A simple low-frequency BPM

Detection of the eld induced by a beam outside of the beam pipe can be used for the beam diagnostics. A wire in a longitudinal slot in the beam pipe wall can be used as a beam position monitor with a very small coupling impedance avoiding complications of the feed-through. The signal can be reasonably high at low frequencies. We calculate the beam-coupling impedance due to a long longitudinal slot and the signal induced in a wire placed in such a slot and shielded by a thin screen from the beam. Results can be relevant for impedance calculations of the slot to ante-chamber and slots of the DIPs.