Simulation Project tripleaxis: A focusing monochromator

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The RITA-2 monochromator is placed just after the guide exit (0.4 m downstream). It consists of 5 slabs of pyrolytic graphite (PG) crystals with a mosaicity of 37 arc minutes, 0.15 m wide and 0.025 m tall, displaced 0.026 m vertically with respect to the neighbour slaps. We denote the scattering angle at the monochromator TTM.

The five slabs can be rotated individually around their horizontal axis. The idea behind this is to focus the beam vertically on to the sample, which is positioned 1.54 m from the monochromator centre.

Analyze the geometry to find an expression for the optimal tilting angle of one blade in a vertically focusing monochromator as a function of neutron wavelength (or scattering angle).

Hint

You can consider the beam leading the guide as being parallel and horizontal.

Hint

It is an advantage to consider the neutron \({\bf k}\)-vectors, and to focus on its \(y\)-component.