    & Energy Slit  \\
       \midrule
        FC1, FC2& Faraday Cups \\
       \midrule
        Q1,...Q10	     & Quadrupoles \\
       \midrule
         D1, D2	    & Dipoles \\
       \midrule
        NaI     &  NaI Detecotrs \\
       \midrule
        OTR     &  Optical Transition Radiaiton screen\\
       \midrule
        YAG    & Yttrium Aluminium Garnet screen\\
 \bottomrule

\end{tabular} \label{tab:new-hrrl-line-elements} \end{table}

%00000000000000000000000000000000000000000000000000000000000 \section{Preparation for the Positron \\ Production Experiment} \subsection{HRRL Emittance measurements} \indent


Emittance, a key parameter in accelerator physics, is used to quantify the quality of an electron beam produced by an accelerator. The beam size and divergence at any point in the beamline can be described using emittance and Twiss parameters.

An Optical Transition Radiation (OTR) based viewer was installed to allow measurements at the high electron currents available from 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 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.

The emittance of the HRRL was measured to be less than 0.4~$\mu$m using the OTR based tool at an energy of 15~MeV. The details of this emittance measurement using the quadrupole scanning method were described in the IPAC12 proceedings~\cite{setiniyaz-q-scan}. The results are summarized in Table~\ref{results}.

\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 & 35 \\ 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}

\subsection{Positron Detection using NaI crystals} \indent

A tungsten target will be placed at the end of the 90 degree beamline to annihilate positrons. I want to use two NaI detectors to detect the 511~keV photons created when positrons annihilate. I acquired some NaI crystals from Idaho Accelerator Center (IAC). Since their original bases used a slow post-amplifier, I built new PMT bases. I modified the design of model PA-14 from Saint-Gobain Crystals \& Detectors Ltd. These detectors are tested, calibrated, and ready to be used for the measurement. Fig.~\ref{fig:IAC-dets} shows the crystals and the bases I built. Fig.~\ref{fig:IAC-dets-Co60-Na22-spec} shows the spectrum taken by the detector using button sources. %I expect by doing coincidence, the resolution of 511~keV peak in the spectrum will be improved.

\begin{figure}[htbp] \centering \includegraphics[scale=0.08]{IAC_NaI_Detectors} \caption{The NaI detector and base built.} \label{fig:IAC-dets} \end{figure}

\begin{figure}[htbp] \centering \includegraphics[scale=0.18]{Na22_Co60Spectrum_by_IAC_Detectors} \caption{Detector 3 calibrated Spectrum.} \label{fig:IAC-dets-Co60-Na22-spec} \end{figure}

%\subsection{Positron Target Installation} %\indent % %A step motor is ready to be installed once the vacuum chamber is ready. The step motor, shown in the Fig.~\ref{fig:step-motor}, will hold 8 tungsten targets. % %\begin{figure}[htbp] %\centering %\includegraphics[scale=0.08]{setep_motor} %\caption{Step motor for holding W targets.} %\label{fig:step-motor} %\end{figure}

\section{Future Plan} \indent

We want to produce positrons using the HRRL beam line. We can improve positron collection efficiency by applying following methods:

1. By using a quadrupole triplet before tungsten a target, we will have control over the beam size and divergence at the target.

2. Cryogenically cooled converter will be installed, and these targets will be able to take on more beam power and increase positron yield.

3. Positrons will be collected by the quadrupole triplet system, which will improve collection efficiency.

4. Simulations will optimize beam elements for positron collection.

%\bibliographystyle{unsrt} % Order by citation %\bibliography{report}

\begin{thebibliography}{9} %{stancari} %@techreport{stancari, % title =Template:Stancari's proposal-------, % month ={Nov.}, % year = {2005}, % author ={J. Stancari}, % address ={Frascati, Italy}, % number ={}, % institution ={DAFNE Technical Note} \bibitem{stancari} 

G. Stancari and T. Forest "Design of a new beamline for electrons, positrons and photons at the HRRL lab", Pocatello, ID, USA (2009).


%@techreport{OTR, % title =Template:Optical Transition Radiation, % month ={}, % year = {1992}, % author ={B. Gitter}, % address ={Los Angeles, CA 90024}, % institution ={Particle Beam Physics Lab, Center for Advanced Accelerators, UCLA Department of Physics} %}

\bibitem{OTR} B. Gitter, Tech. Rep., Los Angeles, USA (1992).

%\bibitem{setiniyaz-q-scan} %@InProceedings{setiniyaz-q-scan, % author = {S. Setiniyaz, K. Chouffani, T. Forest, and Y. Kim}, % title = {TRANSVERSE BEAM EMITTANCE MEASUREMENTS OF A 16 MeV LINAC AT THE IDAHO ACCELERATOR CENTER}, % booktitle = {IPAC2012},%pages = {151--158}, % year = 2012, % address = {New Orleans, USA} %} \bibitem{setiniyaz-q-scan} S. Setiniyaz, K. Chouffani, T. Forest, and Y. Kim, in $Proc$. $IPAC2012$, New Orleans, USA.

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


\end{thebibliography}

\end{document}

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