William H. Matthaeus

Observational constraints on the dynamics of the interplanetary magnetic field dissipation range

The dissipation range for interplanetary magnetic field fluctuations is formed by those fluctuations with spatial scales comparable to the gyroradius or ion inertial length of a thermal ion. It is reasonable to assume that the dissipation range represents the final fate of magnetic energy that is transferred from the largest spatial scales via nonlinear processes until kinetic coupling with the background plasma removes the energy from the spectrum and heats the background distribution. Typically, the dissipation range at 1 AU sets in at spacecraft frame frequencies of a few tenths of a hertz. It is characterized by a steepening of the power spectrum and often demonstrates a bias of the polarization or magnetic helicity spectrum. We examine Wind observations of inertial and dissipation range spectra in an attempt to better understand the processes that form the dissipation range and how these processes depend on the ambient solar wind parameters (interplanetary magnetic field intensity, ambient proton density and temperature, etc.). We focus on stationary intervals with well-defined inertial and dissipation range spectra. Our analysis shows that parallel-propagating waves, such as Alfven waves, are inconsistent with the data. MHD turbulence consisting of a partly slab and partly two-dimensional (2-D) composite geometry is consistent with the observations, while thermal paxticle interactions with the 2-D component may be responsible for the formation of the dissipation range. Kinetic Alfven waves propagating at large angles to the background magnetic field are also consistent with the observations and may form some portion of the 2-D turbulence component.

Dominant two‐dimensional solar wind turbulence with implications for cosmic ray transport

Two new methods for distinguishing two-dimensional (2D) turbulence from slab turbulence are applied to Helios magnetometer data. Two-component models with varying slab and 2D ingredients are considered. Both methods indicate that solar wind magnetic turbulence possesses a dominant (∼85 % by energy) 2D component. The presence of such a large 2D component provides a natural solution to the long-standing problem of “too small” cosmic ray mean free paths derived from quasilinear scattering theory when using the slab model.

Nonlinear Collisionless Perpendicular Diffusion of Charged Particles

A nonlinear theory of the perpendicular diffusion of charged particles is presented, including the influence of parallel scattering and dynamical turbulence. The theory shows encouraging agreement with numerical simulations. Subject headings: diffusion — turbulence

Evolution of turbulent magnetic fluctuation power with heliospheric distance

On the basis of transport theories appropriate to a radially expanding solar wind, new results for the evolution of the energy density in solar wind fluctuations at MHD scales are derived. The models, which represent a departure from the well-known WKB description, include the effects of “mixing”, driving by stream-stream interactions (compression and shear) and interstellar pick-up ions as well as non-isotropic MHD turbulence. Magnetometer data from Voyager 1 and 2 and Pioneer 11 are compared to the turbulence-based models and close agreement is found between theory and data for a reasonable choice of parameters.

MHD-driven Kinetic Dissipation in the Solar Wind and Corona

Mechanisms for the deposition of heat in the lower coronal plasma are discussed, emphasizing recent attempts to reconcile the —uid and kinetic perspectives. Structures at magnetohydrodynamic (MHD) scales may drive a nonlinear cascade, preferentially exciting high perpendicular wavenumber —uctuations. Relevant dissipative kinetic processes must be identi—ed that can absorb the associated energy —ux. The relationship between the MHD cascade and direct cyclotron absorption, including cyclotron sweep, is discussed. We conclude that for coronal and solar wind parameters the perpendicular cascade cannot be neglected and may be more rapid than cyclotron sweep. Solar wind observational evidence suggests the relevance of the ion inertial scale, which is associated with current sheet thickness during reconnection. We conclude that a signi—cant fraction of dissipation in the corona and solar wind likely proceeds through a perpendicular cascade and small-scale reconnection, coupled to kinetic processes that act at oblique wavevectors. Subject headings: MHDsolar windSun: coronaSun: magnetic —eldsturbulence

Heating of the low-latitude solar wind by dissipation of turbulent magnetic fluctuations

We test a theory presented previously to account for the turbulent transport of magnetic fluctuation energy in the solar wind and the related dissipation and heating of the ambient ion population. This theory accounts for the injection of magnetic energy through the damping of large-scale flow gradients, such as wind shear and compression, and incorporates the injection of magnetic energy due to wave excitation by interstellar pickup ions. The theory assumes quasi-two-dimensional spectral transport of the fluctuation energy and subsequent dissipation that heats the thermal protons. We compare the predictions of this theory with Voyager 2 and Pioneer 11 observations of magnetic fluctuation energy, magnetic correlation lengths, and ambient proton temperatures. Near-Earth Omnitape observations are used to adjust for solar variability, and the possibility that high-latitude effects could mask possible radial dependences is considered. We find abundant evidence for in situ heating of the protons, which we quantify, and show that the observed magnetic energy is consistent with the ion temperatures.

Anisotropic three‐dimensional MHD turbulence

Direct spectral method simulation of the three-dimensional magnetohydrodynamics (MHD) equations is used to explore anisotropy that develops from initially isotropic fluctuations as a consequence of a uniform applied magnetic field. Spectral and variance anisotropies are investigated in both compressible and incompressible MHD. The nature of the spectral anisotropy is consistent with the model of Shebalin et al. [1983] in which the spectrum broadens in the perpendicular wavenumber direction, the anisotropy being greater for smaller wavenumbers. Here this effect is seen for both incompressible and polytropic compressible MHD. In contrast, the longitudinal (compressive) velocity fluctuations remain isotropic. Variance anisotropy is observed for low plasma beta compressible MHD but not for incompressible MHD. Solar wind observations are qualitatively consistent with both variance and spectral anisotropies of the type discussed here.

Electron and proton heating by solar wind turbulence

[1] Previous formulations of heating and transport associated with strong magnetohydrodynamic (MHD) turbulence are generalized to incorporate separate internal energy equations for electrons and protons. Electron heat conduction is included. Energy is supplied by turbulent heating that affects both electrons and protons and is exchanged between them via collisions. Comparison to available Ulysses data shows that a reasonable accounting for the data is provided when (1) the energy exchange timescale is very long and (2) the deposition of heat due to turbulence is divided, with 60% going to proton heating and 40% into electron heating. Heat conduction, determined here by an empirical fit, plays a major role in describing the electron data.

Nearly incompressible fluids. II: Magnetohydrodynamics, turbulence, and waves

The theory of nearly incompressible (NI) fluid dynamics developed previously for hydrodynamics is extended to magnetohydrodynamics (MHD). On the basis of a singular expansion technique, modified systems of fluid equations are derived for which the effects of compressibility are admitted only weakly in terms of the different possible incompressible solutions (thus ‘‘nearly incompressible MHD’’). NI MHD represents the interface between the compressible and incompressible magnetofluid descriptions in the subsonic regime. The theory developed here does not hold in the presence of very large thermal, gravitational, or field gradients. It is found that there exist three distinct NI descriptions corresponding to each of the three possible plasma beta (β ≡ the ratio of thermal to magnetic pressure) regimes (β≪1, β∼1, β≫1). In the β≫1 regime, the compressible MHD description converges in the low Mach number limit to the equations of classical incompressible three‐dimensional (3‐D) MHD. However, for the remaining p...

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.