  We investigate the Unruh effect for a massless scalar field in the two
dimensional Minkowski space in the presence of a uniformly accelerated perfect
mirror, with the trajectory of the mirror chosen in such a way that the mirror
completely masks the Rindler horizon from the space-time region of interest. We
find that the characteristic thermodynamical properties of the effect remain
unchanged, i.e. the response of a uniformly co-accelerated Unruh detector and
the distribution of the Rindler particles retain their thermal form. However,
since in this setup there are no unobserved degrees of freedom of the field the
thermal statistics of the Rindler particles is inconsistent with an initial
pure vacuum, which leads us to reconsider the problem for the more physical
case when the mirror is inertial in the past. In these conditions we find that
the distribution of the Rindler particles is non-thermal even in the limit of
infinite acceleration times, but an effective thermal statistics can be
recovered provided that one restricts to the expectation values of smeared
operators associated to finite norm Rindler states. We explain how the thermal
statistics in our problem can be understood in analogy with that in the
conventional version of the effect.
