where N(t) is average neutron flux density, (neutron/[cm.sup.3]), [C.sub.i](t) is Gth groups of delayed neutron
precursors, (i = 1, 2, ..., G), (atom/[cm.sup.3]), [rho](t) is reactivity, where 1.0$ = [rho]/[beta], [[lambda].sub.i] is the ith group decay constant ([s.sup.-1]), [[beta].sub.i] is the ith group delayed fraction, [beta] = [[summation].sup.G.sub.i=1][[beta].sub.i], [LAMBDA] is the neutron generation time (s), [k.sub.c] is the reciprocal of the reactor heat capacity, and G is the total number of delayed neutron
Unlike differential die-away or delayed neutrons
and gamma rays, this signature can be detected with passive means provided the SNM is not well shielded.
The effective delayed neutron
fraction is a key reactor safety parameter involved in the control rods worth calculations and transient (reactivity feedback effect) studies.
where i = 1, ..., N, [n.sub.r,i] is the relative neutron flux of the ith node, [C.sub.r,i,k] is the relative concentration of the kth delayed neutron
group of the ith node, [[alpha].sub.i,i] and [[alpha].sub.i,i] (j = 1, ..., [N.sub.i]) are the coupling coefficients corresponding to the ith node, [N.sub.i] is the number of adjacent nodes of the ith node, [[LAMBDA].sub.i] is the prompt neutron lifetime in the ith node, [[rho].sub.i] is the reactivity of the ith node, [beta] is the fraction of all the delayed neutrons
in all the nodes, and [[beta].sub.k] is the fraction of the fcth delayed neutron
group in every node.
The neutron dynamics of the reactor core is simplified with 6 precursor groups of delayed neutron
point-kinetics as shown in (3).
Since most neutrons released by fission of SNM are "prompt" (released immediately), the prompt neutron signal is much larger, and thus easier to detect, than that of delayed neutrons
. Fission of SNM generates high-energy neutrons; by adding detectors that can discriminate between neutrons on the basis of their energies, SAIC expects that its system will be able to determine if a high-Z object is SNM.