Sandra C. Chapman

Coherent structures, intermittent turbulence, and dissipation in high-temperature plasmas

An unsolved problem in plasma turbulence is how energy is dissipated at small scales. Particle collisions are too infrequent in hot plasmas to provide the necessary dissipation. Simulations either treat the fluid scales and impose an ad hoc form of dissipation (e.g., resistivity) or consider dissipation arising from resonant damping of small amplitude disturbances where damping rates are found to be comparable to that predicted from linear theory. Here, we report kinetic simulations that span the macroscopic fluid scales down to the motion of electrons. We find that turbulent cascade leads to generation of coherent structures in the form of current sheets that steepen to electron scales, triggering strong localized heating of the plasma. The dominant heating mechanism is due to parallel electric fields associated with the current sheets, leading to anisotropic electron and ion distributions which can be measured with NASAs upcoming Magnetospheric Multiscale mission. The motion of coherent structures also generates waves that are emitted into the ambient plasma in form of highly oblique compressional and shear Alfven modes. In 3D, modes propagating at other angles can also be generated. This indicates that intermittent plasma turbulence will in general consist of both coherent structures and waves. However, the current sheet heating is found to be locally several orders of magnitude more efficient than wave damping and is sufficient to explain the observed heating rates in the solar wind.

A simple avalanche model as an analogue for magnetospheric activity

The power law dependence of the power spectrum of auroral indices, and in-situ magnetic field observations in the earths geotail, may be evidence that the coupled solar wind-magnetospheric system exhibits scale free self organised criticality and can to some extent be described by avalanche models. In contrast, the intensity of, and time interval between, substorms both have well defined probability distributions with characteristic scales. We present results from a simple cellular automaton that models avalanches in a one dimensional “sandpile”; here we examine the simplest case of constant inflow. This model generates a probability distribution of energy discharges due to internal reorganization that is a power law implying SOC, whereas systemwide discharges (flow of “sand” out of the system) form a distinct group which do not exhibit SOC. The energy dissipated in a systemwide discharge follows a probability distribution with a well defined mean, as does the time interval between one systemwide discharge and the next. Internal and external avalanches can therefore in principle be identified with distinct processes in the dynamic geotail. If so, the avalanche model places restrictions on the class of physical process that may be invoked to explain the observed geomagnetic dynamics.

Global Scale-Invariant Dissipation in Collisionless Plasma Turbulence

A higher-order multiscale analysis of the dissipation range of collisionless plasma turbulence is presented using in situ high-frequency magnetic field measurements from the Cluster spacecraft in a stationary interval of fast ambient solar wind. The observations, spanning five decades in temporal scales, show a crossover from multifractal intermittent turbulence in the inertial range to non-Gaussian monoscaling in the dissipation range. This presents a strong observational constraint on theories of dissipation mechanisms in turbulent collisionless plasmas.

ENHANCED MAGNETIC COMPRESSIBILITY AND ISOTROPIC SCALE INVARIANCE AT SUB-ION LARMOR SCALES IN SOLAR WIND TURBULENCE

The anisotropic nature of solar wind magnetic turbulence fluctuations is investigated scale by scale using high cadence in situ magnetic field measurements from the Cluster and ACE spacecraft missions. The data span five decades in scales from the inertial range to the electron Larmor radius. In contrast to the inertial range, there is a successive increase toward isotropy between parallel and transverse power at scales below the ion Larmor radius, with isotropy being achieved at the electron Larmor radius. In the context of wave-mediated theories of turbulence, we show that this enhancement in magnetic fluctuations parallel to the local mean background field is qualitatively consistent with the magnetic compressibility signature of kinetic Alfven wave solutions of the linearized Vlasov equation. More generally, we discuss how these results may arise naturally due to the prominent role of the Hall term at sub-ion Larmor scales. Furthermore, computing higher-order statistics, we show that the full statistical signature of the fluctuations at scales below the ion Larmor radius is that of a single isotropic globally scale-invariant process distinct from the anisotropic statistics of the inertial range.

Self-organization of internal pedestals in a sandpile

The temperature profiles of magnetically confined plasmas can display distinctive longlived internal pedestals, caused by self-created transport barriers. This raises theoretical physics issues, distinct from the plasma physics modelling challenge, which concern the class of transport processes, physical principles, and control parameters that can generate such phenomenology. Here, we show that such structures can arise naturally through avalanching transport in a sandpile model. A single control parameter, that governs the spatial range of each rapid critical-gradient-triggered redistribution event, determines the occurrence and regularity of these effects.

