Showing papers by "William H. Matthaeus published in 2001"

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

Abstract: 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.

Wave-driven Turbulent Coronal Heating in Open Field Line Regions: Nonlinear Phenomenological Model

Abstract: A model is presented to investigate the driving of coronal turbulence in open field line regions, powered by low-frequency oscillatory field line motions at the coronal base. The model incorporates the combined effects of wave propagation, reflection associated with gradients of Alfven speed, and low-frequency quasi-two-dimensional turbulence, which is treated using a one-point closure phenomenology appropriate to a transverse cascade in the reduced magnetohydrodynamic regime. Considering a sample of the corona and employing open boundary conditions, we use the model to investigate the dynamical efficiency of turbulent dissipation, which competes with propagation of fluctuations away from the coronal base. We examine the dependence of the heating efficiency on wave-forcing frequency, the sensitivity to parameters controlling the Alfven speed profile, the behavior of the model for varying the phenomenological correlation length of turbulence, including asymptotic limits of negligible or very intense nonlinearities, and the confinement of turbulent dissipation to the region near the coronal base. Each of these issues may be of importance in understanding the heating of the corona and the origin of the solar wind.

Local anisotropy in incompressible magnetohydrodynamic turbulence

Abstract: It is a well known fact that in the presence of a dc applied magnetic field, magnetohydrodynamic (MHD) turbulence develops spectral anisotropy from isotropic initial conditions. Typically, the reduced spectrum is steeper in the direction of the magnetic field than it is in any transverse direction. One might expect that a dc field is not essential, and it is the local mean field that is responsible. To address this issue, three-dimensional MHD pseudo-spectral incompressible relaxation simulations are performed, and structure functions computed according to whether the separation is parallel to, or transverse to, the local mean magnetic field. Correlation lengths are longer in the locally averaged magnetic field direction than in any perpendicular direction, even when the global mean magnetic field is zero. Local anisotropy is observed to be stronger in regions of strong magnetic field. A general definition of anisotropy angles and a methodology to study local anisotropy are proposed.

A Reduced Magnetohydrodynamic Model of Coronal Heating in Open Magnetic Regions Driven by Reflected Low-Frequency Alfvén Waves

Abstract: A reduced magnetohydrodynamic (RMHD) description is employed to examine a suggestion made by W. H. Matthaeus and colleagues in 1999 that coronal heating might be sustained by a cascade of lowfrequency MHD turbulence. Here RMHD simulations show that the low-frequency cascade to high transverse wavenumbers can be driven by an externally maintained —ux of low-frequency propagating waves, in combination with re—ection caused by an inhomogeneous background medium. The Alfvec n simulations show that the suggestions made previously on the basis of a phenomenology are indeed realizable. In addition, the eUect is seen to sensitively depend on the presence of re—ection, as the background turbulence level needed to maintain the cascade can be sustained only when re—ection is imposed. The steady level of turbulence is insensitive to the initial seed turbulence level (provided it is nonzero). Consequences of this model for realistic models of coronal heating in open —eld-line regions are discussed.

Distribution of magnetic field components in the solar wind plasma

Abstract: We examine the probability distribution functions (PDFs) of fluctuations of magnetic field components using the Ulysses and Omnitape data sets to evaluate departures from Gaussian distributions. Functional fits as well as moment comparisons (kurtoses) are used in drawing conclusions concerning the degree of non-Gaussianity. Short-timescale fluctuations are separated, to the extent possible, from the longer-timescale variation of the mean field, and attention is paid to data selection issues such as stationarity. At the present level of comparison it seems that departures from Gaussianity of the distributions of the fluctuations are not severe. The analysis is carried out in the mean field coordinates in which the fluctuations of components are close to being uncorrelated, and it is observed that the perpendicular components are closer to being Gaussian than the parallel one. It is shown that the kurtosis is highly exaggerated when the variation of the mean field is not taken into account. We further examine the distributions of hourly magnetic field fluctuations in fast and slow solar wind at different phases in the solar cycle in order to quantitatively describe departures from the Gaussian distribution. It is found that the kurtosis lies between 2.8 and 4.8 for all components in the mean field coordinates, in both fast and slow wind and near solar maximum and near solar minimum. It appears that the distributions of fluctuations are rather more similar with regard to their degree of non-Gaussianity than might have been expected based upon the well-documented differences in the characteristics of fast and slow solar wind intervals. This suggests a robust form of statistical similarity that may be associated with either in situ or source region nonlinear effects. In addition to the distributions of the fluctuations, we present the distributions of the mean field and of the variances of the components which are more likely to be influenced by solar sources than by interplanetary dynamical processes. The PDFs of variances of the magnetic field components over different subintervals approximate lognormal curves, and provide the motivation to compute the PDFs of the fluctuations using the approach of Castaing et al. [1990], which is a superposition of Gaussian distributions with variances that are distributed lognormally. The resulting PDFs of the fluctuations provide a good model to describe the small departures from Gaussian distributions seen in the observed PDFs. An additional step is taken to compute the expected PDF of the magnitude of the fluctuations from the Castaing PDFs of the components and is also seen to be in good agreement with the observed PDF.

