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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).
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.
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
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
Magnetic reconnection and dynamos in the presence of plasma turbulence
Evolving magnetic fields are frequently embedded in plasmas that are turbulent. When the primary interest is in effects that are on a large scale compared to that of the turbulence, it is desirable to average over the turbulence to obtain equations for mean-field magnetohydrodynamics. An obvious constraint on the validity of the averaging is that large-scale quantities that evolve slowly using the exact evolution equations must remain slowly evolving in the mean-field theory. Magnetic helicity is the primary example of such a quantity, and maintaining its slow evolution has been controversial in mean-field magnetohydrodynamics. A full theory of magnetic reconnection in turbulent plasmas is not the intent of this paper. The intent is to show how exact results from Maxwell's equations explain why fast reconnection is so ubiquitous and what constraints these results place on the theory of magnetic field evolution, including dynamos, whether the plasma is turbulent or not. These constraints are commonly broken in the reconnection literature, which has been heavily influenced by two-dimensional theory that is not applicable to three-dimensional problems.
Conservation equations for weakly turbulent plasmas.
Conservation equations for weakly turbulent plasma in magnetic field derived in quasi-linear approximation
Very long baseline interferometer measurements of plasma turbulence in the solar wind
Plasma turbulence in the solar wind is investigated using angular broadening VLBI measurements at 4.99 GHz of ten extragalactic compact radio sources (quasars). The measured broadening size was corrected for intrinsic source structures which were obtained from separate VLBI observations. It was found that the measured angular sizes are considerably less than those predicted by the Erickson's (1964) empirical relationship, as well as by two other models for the strength of scattering as a function of solar elongation. However, the measurements are in good agreement with a model for the spatial power spectrum of turbulence, proposed by Coles and Harmon (1989).
On the use of a priori statistics in problems of plasma turbulence
Statistical averaging procedure in problems of plasma turbulence involving Vlasov equation
The interaction of charged particles with a turbulent plasma <o vzaimodeystvii zaryazhennykh chastits s turbulentnoy plazmoy<
Charged particles interaction with turbulent plasma
A unified quasilinear theory of weakly turbulent plasmas
Quasi-linear theory of turbulent plasmas with fluctuation fields and coherent waves