INTERMITTENT HEATING IN SOLAR WIND AND KINETIC SIMULATIONS

Low-density astrophysical plasmas may be described by magnetohydrodynamics at large scales, but require kinetic description at ion scales in order to include dissipative processes that terminate the cascade. Here kinetic plasma simulations and high-resolution spacecraft observations are compared to facilitate the interpretation of signatures of various dissipation mechanisms. Kurtosis of increments indicates that kinetic scale coherent structures are present, with some suggestion of incoherent activity near ion scales. Conditioned proton temperature distributions suggest heating associated with coherent structures. The results reinforce the association of intermittent turbulence, coherent structures, and plasma dissipation.

Recurrence plot statistics and the effect of embedding

Abstract Recurrence plots provide a graphical representation of the recurrent patterns in a timeseries, the quantification of which is a relatively new field. Here we derive analytical expressions which relate the values of key statistics, notably determinism and entropy of line length distribution, to the correlation sum as a function of embedding dimension. These expressions are obtained by deriving the transformation which generates an embedded recurrence plot from an unembedded plot. A single unembedded recurrence plot thus provides the statistics of all possible embedded recurrence plots. If the correlation sum scales exponentially with embedding dimension, we show that these statistics are determined entirely by the exponent of the exponential. This explains the results of Iwanski and Bradley [J.S. Iwanski, E. Bradley, Recurrence plots of experimental data: to embed or not to embed? Chaos 8 (1998) 861–871] who found that certain recurrence plot statistics are apparently invariant to embedding dimension for certain low-dimensional systems. We also examine the relationship between the mutual information content of two timeseries and the common recurrent structure seen in their recurrence plots. This allows time-localized contributions to mutual information to be visualized. This technique is demonstrated using geomagnetic index data; we show that the AU and AL geomagnetic indices share half their information, and find the timescale on which mutual features appear.

Magnetic Reconnection and Intermittent Turbulence in the Solar Wind

A statistical relationship between magnetic reconnection, current sheets, and intermittent turbulence in the solar wind is reported for the first time using in situ measurements from the Wind spacecraft at 1 AU. We identify intermittency as non-Gaussian fluctuations in increments of the magnetic field vector B that are spatially and temporally nonuniform. The reconnection events and current sheets are found to be concentrated in intervals of intermittent turbulence, identified using the partial variance of increments method: within the most non-Gaussian 1% of fluctuations in B, we find 87%–92% of reconnection exhausts and ∼9% of current sheets. Also, the likelihood that an identified current sheet will also correspond to a reconnection exhaust increases dramatically as the least intermittent fluctuations are removed from the data set. Hence, the turbulent solar wind contains a hierarchy of intermittent magnetic field structures that are increasingly linked to current sheets, which in turn are progressively more likely to correspond to sites of magnetic reconnection. These results could have far reaching implications for laboratory and astrophysical plasmas where turbulence and magnetic reconnection are ubiquitous.

Intermittency, scaling and the Fokker-Planck approach to fluctuations of the solar wind bulk plasma parameters as seen by the WIND spacecraft.

The solar wind provides a natural laboratory for observations of magnetohydrodynamic (MHD) turbulence over extended temporal scales. Here, we apply a model independent method of differencing and rescaling to identify self-similarity in the probability density functions (PDF) of fluctuations in solar wind bulk plasma parameters as seen by the WIND spacecraft. Whereas the fluctuations of speed v and interplanetary magnetic field (IMF) magnitude B are multifractal, we find that the fluctuations in the ion density rho, energy densities B2 and rhov(2) as well as MHD-approximated Poynting flux vB(2) are monoscaling on the time scales up to 26 hr. The single curve, which we find to describe the fluctuations PDF of all these quantities up to this time scale, is non-Gaussian. We model this PDF with two approaches--Fokker-Planck, for which we derive the transport coefficients and associated Langevin equation, and the Castaing distribution that arises from a model for the intermittent turbulent cascade.

Kinetic signatures and intermittent turbulence in the solar wind plasma

A connection between kinetic processes and intermittent turbulence is observed in the solar wind plasma using measurements from the Wind spacecraft at 1 A.U. In particular, kinetic effects such as temperature anisotropy and plasma heating are concentrated near coherent structures, such as current sheets, which are nonuniformly distributed in space. Furthermore, these coherent structures are preferentially found in plasma unstable to the mirror and firehose instabilities. The inhomogeneous heating in these regions, which is present in both the magnetic field parallel and perpendicular temperature components, results in protons at least 3-4 times hotter than under typical stable plasma conditions. These results offer a new understanding of kinetic processes in a turbulent regime, where linear Vlasov theory is not sufficient to explain the inhomogeneous plasma dynamics operating near non-Gaussian structures.