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Tune-shift and the Kick Conversion Factor

A general problem arises when comparing measurement data (after applying kicks) to theoretical predictions by Tracy: In experiments kicks are applied to the beam by giving a certain current on a corrector magnet. The current setting is in Amperes whereas the kicks in the Tracy model are applied in radians. Fortunately the current and the angle of the kick can easily be related. Recall the magnetic rigidity $B\rho$ defined by:


\begin{displaymath}
\ F=evB=\frac{\gamma mv^2}{\rho}
\end{displaymath} (1)


\begin{displaymath}
\ B\rho =\frac{\gamma mv}{e}=\frac{E}{ce}
\end{displaymath} (2)

The angle of the kick can be described by:


\begin{displaymath}
\theta=\frac{1}{B\rho}\cdot{\oint B \ ds}=\frac{1}{B\rho}\cdot 2 \mu_{0}N I h
\end{displaymath} (3)

where $N$ is the number of turns of coil, $I$ the current in the coils and $h$ is the size of the vacuum chamber. Therefore the kick can be expressed as a linear function of the current:


\begin{displaymath}
\theta=\frac{ce}{E}\cdot 2 \mu_{0} N I h
\end{displaymath} (4)

In a given accelerator where energy and magnet properties are known, this can be reduced to:


\begin{displaymath}
\theta [rad] = calconst \cdot I [A]
\end{displaymath} (5)

This calibration allows comparison of the model with the measured tune-shift resulting from a corrector kick. Figure 5 shows the theoretically resulting tune-shift from various (horizontal) kicks. As expected the dependency is parabolic. Using the above mentioned conversion scheme (from a current in A to a kick in rad on a corrector magnet) one can now look at measured tune-shift vs. kick on a (horizontal) corrector magnet. This is done in figure 6.

\includegraphics [width=0.8\textwidth]{fig05}
Figure 5: Theoretical prediction of resulting horizontal tune-shifts for different horizontal corrector magnet kicks.

\includegraphics [width=0.8\textwidth]{fig06}
Figure 6: Measured values of resulting horizontal tune-shifts for different horizontal corrector magnets kicks.

Figure 7 shows a comparison between the model and the measured tune-shifts. One can see easily that the curves have the same shape, but a different slope, which is very bothering. The slope, i.e. the first derivative results from the sextupole terms, so an obvious idea would be to change the sextupole strength until the slopes are equal. This is basically an experimental check of the assumed value of sextupole strength. Another idea is to find a new calibration constant (see equation 5) for the conversion in the corrector magnets. It is possible, that due to inaccuracies in magnetic field measurement the original calibration constants were wrong. Both ideas were pursued and the results will be presented in the next two sections.

\includegraphics [width=1.0\textwidth]{fig07}
Figure 7: Comparison between the theoretical and the measured tune-shifts.



Subsections
next up previous contents
Next: Varying Sextupole Strength Up: SLS Storage Ring Orbit Previous: A Peculiarity Detected in   Contents
Simon Leemann
2001-03-29