On Frequency / Time Invariance of Certain Temporal and Complex Transfer Functions for the 1d Interfacial Monochromatic Neutron Density Wave

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, addressed in this paper, can be essential ingredients of such optimization. Accordingly, we study the dynamics of a 1D monochromatic neutron density wave generated by time modulation of a boundary neutron current. It is demonstrated that a certain temporal transfer function of both parabolic (diffusion) and low frequency hyperbolic (P?1 transport) interfacial neutron density wave happens to be frequency non-invariant 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.