  The operation of a Free Electron Laser (FEL) in the ultraviolet or in the
X-ray regime requires the acceleration of electron bunches with an rms length
of 25 to 50 micro meters. The wakefields generated by these sub picosecond
bunches extend into the frequency range well beyond the threshold for Cooper
pair breakup (about 750 GHz) in superconducting niobium at 2 K. It is shown,
that the superconducting cavities can indeed be operated with 25 micro meter
bunches without suffering a breakdown of superconductivity (quench), however at
the price of a reduced quality factor and an increased heat transfer to the
superfluid helium bath. This was first shown by wakefield calculations based on
the diffraction model. In the meantime a more conventional method of computing
wake fields in the time domain by numerical methods was developed and used for
the wakefield calculations. Both methods lead to comparable results: the
operation of TESLA with 25 micro meter bunches is possible but leads to an
additional heat load due to the higher order modes (HOMs). Therefore HOM
dampers for these high frequencies are under construction. These dampers are
located in the beam pipes between the 9-cell cavities. So it is of interest, if
there are trapped modes in the cavity due to closed photon orbits. In this
paper we investigate the existence of trapped modes and the distribution of
heat load over the surface of the TESLA cavity by numerical photon tracking.
