Commit 91db7ef7 authored by Thomas Planche's avatar Thomas Planche
Browse files

working on the report

parent e78492f2
**HRS FIT DIPOLE
!!Simplest HRS (i.e. magnifying section quads OFF) but only up to the center of the first dipole;
!!the purpose here is to fit dipole position and strength to get the righ beam position and angle in the center of the dipole
'OBJET' 1
546.198 !60 keV U1+ = 546.198
2 !2: All the initial coordinates must be entered explicitly
'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'
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)
'DRIFT' 2
'DRIFT'
80.0 !80 cm long drift
'CHANGREF' 3
'CHANGREF'
YS -120.0 ZR 20. !shift the optical axis by 120 cm (the reference radius of the dipole); then rotate around the vertical axis by 20 deg (20=AT-W)
'DIPOLE' 4
'DIPOLE'
0 !output flag: 0: no outpot, 2: output trajectory to zgoubi.plt, etc.
65 120. !AT, RM
65 4.6 0. 0. 0. !ACENT;B0; N; B; GX
......@@ -33,15 +31,15 @@ YS -120.0 ZR 20. !shift the optical axis by 120 cm (the reference radius
2 0. 0. 0. 0. !KPOS RE[cm]; TE[rad]; RS[cm]; TS[rad]
'FIT' 5
'FIT'
2 !Number of physical parameters to be varied
3 1 0. 0.1 !in element #3 (i.e. CHANGREF); vary parameter #1 (i.e YS); coupling switch OFF=0; relative range +/- 10%
4 5 0. 0.2 !in element #5 (i.e. DIPOLE); vary parameter #6 (i.e. B0); coupling switch OFF=0; relative range +/- 20%
2 1e-10 500 !Number of constraints; Convergence threshold; maximum number of iterations
4 5 0. 0.1 !in element #5 (i.e. DIPOLE); vary parameter #6 (i.e. B0); coupling switch OFF=0; relative range +/- 20%
2 1e-10 1 !Number of constraints; Convergence threshold; maximum number of iterations
3 1 2 4 120.0 1. 0 !IC (type of constraint. =3 is for a constraint on a particle coordinate); Particle number; Particle coordinate (=2 for Y);Where?:at the end of element #4(i.e. DIPOLE);Wanted value(=120 cm); Weigth ; 0:no additional parameters
3 1 3 4 0.0 1. 0 !IC (type of constraint. =3 is for a constraint on a particle coordinate); Particle number; Particle coordinate (=3 for T);Where?:at the end of element #4(i.e. DIPOLE);Wanted value(=0 deg.); Weigth ; 0:no additional parameters
'END' 6
'END'
!!The FIT should converge to YS=-120.2408355 and B0=4.552771183 after 105 iteration.
......
......@@ -11,7 +11,13 @@
\usepackage{hyperref}%to include hyper links
\hypersetup{colorlinks,linkcolor=blue,citecolor=blue}%links
\definecolor{listinggray}{gray}{0.9}
\usepackage{listings}%to include lines of code
\usepackage{listings}
\lstset{language=[90]Fortran,
basicstyle=\tt\scriptsize ,
keywordstyle=\color{red},
commentstyle=\color{blue},
morecomment=[l]{!\ }% Comment only with space after !
}
\usepackage[section]{placeins}% to be able to use \FloatBarrier
\usepackage{cleveref}%to use \cref
\usepackage{longtable}
......@@ -23,7 +29,7 @@
%opening
\title{Zgoubi, would you do for me\\TRIUMF's High Resolution Spectrometer?}
\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.}}
......@@ -31,6 +37,49 @@
\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]
......@@ -83,6 +132,6 @@
\bibliographystyle{/home/tplanche/utils/latex/formating/elsarticle-num}
\bibliography{/home/tplanche/utils/latex/Mybib,/home/tplanche/utils/latex/AllDN}
\bibliography{/home/tplanche/utils/latex/Mybib,/home/tplanche/utils/latex/bib/AllDN}
\end{document}
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