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GiulioStancariDesign

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\begin{document}

\title{Design of a new beamline for electrons, positrons and photons
  at the HRRL lab}
\author{Giulio Stancari and Tony Forest\\
\textit{\small Idaho State University, Department of Physics,
  Pocatello, Idaho 83209 U.S.A.}}
\date{\fbox{DRAFT}: \today}
\maketitle

\section{Motivation}

The HRRL is an S-band electron linac providing pulsed
beams with energies between 3~MeV and 16~MeV. The maximum repetition
rate is 1.2~kHz, the maximum peak current is 80~mA, and the minimum pulse
length is 25~ns.

The HRRL laboratory is located in the basement of the Physical Science
Building. This lab consists of a shielded accelerator cell and an
experimental area. Currently, a $\sim$4-m beamline with a 90-degree bend
delivers electron and photon beams to the experimental area.

This project has two main goals:
(a)~to improve the quality of electron and photon beams in the HRRL lab;
(b)~to build a positron source for the IAC which could serve as a
prototype for the CEBAF machine at Jefferson Lab~\cite{JPOS09}.

\begin{figure*}
\resizebox{\textwidth}{!}{\includegraphics{HPBv1_layout}}
\caption{Floor plan of the proposed beamline: HRRL power supplies
  (PS); linac with stand (HRRL); collection quadrupole or doublet
  (Q0); positron production target (PT); 45-degree dipoles (D1 and
  D2); quadrupole triplets (QT1, QT2, and QT3); correction steerers
  (S1, S2, and S3); current monitor (CM); beam-position monitors
  (BPM); profile monitors (PM); Faraday cups (FC); secondary target (ST).}
\label{fig:HPBv1_layout}
\end{figure*}

For this project, we envision moving the HRRL machine and building a
6-m beamline with two 45-degree bends (Fig.~\ref{fig:HPBv1_layout}).
Specifically, we want to achieve the following:
\begin{itemize}
\item measure the properties of the $e^-$ beam;
\item provide a test stand for positron production targets;
\item provide space for testing positron collection systems;
\item measure the properties of the outcoming $e^+$ beam;
\item retain the capability to deliver photon beams produced in a
  secondary target downstream of the second bend.
\end{itemize}

The electron beam properties include intensity, position, profile, and
momentum distribution. The intensity will be measured with a current
transformer at the exit port of the HRRL cross-calibrated with a Faraday cup
downstream of the 0-degree port of the first bend. The beam profile
can be inferred from the image on a fluorescent screen placed upstream
of the production target. For the momentum distribution, we need to
provide slits in a dispersive region after the first bend and a
Faraday cup downstream of the 0-degree port of the second bend.

For positron production, we would like to study tungsten foils of
various thicknesses, approximately between 0.1~mm and 1~mm. Enough
space ($\sim$50~cm) should also be provided to test high-power
targets: rotating radiation-cooled metal disks and, possibly in the
future, liquid metal targets.

Positrons are produced with a wide spread in momentum and
divergence. The efficiency of the collection system is critical to
achieve reasonable intensities. A collection system based on
quadrupole triplets has been proposed and needs to be
tested. Alternatively, we should provide enough space ($\sim$50~cm)
for a DC solenoid or adiabatic matching device.

The intensity, position, profile, and momentum distribution of the
positron beam can be measured with a microchannel plate placed
downstream of the 0-degree port of the second bend. The same slits in
the high-dispersion region can be used for both electrons and
positrons. An emittance filter should also be installed to estimate
the phase-space distribution of the positron beam. The background level from
scattered photons needs to be measured to ensure the positron beam is
detectable.

\section{Design of beamline optics}

The beamline optics is subject to several constraints. First of all,
the geometry of the HRRL cell, including the position of the beam
hole, limits the total length of the beamline to about 6~m.

The design is based on the following optical elements, which are
available at the IAC:
\begin{itemize}
\item orange `kiwi' dipoles: pole gap 1~in; 45$^\circ$ bend; radius of
  curvature $\rho = \q{290}{mm}$;
\item Tesla Type 1 Quadrupoles: pole gap 1~in; physical length 100~mm; maximum
  gradient \q{19}{T/m};
\item Tesla Type 2 Quadrupoles: pole gap 2~in; physical length 150~mm; maximum
  gradient \q{9}{T/m}.
\end{itemize}

Some dispersion is needed in the beamline for two reasons: to measure
the momentum distribution of electrons and positrons; and to have the
capability to mimick a given longitudinal admittance with slits (for
the CEBAF machine, $\dmax = (\Delta p / p)_\mathrm{max} = \pm 2\%$).
We also require a dispersion-free region ($D=0$, $D'=0$) downstream of
the last steerer and in the secondary target. This is useful for
reducing correlations between energy and position in electron,
positron, and photon beams sent to the experiments. These dispersion
requirements can be met by a double-bend achromat, which, in this
case, includes two 45-degree bends.

For the electron beam, we assume a typical 10-MeV linac emittance of
\q{1}{\mu m} and a focus with a $3\sigma$ beam size of 3~mm at the
positron production target. This implies amplitude functions equal to
$\beta = (\q{3}{mm})^2/(\q{1}{\mu m}) = \q{9}{m}$ at the target in
both planes. Of course, these assumptions need to be tested
experimentally. We also require a focus of same size at the secondary
target.