Conditions for sustainment of magnetohydrodynamic turbulence driven by Alfvén waves

Abstract: In a number of space and astrophysical plasmas, turbulence is driven by the supply of wave energy. In the context of incompressible magnetohydrodynamics (MHD) there are basic physical reasons, associated with conservation of cross helicity, why this kind of driving may be ineffective in sustaining turbulence. Here an investigation is made into some basic requirements for sustaining steady turbulence and dissipation in the context of incompressible MHD in a weakly inhomogeneous open field line region, driven by the supply of unidirectionally propagating waves at a boundary. While such wave driving cannot alone sustain turbulence, the addition of reflection permits sustainment. Another sustainment issue is the action of the nonpropagating or quasi-two dimensional part of the spectrum; this is particularly important in setting up a steady cascade. Thus, details of the wave boundary conditions also affect the ease of sustaining a cascade. Supply of a broadband spectrum of waves can overcome the latter difficu...

The Injection Problem for Anomalous Cosmic Rays

Abstract: The precise mechanism by which some interstellar pickup ions are selected to be accelerated up to anomalous cosmic-ray (ACR) energies at the heliospheric termination shock is a central puzzle in the physics of the outer heliosphere. Observations by Gloeckler et al. of the mass dependence of the efficiency with which low-energy pickup ions are accelerated at an interplanetary shock is in the opposite sense of related ACR observations made by Cummings and Stone. Furthermore, the rapidity with which ions must be accelerated at the termination shock requires that the scattering of these ions be weak, an effect which requires that relatively energetic ions exist initially. It is shown here that these three sets of observations can be reconciled by using a multiply reflected ion acceleration mechanism to provide a preaccelerated population of pickup ions at the termination shock. The precise fraction of preenergized pickup ions that can subsequently be diffusively shock accelerated depends on the ion scattering strength at the termination shock. It is shown that the assumption of weak scattering yields an anomalously low injection efficiency for pickup H+ compared to those of He+, O+, and Ne+, and those inferred for C+ and N+. The predicted injection efficiencies of C+, N+, O+, and Ne+ are clustered together closely whereas He+ is a little less efficiently injected. Computed ACR termination shock and modulated fluxes compare well to those observed and inferred by Cummings and Stone. Finally, strong scattering of ions at the termination shock is found to eliminate the mass dependence of the ACR injection efficiency.

The interaction of turbulence with shock waves: a basic model

Abstract: The interaction of turbulence and shock waves is considered self-consistently so that the back-reaction of the turbulence and its associated reaction on the turbulence is addressed. This approach differs from previous studies which considered the interaction of linear modes with a shock. The most basic model of hypersonic flow, described by the inviscid form of Burgers’ equation, is used. An energy-containing model which couples the turbulent energy density and correlation length of the flow with the mean flow is developed. Upstream turbulence interacting with a shock wave is found to mediate the shock by (1) increasing the mean shock speed, and (2) decreasing the efficiency of turbulence amplification at the shock as the upstream turbulence energy density is increased. The implication of these results is that the energy in upstream turbulent fluctuations, while being amplified at the shock, is also being converted into mean flow energy downstream. The variance in both the shock speed and position is comp...

