Measurement of low energy longitudinal polarised positron beams via a Bhabha polarimeter

The introduction of a longitudinal polarised positron beam in an $e^+e^-$ linear collider calls for its polarisation monitoring and measurement at low energies near its production location. Here it is shown that a relatively simple Bhabha scattering polarimeter allows, at energies below 5000 MeV, a more than adequate positron beam longitudinal polarisation measurement by using only the final state electrons. It is further shown that out of the three, 10, 250 or 5000 MeV positron beam energy locations, where the polarisationmeasurement in the TESLA linear collider can be performed, the 250 MeV site is best suited for this task.