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Implications of Navier-Stokes turbulence theory for plasma turbulence
Plasma turbulence is considered within the framework of the Navier-Stokes turbulence theory. Two-dimensional turbulence is discussed, noting inverse cascades, and compared to three-dimensional turbulence. MHD turbulence is described with reference to applications of the Navier-Stokes theory and the possibility of inverse magnetic cascades. Turbulence in Vlasov plasmas is outlined on the basis of the direct interaction approximation developed for Navier-Stokes fluids (Kraichnan, 1958-1959).
Uncovering turbulent plasma dynamics via deep learning from partial observations
One of the most intensely studied aspects of magnetic confinement fusion is edge plasma turbulence which is critical to reactor performance and operation. Drift-reduced Braginskii two-fluid theory has for decades been widely applied to model boundary plasmas with varying success. Towards better understanding edge turbulence in both theory and experiment, we demonstrate that a novel multi-network physics-informed deep learning framework constrained by partial differential equations can accurately learn turbulent fields consistent with the two-fluid theory from partial observations of electron pressure which is not otherwise possible using conventional equilibrium models. Furthermore, this technique presents a novel paradigm for the advanced design of plasma diagnostics and validation of magnetized plasma turbulence theories in challenging thermonuclear environments.
Uncovering turbulent plasma dynamics via deep learning from partial observations
One of the most intensely studied aspects of magnetic confinement fusion is edge plasma turbulence which is critical to reactor performance and operation. Drift-reduced Braginskii two-fluid theory has for decades been widely applied to model boundary plasmas with varying success. Towards better understanding edge turbulence in both theory and experiment, we demonstrate that a novel multi-network physics-informed deep learning framework constrained by partial differential equations can accurately learn turbulent fields consistent with the two-fluid theory from partial observations of electron pressure which is not otherwise possible using conventional equilibrium models. This technique presents a novel paradigm for the advanced design of plasma diagnostics and validation of magnetized plasma turbulence theories in challenging thermonuclear environments.
Resonant diffusion in the presence of strong plasma turbulence
The diffusion equation which describes the evolution of the average one particle distribution function for an ensemble of strongly turbulent plasmas is derived. The diffusion tensor is a time integral of the autocorrelation tensor of the fluctuations as observed by particles moving along statistically distributed orbits. These orbits contain the effects of fluctuations and thus differ from those encountered in weak turbulence theory. The plasma trajectory equations are used to relate each to the diffusion tensor itself when the turbulence is electrostatic. The diffusion tensor is explicity evaluated for a strongly turbulent unmagnetized plasma.
Implications of Navier-Stokes turbulence theory for plasma turbulence
The methodology of Navier-Stokes fluid turbulence theory is reviewed, with emphasis placed on the relevance of the Navier-Stokes concepts for understanding plasma turbulence. After a brief consideration of the three-dimensional case, two-dimensional problems are discussed. In addition, MHD turbulence and turbulence in Vlasov plasmas are treated. In particular, the direct interaction approximation developed by Kraichnan (1959) is generalized from Navier-Stokes turbulence theory to produce a computable set of differentio-integral equations for a Vlasov plasma.
Resonant diffusion in the presence of strong plasma turbulence.
The diffusion equation which describes the evolution of the average one-particle distribution function for an ensemble of strongly turbulent plasmas is derived. The diffusion tensor is a time integral of the autocorrelation tensor of the fluctuations as observed by particles moving along statistically distributed orbits. These orbits contain the effects of fluctuations and thus differ from those encountered in weak turbulence theory. Two statistical orbit effects quadratic in the strength of the fluctuations affect the magnitude of the diffusion: (a) modification of the ensemble average orbits by the fluctuations, and (b) statistical dispersion in particle orbits about the average. The plasma trajectory equations are used to relate each to the diffusion tensor itself when the turbulence is electrostatic. The diffusion tensor is explicitly evaluated for a strongly turbulent unmagnetized plasma.
Millimeter-wave beam scattering and induced broadening by plasma turbulence in the TCV tokamak
The scattering of millimeter-wave beams from electron density fluctuations and the associated beam broadening are experimentally demonstrated. Using a dedicated setup, instantaneous deflection and (de-)focusing of the beam due to density blobs on the beam path are shown to agree with full-wave simulations. The detected time-averaged wave power transmitted through the turbulent plasma is reproduced by the radiative-transfer model implemented in the WKBeam code, which predicts a ~50% turbulence-induced broadening of the beam cross-section. Finally, the role of core turbulence for the considered geometry is highlighted.
Cascade mechanism of nonlinear interactions between modes in a turbulent plasma
Cascade mechanism for developing hydrodynamical model of nonlinear plasma turbulence
Electric conductivity of weakly turbulent plasmas
Weakly turbulent plasmas static electric conductivity derivation from kinetic equation for linear response to one-particle distribution function
Scale Separation Effects on Simulations of Plasma Turbulence
Abstract Understanding plasma turbulence requires a synthesis of experiments, observations, theory, and simulations. In the case of kinetic plasmas such as the solar wind, the lack of collisions renders the fluid closures such as viscosity meaningless and one needs to resort to higher-order fluid models or kinetic models. Typically, the computational expense in such models is managed by simulating artificial values of certain parameters such as the ratio of the Alfvén speed to the speed of light ( v A / c ) or the relative mass ratio of ions and electrons ( m i / m e ). Although, typically care is taken to use values as close as possible to realistic values within the computational constraints, these artificial values could potentially introduce unphysical effects. These unphysical effects could be significant at sub-ion scales, where kinetic effects are the most important. In this paper, we use the 10-moment fluid model in the Gkeyll framework to perform controlled numerical experiments, systematically varying the ion–electron mass ratio from a small value down to the realistic proton–electron mass ratio. We show that the unphysical mass ratio has a significant effect on the kinetic range dynamics as well as the heating of both plasma species. The dissipative process for both ions and electrons becomes more compressive in nature, although the ions remain nearly incompressible in all cases. The electrons move from being dominated by incompressive viscous-like heating/dissipation to very compressive heating/dissipation dominated by compressions/rarefactions. While the heating change is significant for the electrons, a mass ratio of m i / m e ∼ 250 captures the asymptotic behavior of electron heating.
