Neutrons have a measureable magnetic dipole momentum from their intrinsic spin. Is it possible to slow down and catch the neutron by imposing a force by an inhomogeneous magnetic field. I think the force the neutron experiences in a magnetic field is \begin{align} \bar{F} = \bar{\nabla}(\bar{m}\cdot\bar{B}). \end{align}
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As far as I know the first 3D magnetic neutron trap was build at NIST in 2000. See this popular article for an overview, or if you can get past the paywall this article in Nature or I think this paper on the Arxiv is the same publication.
It's a standard magnetic trap, after all a magnetic dipole is a magnetic dipole is a magnetic dipole. However because the neutron magnetic moment is small the trap depth was only a millikelvin or so. It took considerable effort to get neutrons cold enough to be trapped.

Urb
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John Rennie
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I find that to be very depressing to know. Neutrons are very bad for fusion reactions. I wish there was a way to harness their wasteful kinetic energy. I was wondering if a carbon nanotube with a AC bulk electron transport current could somehow induce an electromagnetic field that slows the neutron by wrenching on its spin. – linuxfreebird Mar 15 '14 at 16:07