next up previous
Next: Chromaticity (1,1) Up: Application to the SLS Previous: Application to the SLS

Simulation

We have used Tracy2 [4] to evaluate the chromaticity during the ramping. The model used is the 4th order symplectic integrator. This model allows us to do a good simulation of the integrated sextupole component of the dipoles. The sextupole component is treated in the same way than the dipolar and quadrupolar component. Table 2 shows the parameters for the booster vacuum chamber and magnets.

 
Table 2: Parameters for the combined-function magnets.
Vacuum chamber wall thickness D 0.7 mm
Steel conductivity $\kappa$ $1.3\times 10^6 $ $\Omega\cdot$ m
Gap in D-magnets   23.3 mm
Gap in F-magnets   26.2 mm
Minimum Energy Einjection 0.1 GeV
Maximum Energy Eextraction 2.4 GeV
  $\alpha_E$ 1.0869  
Maximum BD dipolar field BextractionD 0.714 T
bending radius at maximum field $\rho_D$ 11.22 m
Maximum BF dipolar field BextractionF 0.158 T
bending radius at maximum field $\rho_F$ 50.72 m
Sextupole SF,D half-aperture   18 mm
 

Figure 3 shows the energy ramping in function of time for the SLS booster. We assume that the injection takes place at the start of the ramping and extraction at the end. Figure 4 shows the required ramp for the dipolar field of the bending magnets.


  
Figure 3: Energy ramping.
\begin{figure}
\begin{center}
\mbox{\epsfig{figure=energy.eps, width=.9\textwidth} }
\end{center}\end{figure}


  
Figure 4: Dipolar fields (BF,d) during ramping.
\begin{figure}
\begin{center}
\mbox{\epsfig{figure=bfield.eps, width=.9\textwidth} }
\end{center}\end{figure}

The sextupolar component produced by eddy currents, during the ramping is shown in figure 5. As expected, the contribution is more important at low energies, with the maximum at 0.2 GeV (0.025 s after injection). Also, the contribution of the BDmagnets is much more important that the one from BF magnets, due to the smaller bending radius in the BD magnets. The chromaticity during the ramping cycle is shown in figure 6.


  
Figure 5: Sextupolar component generated by eddy currents in the vacuum chamber of the bending magnets.
\begin{figure}
\begin{center}
\mbox{\epsfig{figure=vsext.eps, width=.9\textwidth} }
\end{center}\end{figure}

The horizontal chromaticity remains positive during the process, but we need to compensate the vertical one, that goes very soon to negative values at the start of the ramping, with a maximum of $\approx$ -5 at 0.2 GeV, and remain negative up to $\approx$2 GeV. However, due to the integrated sextupole component in the bending magnets, the value of the vertical chromaticity remains relatively small and the compensation with the two sextupoles families SF and SD will be easy.


  
Figure 6: Chromaticity during the ramping, with pole shims and eddy current contributions.
\begin{figure}
\begin{center}
\mbox{\epsfig{figure=chrom1.eps, width=.9\textwidth} }
\end{center}\end{figure}

We contemplate two scenarios for running the booster:

1.
Fixed chromaticity during the ramping of (1,1).
2.
Fixed chromaticity during the ramping of (5,5).


next up previous
Next: Chromaticity (1,1) Up: Application to the SLS Previous: Application to the SLS
Marc Munoz
1998-11-18