Neutron sources that produce fast neutrons uses a Spallation process but why not use a non-uniform magnetic field to act on the magnetic moment of the neutron to accelerate it, we know that the neutron will precess around the field say in the z-axis, then a gradient of the magnetic field in the plus z-direction will accelerate the neutron in the minus z-direct.
Neutrons are not influenced by magnetic field. They small microscopically small magnetic moment. Reactors and Neutron sources are sufficient to produce Neutrons of varying energy. In addition proton accelerators can be used to generate Neutrons.
Of course, one might think of a field gradient accellerating spin polarized neutrons. In practice you will have difficulties to (a) confine and steer a neutron beam this way and (b) generating significant energy differences with manageable fields (calculate e.g. the Zeeman energy splitting for a neutron in 100T, for example, think what field gradients could be manageable technically and make an order of magnitude estimate of the spatial scales involved...)
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