Non-modal stability analysis of magnetohydrodynamic flows for liquid metal blankets of fusion reactors

The research and experimentation in the field of magnetic confinement fusion is constantly advancing. For precise control of the thermonuclear plasma and the operating fluids in fusion reactors, it is essential to reach a comprehensive understanding of the behavior of conducting fluids interacting with magnetic fields. This study focuses on one of the options envisaged for the breeding blanket of the future tokamaks and explores the impact of different magnetic profiles on the flow regime of lead-lithium. The stability of magnetohydrodynamic (MHD) flow in an infinite pipe is investigated, with a focus on the influence of the applied magnetic field on fluid dynamics. This study specifically compares the effects of magnetic fields with different intensity on the general stability. Both the classical modal stability analysis and the more recent non-modal approach have been adopted to study, respectively, the asymptotic and the short-term evolution of the magnetohydrodyamic system after perturbations in the applied magnetic field or in the thermofluid regime. The results highlight the importance of using the non-modal stability, which allows to investigate the transient growths experienced by the perturbed system, a phenomenon not observable by modal stability analysis alone. Additionally, a zero-dimensional lumped model of the lead-lithium pipe flow is examined to study the impact of thermal effects on system stability and wall deformations of the pipe. The results suggest that the deformation effects experienced by the walls due to temperature oscillations in the perturbed system are negligible.