The properties of the positron source were simulated with a GEANT4
Monte Carlo assuming a 10-MeV electron beam on a 0.5-mm tungsten
target~\cite{GEANT4}. The momentum distribution of positrons peaks at
1.7~MeV and it is relatively flat within $\pm \q{0.2}{MeV}$. We choose
1.7~MeV as the design momentum for the beamline.

The spatial distribution of the outcoming positron beam is only
slightly wider than that of electrons. For this design, we assume a
focus (i.e., no correlation between positions and momenta) with
$3\sigma$ beam size of 4~mm.

For calculating transverse admittances, we assume the beamline
elements, including the vacuum pipe, have a half aperture of 12~mm.
We need a beamline admittance (which will be filled by the positrons)
larger than the CEBAF admittance \q{1}{\mu m}. We choose to aim at an
admittance $A = \q{10}{\mu m}$, which can then be restricted with
slits to mimick the CEBAF admittance.

In practice, to take both transverse and longitudinal constraints into
account, we require the maximum beam size in both planes to be smaller
than the half aperture~$a$ of the beamline:
\[ \sqrt{\beta A + \left(D \dmax \right)^2} < a. \]

The positions of the correction steerers S2 and S3 are chosen so that the phase advance between the two is approximately 90$^\circ$.

%Constraints on collection triplet?

The beamline optics was designed using the MAD program.

%\subsection{Electron beamline}

%Partial beamlines for diagnostics?

%\subsection{Positron beamline}

\begin{figure*}
\resizebox{\textwidth}{!}{\includegraphics[angle=-90]{HPBv2_CoSn}}
\caption{Amplitude functions (left axis) and horizontal dispersion (right axis) in m.}
\label{fig:HPB_CoSn}
\end{figure*}

\begin{figure*}
\resizebox{0.95\textwidth}{!}{\includegraphics[angle=-90]{HPBv2_phase}}
\caption{Phase advances in $\mathrm{rad}/(2\pi)$.}
\label{fig:HPB_phase}
\end{figure*}

\begin{figure*}
\resizebox{0.95\textwidth}{!}{\includegraphics[angle=-90]{HPBv2_prof}}
\caption{Beam profiles for $\emix = \emiy = \q{10}{\mu m}$. Horizontal profiles are shown for both design momentum (black, solid) and for a momentum spread $\Delta p / p = 2\%$ (green, dotted).}
\label{fig:HPB_prof}
\end{figure*}

\begin{table}
\begin{center}
\begin{tabular}{ccc}
Triplet & Element & Strength (T/m) \\
\hline
QT1 & Q1 & $+0.214$ \\
    & Q2 & $-0.059$ \\
    & Q3 & $-0.102$ \\
\hline
QT2 & Q4 & $+0.181$ \\
    & Q5 & $-0.204$ \\
    & Q6 & $+0.195$ \\
\hline
QT3 & Q7 & $-0.030$ \\
    & Q8 & $-0.073$ \\
    & Q9 & $+0.078$ \\
\end{tabular}
\end{center}
\caption{Quadrupole settings for positrons at \q{1.7}{MeV/c}.}
\label{tab:settings}
\end{table}

Optics for the positron beamline is shown in Figs.~\ref{fig:HPB_CoSn} and~\ref{fig:HPB_phase}. The horizontal and vertical amplitude functions are plotted together with the horizontal dispersion function. Beam profiles are shown in Fig.~\ref{fig:HPB_prof}. The settings for the 3 triplets (9 quadrupoles total) can be found in Table~\ref{tab:settings}.

%Doublets sufficient?

%Partial beamlines for diagnostics?

\section{Diagnostics}

\begin{table*}
\begin{center}
\begin{tabular}{llll}
Component & Model & Features & Approx. unit price \\
\hline
Fast current transformer & Bergoz FCT-028 & inner diam. 28-mm & \$2,000 \\
Faraday cup & Radiabeam FARC-02-300 & & \$1,295 \\
Emittance slits & Radiabeam EMTS-\#\#-\#\#\# & custom & \\
Integrated transverse diagnostics & Radiabeam IBIS-02-VAC-OPT & YAG:Ce & \\
Beam position monitors & Bergoz & S-band & \$10,000 (w/readout) \\
X-Y Steerers & Radiabeam STM-02-340-110 & length 30~mm & \$1,250 \\
Microchannel plates & Hamamatsu & & \$3,000 (w/ pow. supply) \\
\end{tabular}
\end{center}
\caption{Diagnostic components.}
\label{tab:diag}
\end{table*}

Some diagnostic components will need to be acquired.
A possible set of choices is shown in Table~\ref{tab:diag}.

\begin{thebibliography}{9}
\bibitem{JPOS09} International Workshop on Positrons at Jefferson Lab
  (JPOS09), Newport News, Virginia, 25--27 March 2009,
  \url{<http://conferences.jlab.org/JPOS09>}.

\bibitem{GEANT4} S.~Golge et al., Simulation of a CW Positron Source
  for CEBAF, Proceedings of PAC07, p.~3133,
  \url{<http://www.jacow.org>}; J.~Dumas, Design of a High Intensity
  Positron Source, Internship Report, LPSC Grenoble, June 2007;
  M.~Stancari, private communication.
\end{thebibliography}

\end{document}