  Self-seeding is a promising approach to significantly narrow the SASE
bandwidth of XFELs to produce nearly transform-limited pulses. The
implementation of this method in the soft X-ray wavelength range necessarily
involves gratings as dispersive elements. We study a very compact self-seeding
scheme with a grating monochromator originally designed at SLAC, which can be
straightforwardly installed in the SASE3 type undulator beamline at the
European XFEL. The monochromator design is based on a toroidal VLS grating
working at a fixed incidence angle mounting without entrance slit. It covers
the spectral range from 300 eV to 1000 eV. The optical system was studied using
wave optics method (in comparison with ray tracing) to evaluate the performance
of the self-seeding scheme. Our wave optics analysis takes into account the
actual beam wavefront of the radiation from the coherent FEL source, third
order aberrations, and errors from each optical element. Wave optics is the
only method available, in combination with FEL simulations, for the design of a
self-seeding monochromator without exit slit. We show that, without exit slit,
the self-seeding scheme is distinguished by the much needed experimental
simplicity, and can practically give the same resolving power (about 7000) as
with an exit slit. Wave optics is also naturally applicable to calculations of
the self-seeding scheme efficiency, which include the monochromator
transmittance and the effect of the mismatching between seed beam and electron
beam. Simulations show that the FEL power reaches 1 TW and that the spectral
density for a TW pulse is about two orders of magnitude higher than that for
the SASE pulse at saturation.
