Commit 54e464ce authored by Thomas Planche's avatar Thomas Planche

tuto part 1 completed!

parent ab6bf61c
......@@ -25,7 +25,7 @@ zgoubi HRS tuto: DIPOLE
0 0. 0. 0. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0. 0.
2 4. !IRD(=2, 25 or 4)
0.3 !Integration step size[cm]
0.5 !Integration step size[cm]
2 127.96721 -0.349067 127.96721 0.349067 !KPOS RE[cm]; TE[rad]; RS[cm]; TS[rad]
'DRIFT'
......@@ -49,13 +49,3 @@ zgoubi HRS tuto: DIPOLE
'END'
'FIT'
3 !Number of physical parameters to be varied
3 36 -3.020 0.1 !element #3 (DIPOLE); parameter #36 (exit edge angle); inverse (minus sign) correlation with element#4 parameter#20 (entrance edge angle); relative range
3 5 0. 0.2 !element #3 (DIPOLE); vary parameter #5 (BO); coupling switch; relative range
3 64 0. 0.2 !element #3 (DIPOLE); vary parameter #64 (RE); coupling switch; relative range
4 1e-8 100 !Number of constraints; Convergence threshold; maximum number of iterations
3 1 2 5 0.0 1000. 0 !IC; Particle #; coordinate#=2 for Y;element #; wanted value; weigth ; 0
3 1 3 5 0.0 1000. 0 !IC; Particle #; coordinate#=3 for T;element #; wanted value; weigth ; 0
1 1 1 5 0.0 1. 0 !transfer matrix; matrix element 1 1; FIT after element#5 ('MATRIX');Wanted value(=0.0); Weigth ; 0:no additional parameters
1 2 2 5 0.0 1. 0 !transfer matrix; matrix element 2 2; FIT after element#5 ('MATRIX');Wanted value(=0.0); Weigth ; 0:no additional parameters
zgoubi HRS tuto: DIPOLE
'OBJET'
543.687 !60 keV U1+
6 !5: generate 11 particles used to calculate transfer matrix ('MATRIX')
0.00001 0.001 0.00001 0.001 .0 .0 !step size in Y; T; Z; P; S; D
0.0 0. 0. 0. 0. 1.
'DRIFT'
36.32357
'DIPOLE'
0 !output flag: 0: no outpot, 2: output trajectory to zgoubi.plt, etc.
130 120. !AT[deg.], RM[cm]
65 4.5307259 0. 0. 0. !ACENT[deg.];B0[kG]; N; B; GX
7.0 0. !ENTRANCE FIELD BOUNDARY: fringe field extend[cm]; unused
4 0. 1.8 0. 0. 0. 0. 0. !unused; C0...C5; shift
45. 26.5 220.0 0.0 0.0 220.0 !W+[deg.]; edge angle[deg.]; R1[cm]; U1; U2; R2[cm]
7.0 0. !EXIT FIELD BOUNDARY: lambda; =-1 for Enge like
4 0. 1.8 0. 0. 0. 0. 0. !unused; C0...C5; shift
-45. -26.5 -220.0 0. 0. -220.0 0. !W-; edge angle; R1; U1; U2; R2
0. 0. !FACE 3: (Not used here)
0 0. 0. 0. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0. 0.
2 4. !IRD(=2, 25 or 4)
0.5 !Integration step size[cm]
2 127.96721 -0.349067 127.96721 0.349067 !KPOS RE[cm]; TE[rad]; RS[cm]; TS[rad]
'DRIFT'
36.32357
'MATRIX'
2 0
'FIT'
6 !Number of physical parameters to be varied
3 5 0. 0.2 !element #3 (DIPOLE); vary parameter #5 (BO); coupling switch; relative range
3 64 0. 0.2 !element #3 (DIPOLE); vary parameter #64 (RE); coupling switch; relative range
3 36 -3.020 0.1 !element #3 (DIPOLE); parameter #36 (exit edge angle); inverse (minus sign) correlation with element#4 parameter#20 (entrance edge angle); relative range
3 24 3.021 0.1
3 37 -3.021 0.1
3 40 -3.021 0.1
5 1e-8 100 !Number of constraints; Convergence threshold; maximum number of iterations
1 1 1 5 0.0 1. 0 !transfer matrix; matrix element 1 1; FIT after element#5 ('MATRIX');Wanted value(=0.0); Weigth ; 0:no additional parameters
1 2 2 5 0.0 1. 0 !transfer matrix; matrix element 2 2; FIT after element#5 ('MATRIX');Wanted value(=0.0); Weigth ; 0:no additional parameters
3 1 2 5 0.0 10. 0 !IC; Particle #; coordinate#=2 for Y;element #; wanted value; weigth ; 0
3 1 3 5 0.0 10. 0 !IC; Particle #; coordinate#=3 for T;element #; wanted value; weigth ; 0
2 2 11 5 0.0 1. 0 !2:2nd order map element; transfer map element 2-11 (i.e. x'-x^2); Desired value; 0:no additional parameters
'END'
\ No newline at end of file
../../DIPOLE/edge-curvature/twomasses.eps
\ No newline at end of file
No preview for this file type
......@@ -231,17 +231,86 @@
\begin{figure}[htb]
\centering
\includegraphics*[width=1.0 \linewidth]{figure/twomasses}
\caption{Two isobars with a relative mass difference of 1/20\,000 through the HRS, before correcting non-linear aberration.}\label{fig:twomassesInit}
\caption{Two isobaric beams with a relative mass difference of 1/20\,000 through the HRS, before correcting non-linear aberration.}\label{fig:twomassesInit}
\end{figure}
What you see in~\cref{fig:twomassesInit} is that the two masses completely overlap. This is (mostly) the effect of second order (sextupole) aberration. To achieve the designed resolution, we must correct this aberration.
