User:Chgrech/sandbox

A 'B-train system' is a magnetic field measurement system used for measuring the magnetic field of bending dipole magnets in synchrotrons. For the measurement of the magnetic field in real-time, a combination of induction coils and field markers is used. In fact, the B-train field measurement system consists of a static fluxmeter coil, shaped to follow the nominal beam path, that generates a voltage, $$V_c$$ proportional to the field time variation. This voltage is integrated using a digital integrator in order to calculate the magnetic field $$B(t)$$. A field marker that triggers a digital signal at $$t = t_0$$ when $$B = B_0$$ is then used as an integration constant. Magnetic markers are used to improve the B-train's accuracy and reproducibility, as they consider the remanent field and correct the gain and offset drifts of the electronics. The calculation for the average B(t) is noted in the equation below, where $$A$$ is the induction coil effective area.

$$ B(t) = \dfrac{1}{A}\int_{t_0}^t V_c dt + B_0 $$