Main Web>TWikiUsers>VincentGiangiobbe>CombinedTestBeam>BeamMomentum (2008-03-10, VincentGiangiobbe)

Beam momentum

Calibration of the spectrometer at VLE

Assuming that the VLE spectrometer is not calibrated (i.e. the measured impulsion using the deflexion angle do not correspond to the real beam impulsion) we can propose a method to perform thai calibration. This method is based on the comparison between the 9 GeV beam from the high and low energy periods. The spectrometer was properly calibrated for the HE period. For run 1004161 (9 GeV, $\eta$ =0.40, HE period), the measured impulsion is

=9.198 $\pm$ ... GeV. For electrons, a very precise energy has been performed using the LAr calorimeter :

=8.839 $\pm$ ... GeV. The same energy measurement can be done for a VLE run at the same energy and eta (run 2102096 has been chosen) :

=8.67 $\pm$ 0.01 GeV. We assume now the equality between the ratio

between the two periods :

$\frac{p(9 GeV; HE)}{E(9 GeV; HE)}=\frac{p(9 GeV; VLE)}{E(9 GeV; VLE)}$ where is the true beam impulsion for the VLE run. Let us do the assumption that from the uncalibrated impulsion measurement, we have : $\frac{p_{measured}(VLE)}{p(VLE)}=\frac{p_{measured}(9 GeV; VLE)}{p(9 GeV; VLE)}$ then it comes :

$p(VLE)=p_{measured}(VLE) \times \frac{p(9 GeV; HE)}{E(9 GeV; HE)} \times \frac{E(9 GeV; VLE)}{p_{measured}(9 GeV; VLE)}$

The term $k=\frac{p(9 GeV; HE)}{E(9 GeV; HE)} \times \frac{E(9 GeV; VLE)}{p_{measured}(9 GeV; VLE)}$ is a correcting factor that can be estimate from the measurements. We have : $p_{measured}(9 GeV; VLE)}$ =9.32 $\pm$ 0.01 GeV.

We find that k=0.968 $\pm$ ...

-- VincentGiangiobbe - 22 Jan 2008

Topic revision: r6 - 2008-03-10 - VincentGiangiobbe

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