Vladimir Zhdankin

Statistical Analysis of Current Sheets in Three-dimensional Magnetohydrodynamic Turbulence

We develop a framework for studying the statistical properties of current sheets in numerical simulations of magnetohydrodynamic (MHD) turbulence with a strong guide field, as modeled by reduced MHD. We describe an algorithm that identifies current sheets in a simulation snapshot and then determines their geometrical properties (including length, width, and thickness) and intensities (peak current density and total energy dissipation rate). We then apply this procedure to simulations of reduced MHD and perform a statistical analysis on the obtained population of current sheets. We evaluate the role of reconnection by separately studying the populations of current sheets which contain magnetic X-points and those which do not. We find that the statistical properties of the two populations are different in general. We compare the scaling of these properties to phenomenological predictions obtained for the inertial range of MHD turbulence. Finally, we test whether the reconnecting current sheets are consistent with the Sweet-Parker model.

Magnetic Discontinuities in Magnetohydrodynamic Turbulence and in the Solar Wind

Recent measurements of solar wind turbulence report the presence of intermittent, exponentially distributed angular discontinuities in the magnetic field. In this Letter, we study whether such discontinuities can be produced by magnetohydrodynamic (MHD) turbulence. We detect the discontinuities by measuring the fluctuations of the magnetic field direction, Δθ, across fixed spatial increments Δx in direct numerical simulations of MHD turbulence with an imposed uniform guide field B(0). A large region of the probability density function (pdf) for Δθ is found to follow an exponential decay, proportional to exp(-Δθ/θ(*)), with characteristic angle θ(*)≈(14°)(b(rms)/B(0))(0.65) for a broad range of guide-field strengths. We find that discontinuities observed in the solar wind can be reproduced by MHD turbulence with reasonable ratios of b(rms)/B(0). We also observe an excess of small angular discontinuities when Δx becomes small, possibly indicating an increasing statistical significance of dissipation-scale structures. The structure of the pdf in this case closely resembles the two-population pdf seen in the solar wind. We thus propose that strong discontinuities are associated with inertial-range MHD turbulence, while weak discontinuities emerge from dissipation-range turbulence. In addition, we find that the structure functions of the magnetic field direction exhibit anomalous scaling exponents, which indicates the existence of intermittent structures.

DISTRIBUTION OF MAGNETIC DISCONTINUITIES IN THE SOLAR WIND AND IN MAGNETOHYDRODYNAMIC TURBULENCE

The statistical properties of magnetic discontinuities in the solar wind are investigated by measuring fluctuations in the magnetic field direction, given by the rotation {Delta}{theta} that the magnetic field vector undergoes during time interval {Delta}t. We show that the probability density function, P({Delta}{theta}), can be described by a simple model in which the magnetic field vector purely rotates with a relative increment {Delta}B/B that is lognormally distributed. We find that the probability density function of increments, P({Delta}B/B), has a remarkable scaling property: the normalized variable x = ({Delta}B/B) {center_dot} ({Delta}t/{Delta}t{sub 0}){sup -{alpha}} has a universal lognormal distribution for all time intervals {Delta}t. We then compare measurements from the solar wind with those from direct numerical simulations of magnetohydrodynamic (MHD) turbulence. We find good agreement for P({Delta}{theta}) obtained in the two cases when the magnetic guide field to fluctuations ratio B{sub 0}/b{sub rms} is chosen accordingly. However, the scale invariance of P({Delta}B/B) is broken in the MHD simulations with relatively limited inertial interval, which causes P({Delta}{theta}) to scale with measurement interval differently than in the solar wind.

ENERGY DISSIPATION IN MAGNETOHYDRODYNAMIC TURBULENCE: COHERENT STRUCTURES OR “NANOFLARES”?