Pickup ion acceleration by turbulent electric fields in the slow solar wind

Abstract: Recent spacecraft observations reveal that energetic tails in ion spectra are present continually in the slow low-latitude solar wind, even in the absence of nearby shocks. To explain this phenomenon we take into account growing evidence that MHD turbulence in the solar wind has a strong two-dimensional (2D) component. 2D MHD turbulence simulations exhibit large-scale field-aligned electric field fluctuations which are also observable in the solar wind. We explore pickup ion propagation and acceleration between the Sun and Earth with a newly developed kinetic numerical model which includes a random distribution of large-scale field-aligned electric field fluctuations consistent with observations in the low-latitude solar wind. The model is found to qualitatively reproduce the accelerated interstellar pickup He+ spectra observed at Earth. Like the observations, the simulated accelerated “tail” is approximately a power law f(υ) ∝ υ−4.5 until it reaches particle speeds about ten times the solar wind speed where a rollover occurs.

Challenges for an ab initio theory of cosmic ray modulation

Abstract: School of Physics, Potchefstroom University for CHE, Potchefstroom, South AfricaAbstract. Recent efforts to improve and complete modula-tion theory are described, emphasizing factors that arise inattempts to understand the diffusion tensor based upon tur-bulence theory and the theory of charged particle scattering.Direct numerical solutions of the transport equations are usedto study a new perpendicular diffusion formalism that cansmoothly vary between the field line random walk limit anda recent treatment based upon the Taylor–Green–Kubo equa-tion. Using this new formalism we show that modulation isstrongly influenced by the radial variation of the correlationlength. This variation is still poorly understood, in part ow-ing to the uncertain impact of pickup ion driven turbulencein the outer heliosphere.1 IntroductionCosmic ray modulation is a complex subject relating galac-tic particle populations to heliospheric structure, while in-volving at a detailed level incompletely understood theoreti-cal features of charged particle scattering and plasma turbu-lence. Scattering theory involves turbulence parameters, andthus one needs to understand how plasma turbulence evolvesthroughout the heliosphere. Even in the simplest formula-tions of scattering and turbulence theories this would involvespecification of a turbulence energy density and a similar-ity length scale everywhere in the three dimensional helio-sphere. Boundary data in the inner heliosphere can stand inplace of a fuller understanding of the origins of solar windturbulence, but it is also necessary to understand how tur-bulence is driven within the heliosphere, for example, byshear and excitation of fluctuations by scattering of interstel-lar pickup ions. In more elaborate models of turbulence thefluctuations may be represented as consisting of two or morecomponents, each with a known symmetry (Matthaeus et al.,1990; Bieber et al., 1994). A useful example is the two-component model which includes one dimensional “slab”Correspondence to: S. Parhi (sparhi@bartol.udel.edu)and two dimensional (2D) ingredients. Scattering theory it-self also involves many issues and is incompletely under-stood. Perpendicular diffusion, especially at lower energies(Giacalone and Jokipii, 1999; Mace et al., 2000) is not wellaccounted for theoretically. For these reasons it is obviouswhy there is at present no accepted ab initio modulation the-ory, that is, one in which the diffusion coefficients are deter-mined on the basis of scattering theory and the underlyingmagnetic fluctuation parameters are computed from plasmatheory and known features of heliospheric structure. Re-cently we have been attempting to further develop an ab ini-tio approach to modulation, building on recent efforts alongthese lines (Zank et al, 1998; Burger et al., 2000).?From the start it becomes apparent that modulation isrelatively sensitive to features of turbulence and scatteringwhich themselves are active areas of research. Thus it ap-pears appropriate to view these efforts as investigations ofscattering and turbulence on the same footing as they are in-vestigations of modulation. One such parameter that sensi-tively affects modulation is the parallel correlation scale ofmagnetic fluctuations, and this is the subject of emphasis inthe present short paper. The main point of the present paperis to show the type of effects that can be expected in modula-tion when the assumptions concerning the radial variation ofthe correlation scale are varied in a modulation model.2 Modulation modelThe modulation of galactic cosmic rays is described by Par-ker’s equation. In our model we describe the radial coeffi-cient by 

