Rayleigh-Taylor instability and turbulent mixing governs a wide variety of plasma phenomena in nature and technology, spanning astrophysical to microscopic scales and low to high energy density regimes. It influences the formation of the 'hot spot' in inertial confinement fusion, limits radial compression of imploding Z-pinches, drives penetration of stellar ejecta into pulsar wind nebula, dominates energy transport in core-collapse supernova, provides conditions for synthesis of heavy mass elements in thermonuclear stellar flashes, controls material transformation under high strain rates, and strongly affects the dynamics of shocks and blast waves. Rayleigh-Taylor instability develops when matters (plasmas) of different densities are accelerated against the density gradients. The induced material mixing is a complex (anisotropic, inhomogeneous and statistically unsteady) turbulent process, whose theoretical description requires novel approaches that go well beyond the domain of idealized canonical considerations. The tremendous successes achieved recently in high energy density plasma experiments and in large-scale numerical simulations, and the striking similarity of behavior of Rayleigh-Taylor mixing in vastly different physical regimes make this moment right for a theory to appear and to advance knowledge of fundamental aspects of the non-equilibrium turbulent processes in plasmas.

The core of this theoretical approach is a new concept, the invariance of the rate of momentum loss. This concept will be applied to capture the transports of mass, momentum and energy in Rayleigh-Taylor mixing plasmas and to study invariants, scale coupling, scaling, and statistics of the turbulent process. Group theory and stochastic analysis considerations will be employed, and coherence and randomness of the dynamics will be analyzed and related to space-time symmetries of the conservation laws. Incorporating the high energy density conditions, the dependencies of integral characteristics of plasma mixing will be investigated and their connection will be established to the control parameters of simulations and experiments (e.g. target non-uniformities in high-power laser experiments). The developed theoretical foundations will be further applied to analyze existing datasets and to advance the design of experiments and simulations. The project will impact a broad range of disciplines in science, mathematics and engineering, including plasmas, high energy density physics, astrophysics, mathematical physics, stochastic processes, fluid dynamics, and material science, as well as technology in the areas of nuclear energy and communications. It will also initiate a new program for graduate education on modern methods of theoretical modeling and advanced data analysis techniques. The theoretical tools will be communicated through and contribute to the development of a newly emerging international research community 'Turbulent mixing and beyond.'

Project Report

The research conducted within this project serves to understand the fundamental properties of non-equilibrium turbulent processes in high energy density plasmas, to implement this knowledge for design of experiments and simulations, and to elaborate the new methods of mitigation and control of non-equilibrium plasma processes. The PI, since her move to Carnegie Mellon University (CMU), has built a new active research group involving graduate and undergraduate students at the CMU, who productively work on challenging research problems and get training in physics of high energy density plasmas, as well as in hydrodynamics, theoretical physics and applied mathematics. In the past year the PI and her students have obtained several important results. These include: (1) Accelerated character of blast-wave-driven RT mixing flow on the basis of the first scrupulous quantitative analysis of experimental data of high energy density plasma experiments. (2) Qualitative and quantitative indication of the finite amount of energy of the interfacial mixing that can be deposited by the shock. (3) The first theoretical models of hydrodynamic instabilities and mixing in fusion-relevant conditions with time-dependent acceleration. The problem of hydrodynamic instabilities and interfacial mixing they induce are relevant to a broad range of plasma phenomena under conditions of high or low energy density, including formation of the hot spot in inertial confinement fusion, thermonuclear flashes on the surface of compact stars, premixed and non-premixed combustion, and material transformation under impact. The results of this research can be applied in nuclear energy technology, including target design in inertial confinement fusion, in nano-electronics, as well as in traditional industrial application in aerodynamics and aeronautics.

National Science Foundation (NSF)
Division of Physics (PHY)
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Vyacheslav S. Lukin
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Carnegie-Mellon University
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