Low-Order Bessel-Type PID Dynamics in Lithium-Based Tritium Breeding and Heat Removal Systems

Abstract

Lithium plays a dual role in deuterium-tritium (D-T) fusion systems by enabling tritium breeding in blankets and providing an efficient heat removal medium in liquid-metal components. However, most existing investigations treat neutronic behavior, jet thermohydraulics, and feedback control as largely decoupled layers, and there is currently no compact analytical framework that simultaneously links lithium-based tritium breeding, jet thermal response, and controller dynamics. In this work, we integrate nuclear cross-section data for D-T and lithium reactions with a reduced thermohydraulic model of a liquid lithium jet and an operator theoretic formulation of feedback control. The resulting blanket/jet configuration should be interpreted as a conceptual, reduced-order demonstration of how two Li-based subsystems can be coupled in a unified analytical framework rather than as a fully realistic reactor design in which an International Fusion Materials Irradiation Facility–type neutron source is directly attached to a self-sufficient power blanket. We derive a low-order model describing jet thermal expansion under deuteron beam loading and demonstrate that a continuous-time proportional-integral-derivative (PID) controller, expressed in operator form, can be locally embedded within a family of Bessel-type differential operators acting on the tritium inventory tracking error. The results suggest that lithium-based breeding and heat removal systems admit low-order, PID controllable dynamics that can be interpreted in terms of localized Bessel modes, providing a compact analytical framework for guiding future controller design and blanket/jet optimization.