Showing papers by "William H. Matthaeus published in 1998"

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

Abstract: 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.

The radial and latitudinal dependence of the cosmic ray diffusion tensor in the heliosphere

Abstract: The radial and latitudinal dependence of the cosmic ray diffusion tensor is investigated on the basis of a recently developed model of magnetohydrodynamic turbulence in the expanding solar wind [Zank et al., 1996a,b; Matthaeus et al., 1996]. In the ecliptic plane, decaying magnetohydrodynamic turbulence is assumed to be replenished in situ by turbulence generated through the interaction of streams (both shear and compressional effects) and by the creation of pickup ions. In the polar region, at least during solar minimum, stream interaction driven turbulence is neglected and only pickup ion driven turbulence is included. To model the perpendicular and drift elements of the cosmic ray diffusion tensor, we employ both a quasi-linear theory (QLT) and a newly developed nonperturbative theory (NPT) to describe the field line wandering which drives perpendicular transport. A resonant quasi-linear description is applied to the parallel component. For the QLT approach, we find that in the solar wind ecliptic plane (1) the radial diffusive length scale or mean free path (mfp) is very nearly constant until some 10 AU, after which it experiences some variation with increasing heliocentric distance; (2) the radial mfp is dominated at all radial distances by the component parallel to the mean magnetic field and the perpendicular component is completely unimportant; (3) the length scale associated with the drift component of the cosmic ray diffusion tensor is only comparable to the radial mfp beyond ∼ 10 AU; and (4) the rigidity P dependence of the radial mfp within 10 – 20 AU is weak and proportional to P1/3, but in the far outer heliosphere it is proportional to P2. For the QLT model in the polar region of the solar wind, we find that the radial cosmic ray mfp is much greater than the corresponding mfp in the ecliptic region, consistent with observed mfps for pickup ions reported by Gloeckler et al. [1995]. The polar models are, however, preliminary and assume vanishing cross-helicity. The polar radial mfp is dominated by the parallel component, and drift length scales are never comparable to the radial mfp in the high polar latitudes. By using instead a nonperturbative model for the perpendicular and drift components of the cosmic ray diffusion tensor, it was found that the mfps for these coefficients could be significantly larger than their QLT counterparts. The increased perpendicular mfp was found to be important in the radial mfp only beyond ∼ 20 AU, which remains dominated by the parallel diffusion within this distance. Within the ecliptic, the nonperturbative model yields a radial mfp for cosmic rays that is almost constant with heliocentric distance. Similar order of magnitude differences between the radial mfps in the ecliptic and polar regions of the solar wind are found with the nonperturbative models.

Scaling of anisotropy in hydromagnetic turbulence

Abstract: We present evidence that anisotropy of low frequency plasma turbulence scales linearly with the ratio of fluctuating to total magnetic field strength for a useful range of parameters, for incompressible, weakly compressible, and driven magnetohydrodynamic turbulence.

Waves, structures, and the appearance of two‐component turbulence in the solar wind

Abstract: Spacecraft observations of magnetic field fluctuations in the solar wind reveals a “Maltese Cross” pattern in the two-dimensional correlation function measurements of solar wind fluctuations [Matthaeus et al., 1990]. This pattern suggests the presence of two components: fluctuations with their (Fourier) wave vector approximately parallel to the ambient magnetic field (e.g., slab turbulence) and fluctuations with their (Fourier) wave vector approximately perpendicular to the ambient magnetic field (e.g., quasi two-dimensional turbulence). To date, the appearance of such a pattern has never been reproduced from numerical simulation studies. Here we present results of several MHD simulations that address this issue using both two-and-one-half dimensional and three-dimensional compressible models and a wide variety of initial states and plasma parameters. Slab turbulence and quasi two-dimensional turbulence appear in various runs; however, their simultaneous appearance is difficult to achieve and seems to rely upon their separate existence in the initial data. In contrast, the presence of transverse pressure-balanced magnetic structures causes slab turbulence to evolve in such a manner that a two-component correlation function emerges through time averaging. We suggest that the Maltese Cross and similar observations may be a consequence of either the initial data or of averaging over different parcels of solar wind.

