A Resonated and Synchrophased Three Beams Neutron Cancer Therapy Installation

Abstract

The technique of composite region coupling by a neutron source at a common boundary of different regions that has been introduced in 2019 has allowed for an additive separation of variables neutron-density 3D wave analytical solution to the posing four-regional boundary value problem (BVP) of neutron cancer therapy (NCT). The three employable mutually orthogonal neutron beams, which may have different pulse shapes, have distinct modulation frequencies ω,ϖ, and ŵ and distinct relative time delays ε and ε̂. By employing this solution, we demonstrate in this paper how the therapeutic utility index and the ballistic index for this kind of dynamical NCT form a nonlinear optimization problem. Both of these indices are demonstrated to be remarkably periodically discontinuous in ε or ε̂, even in the neighborhood of the respective ε∗ or ε̂∗. As an extension of a result obtained also in 2019, for a certain lower-dimensional setup, a Pareto optimal control vector ω∗=(ω∗,ϖ∗,ε∗,ŵ∗,ε̂∗) is identified for this 3D problem. The existence of this vector paves the way toward what we call a “resonated and synchrophased three beams neutron cancer therapy (RASP-3BNCT) installation.”