Abstract
Optimization of dynamical multibeam neutron cancer therapy has recently been shown to be possible via employment of the beam frequencies of neutron waves as a control variable. The concepts of transfer functions (TF), addressed in this paper, can be essential ingredients of such optimization. Accordingly, the paper studies the dynamics of a one-dimensional (1D) monochromatic neutron density wave generated by time modulation of a boundary neutron current. It is demonstrated that a certain temporal transfer function (TTF) of both parabolic (diffusion) and low frequency hyperbolic (P−1 transport) interfacial neutron density wave happens to be frequency noninvariant with a vibrating boundary neutron current. It is proved that, only at high frequencies, both parabolic and hyperbolic interfacial neutron waves turn out to have a fully frequency-invariant and time-invariant temporal transfer function relative to such a vibrating neutron beam at the boundary. The frequency response of an associated complex transfer function is studied and demonstrated to change behavior, from a lag compensator to a fixed gain amplifier, with changing the frequency, neutron absorption and employed theory for neutron diffusion. A highlight of this paper is its illustration that mere continuity of these transfer functions can be a reflection of the correctness of the transport theory employed for modeling the neutron density waves.
Issue Section:
Reactor Physics
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