Scaling of spectral anisotropy with magnetic field strength in decaying magnetohydrodynamic turbulence

Abstract: Space plasma measurements, laboratory experiments, and simulations have shown that magnetohydrodynamic (MHD) turbulence exhibits a dynamical tendency towards spectral anisotropy given a sufficiently strong background magnetic field. Here the undriven decaying initial-value problem for homogeneous MHD turbulence is examined with the purpose of characterizing the variation of spectral anisotropy of the turbulent fluctuations with magnetic field strength. Numerical results for both incompressible and compressible MHD are presented. A simple model for the scaling of this spectral anisotropy as a function of the fluctuating magnetic field over total magnetic field is offered. The arguments are based on ideas from reduced MHD (RMHD) dynamics and resonant driving of certain non-RMHD modes. The results suggest physical bases for explaining variations of the anisotropy with compressibility, Reynolds numbers, and spectral width of the (isotropic) initial conditions.

The evolution of slab fluctuations in the presence of pressure‐balanced magnetic structures and velocity shears

Abstract: The traditional view that solar wind fluctuations are well-described as a spectrum of parallel-propagating Alfven waves has been challenged many times but is still a frequently encountered perspective. Here we examine whether it remains consistent to view most of the fluctuation energy as resident in parallel-propagating Alfven waves in situations in which there are also present either transverse pressure-balanced (PB) magnetic structures or transverse velocity shears. We address these questions through direct simulation of compressible magnetohydrodynamics, with expansion effects neglected. We show that parallel-propagating Alfven waves are redirected to large oblique angles after refractive interactions with PB structures or advective interactions with velocity shears, reflecting the nonequilibrium nature of the initial spectral distribution. The timescale for these processes ranges from 2–8 eddy-turnover times or characteristic nonlinear times. Relatively small amounts of PB structure and/or shear energy can redirect initially parallel-propagating Alfven waves to highly oblique angles. Velocity microstreams appear to be particularly efficient at creating highly oblique waves. Even though the excited wave vectors are eventually primarily oblique, the magnetic variance ratios show a minimum variance in the mean magnetic field direction.

Dynamical age of solar wind turbulence in the outer heliosphere

Abstract: In an evolving turbulent medium, a natural timescale can be defined in terms of the energy decay time. The time evolution may be complicated by other effects such as energy supply due to driving, and spatial inhomogeneity. In the solar wind the turbulence appears not to be simply engaging in free decay, but rather the energy level observed at a particular position in the hellosphere is affected by expansion, "mixing," and driving by stream shear. Here we discuss a new approach for estimating the "age" of solar wind turbulence as a function of heliocentric distance, using the local turbulent decay rate as the natural dock, but taking into account expansion and driving effects. The simplified formalism presented here is appropriate to low cross hellcity (non-Alfvnic) turbulence in the outer hellosphere especially at low hello-latitudes. We employ Voyager data to illustrate our method, which improves upon the familiar estimates in terms of local eddy turnover times.

Anisotropy and Energy Decay in Magneto-Hydrodynamic Turbulence: Theory and Solar Wind Observations

Abstract: Anisotropies in the spectra of magnetohydrodynamic (MHD) scale fluctuations are observed or inferred in many plasmas, e.g.,laboratory fusion machines, the solar wind and corona, and the interstellar medium (see [1, 2] for references). Anisotropy is expected since a mean magnetic field B 0 (unlike a mean flow), cannot be transformed away and thus provides a preferred direction. Understanding the evolution and development of this spectral anisotropy is a major theoretical challenge as nonlinear effects play a crucial role. Nonetheless, some progress has been made. Using numerical simulations and a reduced MHD (RMHD) approach, we have developed a relatively simple model of the process [1, 2], which we present below.