Energetic particles and magnetohydrodynamic activity in the Swarthmore Spheromak Experiment

Abstract: Results from the Swarthmore Spheromak Experiment (SSX) [M. R. Brown, Phys. Plasmas 6, 1717 (1999)] indicate that formation and partial merging of two spheromak plasmas can be described well by a magnetohydrodynamic (MHD) picture in which there is substantial evolution towards force free states within each vessel, while reconnection activity, also described reasonably well by MHD, occurs in the region of interaction. MHD simulations [V. S. Lukin et al., Phys. Plasmas 8, 1600 (2001)] support and provide further detail to this interpretation. In the present study, test particle equations are integrated using MHD data from SSX simulations to further understand the energetic particle fluxes that are observed experimentally. The test particle simulation is run with dimensionless parameters similar to the experiment, and particles are permitted to escape when they encounter the simulated SSX boundaries. MHD activity related to reconnection is responsible for accelerating charged particles. The process includes t...

Challenges for an ab initio Theory of Cosmic Ray Modulation

Abstract: School of Physics, Potchefstroom University for CHE, Potchefstroom, South AfricaAbstract. Recent efforts to improve and complete modula-tion theory are described, emphasizing factors that arise inattempts to understand the diffusion tensor based upon tur-bulence theory and the theory of charged particle scattering.Direct numerical solutions of the transport equations are usedto study a new perpendicular diffusion formalism that cansmoothly vary between the field line random walk limit anda recent treatment based upon the Taylor–Green–Kubo equa-tion. Using this new formalism we show that modulation isstrongly influenced by the radial variation of the correlationlength. This variation is still poorly understood, in part ow-ing to the uncertain impact of pickup ion driven turbulencein the outer heliosphere.1 IntroductionCosmic ray modulation is a complex subject relating galac-tic particle populations to heliospheric structure, while in-volving at a detailed level incompletely understood theoreti-cal features of charged particle scattering and plasma turbu-lence. Scattering theory involves turbulence parameters, andthus one needs to understand how plasma turbulence evolvesthroughout the heliosphere. Even in the simplest formula-tions of scattering and turbulence theories this would involvespecification of a turbulence energy density and a similar-ity length scale everywhere in the three dimensional helio-sphere. Boundary data in the inner heliosphere can stand inplace of a fuller understanding of the origins of solar windturbulence, but it is also necessary to understand how tur-bulence is driven within the heliosphere, for example, byshear and excitation of fluctuations by scattering of interstel-lar pickup ions. In more elaborate models of turbulence thefluctuations may be represented as consisting of two or morecomponents, each with a known symmetry (Matthaeus et al.,1990; Bieber et al., 1994). A useful example is the two-component model which includes one dimensional “slab”Correspondence to: S. Parhi (sparhi@bartol.udel.edu)and two dimensional (2D) ingredients. Scattering theory it-self also involves many issues and is incompletely under-stood. Perpendicular diffusion, especially at lower energies(Giacalone and Jokipii, 1999; Mace et al., 2000) is not wellaccounted for theoretically. For these reasons it is obviouswhy there is at present no accepted ab initio modulation the-ory, that is, one in which the diffusion coefficients are deter-mined on the basis of scattering theory and the underlyingmagnetic fluctuation parameters are computed from plasmatheory and known features of heliospheric structure. Re-cently we have been attempting to further develop an ab ini-tio approach to modulation, building on recent efforts alongthese lines (Zank et al, 1998; Burger et al., 2000).?From the start it becomes apparent that modulation isrelatively sensitive to features of turbulence and scatteringwhich themselves are active areas of research. Thus it ap-pears appropriate to view these efforts as investigations ofscattering and turbulence on the same footing as they are in-vestigations of modulation. One such parameter that sensi-tively affects modulation is the parallel correlation scale ofmagnetic fluctuations, and this is the subject of emphasis inthe present short paper. The main point of the present paperis to show the type of effects that can be expected in modula-tion when the assumptions concerning the radial variation ofthe correlation scale are varied in a modulation model.2 Modulation modelThe modulation of galactic cosmic rays is described by Par-ker’s equation. In our model we describe the radial coeffi-cient by