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The core objective of the fusion energy science program is to reach a fundamental physical understanding of the behavior of high-temperature plasmas in the context of plasma configurations capable of plasma confinement sufficient for economic energy extraction. Fusion science aims to study the stability properties and transport behavior of such systems, and in order to conduct these studies, it has made progress in a number of topical areas that have had a broad impact on the larger scientific and industrial community. Examples of some cross-cutting research topics are stability theory; stochasticity, chaos, and nonlinear dynamics; dissipation of magnetic fields; origins of magnetic fields; wave dynamics; and turbulent transport.

Stability Theory

The complex plasma dynamics due to macroinstabilities observed in early plasma experiments motivated the development of powerful energy principles and eigenmode techniques for exploring the linear stability of plasma equilibria. The wide variety of instabilities in plasmas, which span an enormous range of spatial and temporal scales, defines the richness of the plasma medium and challenges us to understand its dynamics. Past research supported by the fusion program greatly improved our ability to predict the thermal pressure beyond which a plasma will disassemble. These predictions were confirmed in experiments in which the plasma temperatures exceeded those found in the core of the Sun. Experimental explorations led to methods that significantly increase the plasma pressure limits set by stability. It speaks to the quality of those studies that the stability analysis techniques developed by the fusion program—such as the energy principle, the notion of convective instability, and weakly nonlinear stability theory—are now essential tools not only in the field of plasma science but also in allied fields such as fluid dynamics, astrophysics, and solar, space, ionospheric, and magnetospheric physics.

Stochasticity, Chaos, and Nonlinear Dynamics

Understanding how magnetic field topology—the existence of bounding magnetic flux surfaces that lead to hot plasma confinement—is controlled by both local and global physical processes and how such bounding flux surfaces break up is a critical research topic for fusion. Interestingly, the same kind of issues also emerged in the description of how an essentially collisionless, unmagnetized plasma is heated; there, the onset of stochasticity needed to be understood in velocity space. This research followed on the heels of the pioneering Kolmogorov-Arnold-Moser (KAM) description of the onset of chaos and therefore contributed to the rapid progress in this field. A number of fundamental tools, including the standard map—now in common use in studies of the onset of stochasticity and chaos in far more general physical settings—came from plasma scientists. Studies of nonlinear wave-wave and wave-particle interactions relevant to both plasma confinement and transport played an important role in the development of tools for dynamical systems theory and nonlinear dynamics, and it was senior scientists trained in the physics of plasmas who developed the first published method for controlling chaos.

Dissipation of Magnetic Fields

A fundamental physics challenge has been to explain the observed very short timescales that characterize the release of magnetic energy in the solar corona, in planetary magnetospheres (including that of Earth), and in fusion experiments. Classical collisional dissipative processes are orders of magnitude too

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