We investigate the intermittency of energy dissipation in magnetohydrodynamic (MHD) turbulence by identifying dissipative structures and measuring their characteristic scales. We find that the probability distribution of energy dissipation rates exhibits a power law tail with index very close to the critical value of -2.0, which indicates that structures of all intensities contribute equally to energy dissipation. We find that energy dissipation is uniformly spread among coherent structures with lengths and widths in the inertial range. At the same time, these structures have thicknesses deep within the dissipative regime. As the Reynolds number is increased, structures become thinner and more numerous, while the energy dissipation continues to occur mainly in large-scale coherent structures. This implies that in the limit of high Reynolds number, energy dissipation occurs in thin, tightly packed current sheets which nevertheless span a continuum of scales up to the system size, exhibiting features of both coherent structures and nanoflares previously conjectured as a coronal heating mechanism.

SPECTRAL BREAKS OF ALFVÉNIC TURBULENCE IN A COLLISIONLESS PLASMA

Recent observations reveal that magnetic turbulence in the nearly colisionless solar wind plasma extends to scales smaller than the plasma microscales, such as ion gyroradius and ion inertial length. Measured breaks in the spectra of magnetic and density fluctuations at high frequencies are thought to be related to the transition from large-scale hydromagnetic to small-scale kinetic turbulence. The scales of such transitions and the responsible physical mechanisms are not well understood however. In the present work we emphasize the crucial role of the plasma parameters in the transition to kinetic turbulence, such as the ion and electron plasma beta, the electron to ion temperature ratio, the degree of obliquity of turbulent fluctuations. We then propose an explanation for the spectral breaks reported in recent observations.

Kinetic Turbulence in Relativistic Plasma: From Thermal Bath to Nonthermal Continuum

We present results from particle-in-cell simulations of driven turbulence in magnetized, collisionless, and relativistic pair plasmas. We find that the fluctuations are consistent with the classical k_{⊥}^{-5/3} magnetic energy spectrum at fluid scales and a steeper k_{⊥}^{-4} spectrum at sub-Larmor scales, where k_{⊥} is the wave vector perpendicular to the mean field. We demonstrate the development of a nonthermal, power-law particle energy distribution f(E)∼E^{-α}, with an index α that decreases with increasing magnetization and increases with an increasing system size (relative to the characteristic Larmor radius). Our simulations indicate that turbulence can be a viable source of energetic particles in high-energy astrophysical systems, such as pulsar wind nebulae, if scalings asymptotically become insensitive to the system size.

Intermittency of energy dissipation in Alfvénic turbulence

We investigate the intermittency of energy dissipation in Alfvenic turbulence by considering the statistics of the coarse-grained energy dissipation rate, using direct measurements from numerical simulations of magnetohydrodynamic turbulence and surrogate measurements from the solar wind. We compare the results to the predictions of the log-normal and log-Poisson random cascade models. We find that, to a very good approximation, the log-normal model describes the probability density function for the energy dissipation over a broad range of scales, but does not accurately describe the scaling exponents of the moments. The log-Poisson model better describes the scaling exponents of the moments, while the comparison with the probability density function is not straightforward.

Universal small-scale structure in turbulence driven by magnetorotational instability

The intermittent small-scale structure of turbulence governs energy dissipation in many astrophysical plasmas and is often believed to have universal properties for sufficiently large systems. In this work, we argue that small-scale turbulence in accretion discs is universal in the sense that it is insensitive to the magnetorotational instability (MRI) and background shear, and therefore indistinguishable from standard homogeneous magnetohydrodynamic (MHD) turbulence at small scales. We investigate the intermittency of current density, vorticity and energy dissipation in numerical simulations of incompressible MHD turbulence driven by the MRI in a shearing box. We find that the simulations exhibit a similar degree of intermittency as in standard MHD turbulence. We perform a statistical analysis of intermittent dissipative structures and find that energy dissipation is concentrated in thin sheet-like structures that span a wide range of scales up to the box size. We show that these structures exhibit strikingly similar statistical properties to those in standard MHD turbulence. Additionally, the structures are oriented in the toroidal direction with a characteristic tilt of approximately 17

Influence of a large-scale field on energy dissipation in magnetohydrodynamic turbulence

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