\section{Dipole edge curvature}
To correct the second order aberration let's try to add curvature to the edges of our dipoles. Once again, we would like to adjust the edge curvature using a {\tt 'FIT'}, but what should the objective of that fit be?
To correct the second order aberration we can try to add curvature to the edges of our dipoles.
A reasonable solution is:
\begin{lstlisting}
zgoubi HRS tuto: DIPOLE
'OBJET' 1
543.701 !BRHO 60 keV 238U1+ in kG.cm
3.01 !read from particles from a file
1 3000 1 !IP1; IP2; IPStep (Read particles numbered IT1 to IT2, step ITStep)
1 1 1 !not used here
1. 1. 2. 0.25 1. 1. 1. * !scaling factors on Y,T,Z,P,S,DP
0 0 0 0 0 0 0 ! not used here
0 ! not sure what this one does
noEspread.beam !file: http://beamphys.triumf.ca/~tplanche/text/designs/HRS/zgoubi/DIPOLE/noEspread.beam
'DRIFT' 2
36.32357
'DIPOLE' 3
0 !output flag: 0: no outpot, 2: output trajectory to zgoubi.plt, etc.
130 120. !AT[deg.], RM[cm]
65 4.5315270 0. 0. 0. !ACENT[deg.];B0[kG]; N; B; GX
7.0 0. !ENTRANCE FIELD BOUNDARY: fringe field extend[cm]; unused
4 0. 1.8 0. 0. 0. 0. 0. !unused; C0...C5; shift
45. 26.486450 227.0 0.0 0.0 227.0 !W+[deg.]; edge angle[deg.]; R1[cm]; U1; U2; R2[cm]
7.0 0. !EXIT FIELD BOUNDARY: lambda; =-1 for Enge like
4 0. 1.8 0. 0. 0. 0. 0. !unused; C0...C5; shift
-45. -26.486450 -227.0 0. 0. -227.0 0. !W-; edge angle; R1; U1; U2; R2
0. 0. !FACE 3: (Not used here)
0 0. 0. 0. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0. 0.
2 4. !IRD(=2, 25 or 4)
0.3 !Integration step size[cm]
2 127.97493 -0.349067 127.97493 0.349067 !KPOS RE[cm]; TE[rad]; RS[cm]; TS[rad]
'DRIFT' 4
36.32357
'DRIFT' 5
36.32357
'DIPOLE' 6
0 !output flag: 0: no outpot, 2: output trajectory to zgoubi.plt, etc.
130 120. !AT[deg.], RM[cm]
65 4.5315270 0. 0. 0. !ACENT[deg.];B0[kG]; N; B; GX
7.0 0. !ENTRANCE FIELD BOUNDARY: fringe field extend[cm]; unused
4 0. 1.8 0. 0. 0. 0. 0. !unused; C0...C5; shift
45. 26.486450 227.0 0.0 0.0 227.0 !W+[deg.]; edge angle[deg.]; R1[cm]; U1; U2; R2[cm]
7.0 0. !EXIT FIELD BOUNDARY: lambda; =-1 for Enge like
4 0. 1.8 0. 0. 0. 0. 0. !unused; C0...C5; shift
-45. -26.486450 -227.0 0. 0. -227.0 0. !W-; edge angle; R1; U1; U2; R2
0. 0. !FACE 3: (Not used here)
0 0. 0. 0. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0. 0.
2 4. !IRD(=2, 25 or 4)
0.3 !Integration step size[cm]
2 127.97493 -0.349067 127.97493 0.349067 !KPOS RE[cm]; TE[rad]; RS[cm]; TS[rad]
'DRIFT' 7
36.32357
'FAISCNL' 8
output-particles.fai
'END'
\end{lstlisting}
Figure~\ref{fig:twomassesCurv} is obtained by plotting the output file output-particles.fai for two masses different by 1 part in 2$10^4$ (i.e.\ $B\rho$ different by 1 part in 4$10^4$).
\begin{figure}[htb]
\centering
\includegraphics*[width=1.0 \linewidth]{figure/twomasses-edgeCurvature}
\caption{Two beams with a relative mass difference of 1/20\,000 through the HRS, with a pole edge curvature of 227.0\,cm.}\label{fig:twomassesCurv}
\end{figure}
Figures~\ref{fig:twomassesInit} and~\ref{fig:twomassesCurv} are plotted with the same scale for easy comparison. With the dipole edge curvature, the two beam are almost separated: it is only for the angles larger than 40\,mrad that the two beam still overlap. Higher order correction is needed to achieve complete separation: this is going to be the topic of the next tutorial.
......
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