Commit 81b6d624 authored by Thomas Planche's avatar Thomas Planche

trying to get organized

parent 2b0436a4
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\title{Zgoubi, would you do for me\\TRIUMF's High Resolution Separator?}
\author{Thomas Planche}
%\footnote{tplanche@triumf.ca}\\~\\ TRIUMF\thanks{This work has been supported by the Natural Sciences and Engineering Research Council of Canada. TRIUMF also receives federal funding via a contribution agreement through the National Research Council of Canada.}}
\begin{document}
\maketitle
\tableofcontents
\section{Basic Layout}
The optical system we will consider in this note is designed to separate rare isotopes with mass/charge differences of only one part in 20\,000 in beams with transverse emittances of at least 3\,$\mu$m\footnote{Un-normalized emittance. Note that to achieve such resolution an energy spread of the order of 1\,eV or less is required.}~\cite{TRI-DN-16-09}.
It is composed of:
\begin{itemize}
\item an emittance defining slit;
\item followed by an 80\,cm drift;
\item followed by two identical 90\,deg.~magnetic dipoles (bending radius~=~120\,cm, edge angle~$\approx$~26.5\,deg.) separated by a 2$\times$80\,cm drift;
\item followed by an 80\,cm drift;
\item followed by a mass selection slit.
\end{itemize}
The basic parameters of this high resolution separator (HRS) were determined using the linear optics code {\tt TRANSOPTR}~\cite{optrOnGitlab}.
To achieve in practice the desired resolving power, it is essential to compensate non-linear aberrations. To this aim an electrostatic multipole corrector is added halfway between the two dipoles. The detailed design of the most critical components -- namely the dipoles and the multipole corrector -- was accomplished using a 3D finite element code ({\tt OPERA}) which provided inputs to non-linear optics codes such as {\tt COSY-INFINITY} and {\tt zgoubi}.
In this note I will go through the steps of the design work done using {\tt zgoubi}.
\section{Define your `object'}
Let's start with something simple and try to track one single particle. Let's say we want to track a 60\,keV $\rm{^{238}U}^+$ ion. At first we will track it through magnetic element only, so the knowing the magnetic rigidity $B\rho$ is sufficient. As a reminder the magnetic rigidity is given by:
\begin{equation}
B\rho=\frac{p}{q}\,,
\end{equation}
where $q$ is the charge of the particle, and $p$ its momentum given by:
\begin{equation}
p^2c^2=E^2-m^2c^4\,,
\end{equation}
where $E$ is the particle's total energy, $m$ its mass, and $c$ the speed of light. For non-relativistic particles, like our 60\,keV uranium ion, the momentum can also be obtained using:
\begin{equation}
p=\sqrt{2mqE_k}\,,
\end{equation}
where $E_k$ is the beam potential (60\,keV in our case), often also referred to as the `kinetic' energy\footnote{Note that it is a true kinetic energy only in the non-relativistic approximation. In the relativistic case the beam potential is given by $(\gamma-1)mc^2$ and cannot be seen as a kinetic energy term, whatever way you look at it~\cite{2014PHYS-1}.}.
If you look into {\tt zgoubi} user's guide~\cite{meot2012zgoubi} you will find you need to call use the keyword 'OBJECT' (or 'OBJET' if you like to talk to {\tt zgoubi} in French). There are several equivalent ways (KOBJ=1 to 6) to have the 'object' you will track be one single particle. I will use KOBJ=2:
\begin{lstlisting}
'OBJET'
544.12 !BORO: Brho of 60 keV 238U+ = 544.12 kG.cm
2 !KOBJ=2: initial coordinates must be entered explicitly
1 1 !total number of particles; number of distinct momenta
0. 0. 0. 0. 0. 1. 'o' !Y; T; Z; P; S; D; 'marker'. Note: Brho=BORO*D
1 !1 or -9 (-9 disables the tracking of this particle)
\end{lstlisting}
% \section{Introduction}
% \begin{figure}[htb]
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% \delta E_k =& q V_{\rm rf} \sin{\phi}\\
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\BOOKMARK [1][-]{section.1}{Basic Layout}{}% 1
\BOOKMARK [1][-]{section.2}{Define your 'OBJECT'}{}% 2
\BOOKMARK [1][-]{section.3}{'DIPOLE'}{}% 3
\BOOKMARK [1][-]{section.4}{'FIT' dipole parameters}{}% 4
\BOOKMARK [1][-]{section.5}{'MATRIX' to fit edge angles}{}% 5
\BOOKMARK [1][-]{section.6}{Multiparticle simulation}{}% 6
\BOOKMARK [1][-]{section.7}{Dipole edge curvature}{}% 7
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\contentsline {section}{\numberline {1}Basic Layout}{1}{section.1}
\contentsline {section}{\numberline {2}Define your {\tt 'OBJECT'}}{2}{section.2}
\contentsline {section}{\numberline {3}{\tt 'DIPOLE'}}{3}{section.3}
\contentsline {section}{\numberline {4}{\tt 'FIT'} dipole parameters}{5}{section.4}
\contentsline {section}{\numberline {5}{\tt 'MATRIX'} to fit edge angles}{6}{section.5}
\contentsline {section}{\numberline {6}Multiparticle simulation}{7}{section.6}
\contentsline {section}{\numberline {7}Dipole edge curvature}{7}{section.7}
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