  The most promising way to increase the output power of an X-ray FEL (XFEL) is
by tapering the magnetic field of the undulator. Also, significant increase in
power is achievable by starting the FEL process from a monochromatic seed
rather than from noise. This report proposes to make use of a cascade
self-seeding scheme with wake monochromators in a tunable-gap baseline
undulator at the European XFEL to create a source capable of delivering
coherent radiation of unprecedented characteristics at hard X-ray wavelengths.
Compared with SASE X-ray FEL parameters, the radiation from the new source has
three truly unique aspects: complete longitudinal and transverse coherence, and
a peak brightness three orders of magnitude higher than what is presently
available at LCLS. Additionally, the new source will generate hard X-ray beam
at extraordinary peak (TW) and average (kW) power level. The proposed source
can thus revolutionize fields like single biomolecule imaging, inelastic
scattering and nuclear resonant scattering. The self-seeding scheme with the
wake monochromator is extremely compact, and takes almost no cost and time to
be implemented. The upgrade proposed in this paper could take place during the
commissioning stage of the European XFEL, opening a vast new range of
applications from the very beginning of operations. We present feasibility
study and examplifications for the SASE2 line of the European XFEL.
