  A surprising small dechanneling length was observed at (111) channeling of
ultrarelativistic electrons in a 60 $\mu$m thick silicon single crystal with a
bending radius of 0.15 m. The experiments were conducted at beam energies
between 3.35 and 14 GeV at the Facility for Advanced Accelerator Experimental
Tests (FACET at SLAC, USA). It is shown in this paper that the small
dechanneling lengths can well be reproduced with a modified Fokker-Planck
equation for plane crystals in which a crystal bending has been heuristically
introduced. Encouraged by this result experiments have been reconsidered which
were performed at the Mainz Microtron MAMI with (110) silicon undulator
crystals. The results obtained with the modified Fokker-Planck equation suggest
that the observed rather low undulator peak intensity originates from the
strongly reduced dechanneling length of electrons in the bent sections of the
undulator. A scaling law derived on the basis of the modified Fokker-Planck
equation reveals optimized parameters of electron based undulators as possible
radiation sources in the $X$- and $\gamma$-ray region.
