  The design, construction and operation of a Compton back-scattering laser
polarimeter at the HERA storage ring at DESY are described. The device measures
the longitudinal polarization of the electron beam between the spin rotators at
the HERMES experiment with a fractional systematic uncertainty of 1.6%. A
measurement of the beam polarization to an absolute statistical precision of
0.01 requires typically one minute when the device is operated in the
multi-photon mode. The polarimeter also measures the polarization of each
individual electron bunch to an absolute statistical precision of 0.06 in
approximately five minutes. It was found that colliding and non-colliding
bunches can have substantially different polarizations. This information is
important to the collider experiments H1 and ZEUS for their future
longitudinally polarized electron program because those experiments use the
colliding bunches only.
