Problem:Neutron velocity selector

A neutron velocity selector is a drum that spins around an axis parallel to the beam. This axis lies below the guide. From the drum, a series of absorbing neutron blades sticks out radially. The ends of the drum are twisted with respect to each other. A principal sketch is shown in velocity selector figure on the Instrumentation page.

This effect of the selector is that only neutrons around a certain velocity (or wavelength) can pass through it.

Assume a selector length of \(L=0.25\) m, \(n=68\) blades, and a twisting angle, \(\phi = 48.3^\circ\), as for the selector at the SANS-2 instrument at PSI. Calculate the rotation speed you should use to select 10 Å neutrons.

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Hint

Consider how long time it will take the neutron to travel through the velocity selector.

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Hint

What should the angular velocity \(\omega\) be, when twisting \(48.3^\circ\) during the same period of time it takes the neutron to travel through the velocity selector?

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Solution

The velocity, \(v\), of neutron with \(\lambda=10\)Å is

\(v=\frac{h}{m_n \lambda}\),

and the time it takes the neutron to travel through the drum of the velocity selector, is

\(\Delta t = \frac{L}{v}=6.34*10^{-4}\).

Thereby the angular velocity, \(\omega\), is

\(\omega = \frac{\phi v}{L} =1333.9 \frac{\text{rad}}{\text{s}} = 12738 \, \text{rpm}\)