  By restricting the spatial energy transmission of an electromagnetic wave,
dielectric waveguides transmit light over long distances at sustained
intensity. Waveguides have been used in the microwave and optical range to
maintain strong signal intensities in connection with lasers, but guiding of
intense short-wavelength radiation such as x-rays has proven more cumbersome.
Here we investigate theoretically how tapered x-ray waveguides can focus and
guide radiation from x-ray free electron lasers. Elliptical waveguides using a
cladding material with high atomic number such as platinum can maintain an
x-ray intensity up to three orders of magnitude larger than in free space. This
feature can be used to significantly enhance resonant interactions of x-rays,
for instance driving nuclear transitions up to transient nuclear population
inversion. This could be the first breakthrough in nuclear state population
control. Our results anticipate the important role of tapered x-ray waveguides
in the emerging field of x-ray quantum optics with nuclear transitions.
