Non-Equilibrium Turbulent Processes in Plasmas

瑞利-泰勒不稳定性和湍流混合控制着自然界和技术中的各种等离子体现象，从天体物理到微观尺度，从低能量密度到高能量密度区域。它影响惯性约束聚变“热点”的形成，限制内爆Z箍缩的径向压缩，驱动恒星抛射物对脉冲星风星云的穿透，主导核心塌缩超新星的能量传输，为热核恒星闪电中重质量元素的合成提供条件，控制高应变率下的物质转变，并强烈影响激波和冲击波的动力学。当不同密度的物质(等离子体)相对于密度梯度加速时，会产生瑞利-泰勒不稳定性。诱导材料混合是一个复杂的(各向异性、非均匀和统计非定常)湍流过程，其理论描述要求新的方法远远超出理想化正则考虑的领域。最近在高能密度等离子体实验和大规模数值模拟中取得的巨大成功，以及Rayleigh-Taylor混合在非常不同的物理区域中行为的惊人相似，使得理论应运而生，并促进了对等离子体中非平衡湍流过程基本方面的认识。该理论方法的核心是一个新的概念，即动量损失率不变性。这一概念将被用来捕捉瑞利-泰勒混合等离子体中质量、动量和能量的输运，并研究湍流过程的不变量、尺度耦合、标度和统计特性。我们将运用群论和随机分析的思想，分析动力学的连贯性和随机性，并将其与守恒定律的时空对称性联系起来。结合高能密度条件，将研究等离子体混合积分特性的相关性，并将它们与模拟和实验的控制参数(例如，高功率激光实验中的目标非均匀性)建立联系。所开发的理论基础将进一步应用于分析现有的数据集，并推进实验和模拟的设计。该项目将影响科学、数学和工程领域的广泛学科，包括等离子体、高能量密度物理、天体物理、数学物理、随机过程、流体力学和材料科学，以及核能和通信领域的技术。它还将启动一个新的研究生教育方案，内容是现代理论建模方法和先进的数据分析技术。这些理论工具将通过这些工具进行交流，并为一个新出现的国际研究界的发展做出贡献，这个国际研究界被称为“湍流混合与超越”。

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.'