Understanding plasma turbulence through exact coherent structures
Plasma turbulence is a key challenge in understanding transport phenomena in magnetically confined plasmas. This work presents a generalized framework to analyze plasma turbulence that utilizes periodic orbit theory. In periodic orbit theory, doubly periodic solutions (coherent structures) of the governing equation(s) serve as building blocks of the considered turbulent dynamics. To illustrate the concept and method, the particularly simple Kuramoto–Sivashinsky (referred to here as LMRT for the original authors: LaQuey, Mahajan, Rutherford, and Tang) trapped-ion mode toy model is used. By applying numerical optimization techniques to the LMRT equation, we extract coherent spacetime patterns that represent the library of allowable fundamental structures of the equation. These structures provide a framework to systematically describe turbulence as a composition of recurrent solutions, revealing an underlying order within chaotic plasma motion. Although illustrated here using the simplified LMRT model for clarity, this framework provides a general strategy that can be extended to more complex and realistic models of plasma turbulence, including gyrokinetic systems. This offers a new method for predicting and potentially controlling transport processes in fusion plasmas by providing a bridge between nonlinear dynamical systems theory and plasma physics in the form of a generalized framework with which to analyze and understand spatially extended nonlinear partial differential equations.
Resonant diffusion in strongly turbulent plasmas.
The effect of turbulent fluctuations on plasma particles is considered, and equations are derived which describe the evolution of macroscopic properties such as temperature and flow speed of the turbulent plasma. Initially, a diffusion equation for a single-particle distribution function averaged over an ensemble of plasmas is derived for an unmagnetized plasma. For the resonant diffusion in strongly turbulent plasmas, an ensemble of three-dimensional plasmas is considered with an approximately homogeneous and stationary distribution of random electromagnetic fluctuations. For each realization, the single-particle distribution function satisfies the Vlasov equation.
Cascade theory of plasma turbulence
Cascade theory of plasma turbulence described by small eddy group mixing with larger ones to provide gradient diffusive flow
Statistical acceleration of particles in turbulent plasma
Statistical mechanics of particle acceleration in turbulent plasma
Propagation of radio frequency waves through turbulent plasmas
The practical and economic viability of tokamak fusion reactors depends, in a significant way, on the efficiency of radio frequency (RF) waves to deliver energy and momentum to the plasma in the core of the reactor. The RF electromagnetic waves, excited by antenna structures placed near the wall of a tokamak, have to propagate through the turbulent edge plasma along their path to the core of the fusion device. In present day experiments, the radial width of the edge region and scrape-off layer is of the order of a few centimeters. In ITER, and in future fusion reactors, this width will be of the order of tens of centimeters. Any effects on RF waves due to plasma turbulence have to be properly understood in order to optimize the delivery of RF energy and momentum into the core. This paper is on a multi-pronged, theoretical and computational, approach that is being pursued to quantify the effect of edge plasma turbulence on the propagation of RF waves. The theoretical and analytical models are based on solutions of the Faraday-Ampere equation in a magnetized plasma and on the Kirchhoff tangent plane approximation. An effective medium approach has been developed so as to approximate the permittivity of a turbulent plasma by analytical expressions. The computations are being carried out with a newly developed code ScaRF that is based on the finite difference finite domain technique for solving Maxwell's equations. The plasma permittivity can be assigned as desired. The code is being used to validate the analytical and theoretical models and to evaluate their limitations.
A reduced-model (nSOLT) simulation of neutral recycling effects on plasma turbulence in the divertor region of MAST-U
The 2D scrape-off-layer turbulence code (nSOLT), which includes 1D kinetic neutral–plasma interactions, is applied to study effects of neutral recycling on plasma turbulence for parameters illustrative of the MAST-U divertor region. Neutral recycling is modeled by injecting a fraction of the parallel plasma flux to the divertor back into the simulation domain as a source of Franck–Condon-distributed neutrals. Stationary sources, concentrated at the magnetic separatrix, model plasma streaming into the divertor region from the upstream scrape-off-layer and sustain plasma turbulence absent neutral recycling. Starting from one such no-neutrals equilibrium, we initiate recycling in a numerical experiment designed to diagnose and identify the effects of various neutral–plasma interactions on the divertor plasma, divertor turbulence, and plasma exhaust. The onset of recycling triggers an initial burst of enhanced cross field plasma transport that is quelled by ionization cooling and charge–exchange (CX) friction, with growing neutral pressure, leading to a quiescent, turbulence-free state. Diagnosis of this transient burst reveals that (1) the sudden increase in plasma density due to ionization dominates the onset of the burst, (2) electron cooling due to ionization increases collisionality and disconnects blob filaments from the sheath, and (3) CX friction drives tripole polarization of a blob that can dominate the curvature-driven dipole polarization, leading to the stagnation of blob propagation and reduced radial turbulent transport. It is shown that CX friction is negligible compared to sheath physics in determining equilibrium mean flow shearing rates, for parameters considered herein (specifically a short connection length to the divertor target), while it can significantly reduce interchange-instability growth rates.