Harmonic-free channel-cut x-ray crystal monochromator with focusing effect

It is shown that a channel-cut crystal monochromator may be harmonics-free in the whole range of Bragg angles, if the second wall is suitably curved (not bent). The curvature is described by the functionf(x)=Cx K, whereC is an arbitrary constant. There are two solutions:K 0 with the surface concave. The concave surface decreases the divergence of the diffracted beam or even it may create slightly convergent beam due to refraction. Both solutions are theoretically compared and it is shown that the concave monochromator may be useful for sufficiently large monochromator-sample distances.