The relation for relative change in field to orbit change is the following:
\frac{\Delta B}{B} = \frac{\Delta p}{p} = \alpha \frac{\Delta \bar{r}}{r}$$ By definition of the momentum compaction factor\frac{\Delta L}{L} = \alpha \frac{\Delta p}{p}
Where $\eta = \frac{1}{\gamma^2} - \frac{1}{\gamma_T^2}$ is the slipfactor, and $\gamma$ is the lorentz factor, and $\gamma_T$ is the transition. For a specific cycle in the [[SPS]] we can get the $\gamma$ and $\gamma_T$ for a corresponding energy and optics respectively from [[LHC Software Architecture|LSA]]. Here also $\alpha = \frac{1}{\gamma_T^2}$. Consequently the mean orbit change from a field change would be\Delta\bar{r} = \alpha r \frac{\Delta B}{B}
\Delta B = \frac{1}{\alpha} \frac{\Delta \bar{r}}{r} B
For an injection plateau for a Q20 beam like the standard 200 GeV MD cycle in the [[SPS]], where $\gamma_T=17.5$, $\gamma=27.6$, and $B=0.1166 ~T$, and $\rho=1100~ m$, and $\Delta B = 1\times10^{-5}~T$ we find $\Delta\bar{r} \approx 0.31 ~ mm$