Measurements from the JET neutron profile monitor are analysed tomographically to deduce the 2-D spatial distribution of neutron emissivity during NBI heating both before and after sawtooth crashes. In a discharge where the global neutron emission decreases slightly to 5/6 of the pre-crash rate of nearly 1016 n/s, the axial emissivity drops much more to only 1/6 of the pre-crash value. The sources of neutron emissivity are analysed with an analytic Fokker-Planck formulation. The main change in neutron emissivity is due to fast ion redistribution during a sawtooth crash and a decrease in beam-beam produced emissivity. The deduced fast ion redistribution is consistent with other observations on sawtooth behaviour in JET.