This set of lectures will introduce concepts in nonlinear dynamics and chaos, illustrated by interdisciplinary examples, ranging from mechanical vibrations to biological rhythms. The topics will include differential equations, bifurcations, phase plane analysis of flows on lines and circles, introduction to characteristics of chaos, iterated maps, routes to chaos, and introductory concepts in renormalization, fractals, multifractals and strange attractors.
A central challenge in fusion energy is reconciling the high-confinement mode required for reactor performance with the intense, intermittent relaxation events it produces, known as edge-localized modes (ELMs). These instabilities arise in the steep pressure pedestal at the plasma edge when magnetohydrodynamic stability thresholds are exceeded, imposing damaging heat loads on reactor components. Here, we show that multiscale interactions between microscopic turbulence and macroscopic magnetohydrodynamic modes offer a promising pathway toward the self-regulation of ELMs. Using direct quantitative measurements of multiscale modes, eddy dynamics, and turbulent fluxes, we demonstrate that small-scale electron drift-wave turbulence actively scatters large-scale peeling–ballooning modes. This scattering decorrelates the pressure and velocity fields associated with the instability, thereby arresting its growth. Our modeling and theoretical analysis confirm that this suppression mechanism remains effective even when conventional linear stability thresholds are exceeded.
This set of lectures will introduce concepts in nonlinear dynamics and chaos, illustrated by interdisciplinary examples, ranging from mechanical vibrations to biological rhythms. The topics will include differential equations, bifurcations, phase plane analysis of flows on lines and circles, introduction to characteristics of chaos, iterated maps, routes to chaos, and introductory concepts in renormalization, fractals, multifractals and strange attractors.
