Matthaeus, W. H. — Page 3 | Engineering Papers

NASA NTRS1987

Magnetic helicity of the Parker field

The topological properties of the interplanetary magnetic field are discussed based on a calculation of the magnetic helicity of the Parker field. The most striking feature of the helicity is that it is negative north of the heliospheric current sheet and positive south of the current sheet, regardless of the sign of the solar poloidal magnetic field. Informal arguments based on MHD turbulence theory suggest that the magnetic helicity of turbulence in the interplanetary medium may be related to the large-scale Parker helicity. Because charged particle scattering in certain types of magnetic turbulence (such as slab turbulence) depends strongly upon helicity, the existence of such a relationship could have important implications to cosmic-ray transport in the heliosphere.

Bieber, J. W.↗

NASA NTRS1987

Density fluctuation spectra in magnetohydrodynamic turbulence

It is shown that within the framework of nearly incompressible magnetohydrodynamics, but not within that of neutral-fluid hydrodynamics, a k exp -5/3 inertial-range wave number density fluctuation spectrum is to be expected at the same times that k exp -5/3 kinetic energy and magnetic energy cascade spectra are present. A previous discrepancy between theory and observation in the local interstellar medium and solar wind is thereby resolved.

Montgomery, D.↗

NASA NTRS1986

Systematic errors in determining the propagation direction of interplanetary Alfvenic fluctuations

Analyses of Alfvenic fluctuations in the solar wind contain a systematic effect in which outward propagation is favored. The effect is generally small at and beyond 1 AU in a Mach 10 flow but can become important where the Mach number is lower, e.g., inside 1 AU. If the propagation speeds of the inward and outward propagating Alfvenic fluctuations are properly included, this systematic effect can be removed. A technique for doing this is illustrated using both artificial and spacecraft data. The results suggest that time intervals originally thought to be outward propagating sometimes contain wave number bands in the cross helicity spectrum of inward propagating Alfvenic fluctuations.

Goldstein, M. L.↗

NASA NTRS1986

Turbulent magnetic reconnection

The results of two-dimensional spectral-method MHD simulations of the effect of turbulence on magnetic-reconnection processes are presented in extensive graphs and tables and characterized in detail. In a periodic sheet-pinch configuration, early-onset, persistent turbulence is found to occur when a low level of broadband fluctuations is introduced into the initial data. Features observed include small-scale unsteady coherent electric-current and vorticity structures, enhanced viscous and resistive dissipation, unsteady and spatially asymmetric fluid flow, large-scale and small-scale magnetic islands, multiple X points, large-amplitude electric-field fluctuations, and spectral characteristics indicating that the turbulence is broadband in both spatial directions and similar to homogeneous MHD turbulence. The importance of reconnection for studies of solar, magnetospheric, and laboratory plasmas in inhomogeneous magnetic fields is indicated.

Matthaeus, W. H.↗

NASA NTRS1986

Low-frequency 1/f noise in the interplanetary magnetic field

Spacecraft observations of the interplanetary magnetic field at 1 AU are shown to have frequency spectra with a 1/f dependence in the range 2.7-80 microHz. It is suggested that the 1/f spectrum results from the superposition of uncorrelated samples of solar surface turbulence that have log-normal distributions of correlation lengths corresponding to a scale-invariant distribution of correlation times over an appropriate range of parameters.

Matthaeus, W. H.↗

NASA NTRS1986

The alpha dynamo parameter and measurability of helicities in magnetohydrodynamic turbulence

Alpha, an important parameter in dynamo theory, is shown to be proportional to either the kinetic, current, magnetic, or velocity helicities of the fluctuating magnetic field and fluctuating velocity field. The particular helicity to which alpha is proportional depends on the assumptions used in deriving the first-order smoothed equations that describe the alpha effect. In two cases, viz., when alpha is proportional to either the magnetic helicity or velocity helicity, alpha can be determined experimentally from two-point measurements of the fluctuating fields in incompressible, homogeneous turbulence with arbitrary rotational symmetry. For the other two possibilities, alpha can be determined if the turbulence is isotropic.

Matthaeus, W. H.↗

NASA NTRS1986

Acceleration of charged particles in magnetic reconnection Solar flares, the magnetosphere, and solar wind

A possible source of free energy available for accelerating charged particles is conversion of magnetic energy to particle energy in reconnecting magnetic fields. Recent simulations using test particles suggests that reconnection may efficiently accelerate particles to the maximum energies that are observed in several astrophysical contexts. A simple analytic formula is used in conjunction with the simulation results to predict the maximum energy achievable in a particular plasma environment with the result that in solar flares reconnection is capable of accelerating particles to several GeV. In magnetospheric substorms the predicted maximum can reach several hundred keV, and near magnetic sector crossings in the solar wind the maximum energy can approach 100 keV.

Goldstein, M. L.↗

NASA NTRS1986

Large-scale disruptions in a current-carrying magnetofluid

Internal disruptions in a strongly magnetized electrically conducting fluid contained within a rigid conducting cylinder of square cross section are investigated theoretically, both with and without an externally applied axial electric field, by means of computer simulations using the pseudospectral three-dimensional Strauss-equations code of Dahlburg et al. (1985). Results from undriven inviscid, driven inviscid, and driven viscid simulations are presented graphically, and the significant effects of low-order truncations on the modeling accuracy are considered. A helical current filament about the cylinder axis is observed. The ratio of turbulent kinetic energy to total poloidal magnetic energy is found to undergo cyclic bounces in the undriven inviscid case, to exhibit one large bounce followed by decay to a quasi-steady state with poloidal fluid velocity flow in the driven inviscid case, and to show one large bounce followed by further sawtoothlike bounces in the driven viscid case.

Dahlburg, J. P.↗

NASA NTRS1986

An interplanetary magnetic field ensemble at 1 AU

A method for calculation ensemble averages from magnetic field data is described. A data set comprising approximately 16 months of nearly continuous ISEE-3 magnetic field data is used in this study. Individual subintervals of this data, ranging from 15 hours to 15.6 days comprise the ensemble. The sole condition for including each subinterval in the averages is the degree to shich it represents a weakly time-stationary process. Averages obtained by this method are appropriate for a turbulence description of the interplanetary medium. The ensemble average correlation length obtained from all subintervals is found to be 4.9 x 10 to the 11th cm. The average value of the variances of the magnetic field components are in the approximate ratio 8:9:10, where the third component is the local mean field direction. The correlation lengths and variances are found to have a systematic variation with subinterval duration, reflecting the important role of low-frequency fluctuations in the interplanetary medium.

Matthaeus, W. H.↗

NASA NTRS1985

Turbulent disruptions from the Strauss equations

Preliminary results are reported from application of a three-dimensional spectral method model to the solution of the Strauss (1976) reduced MHD equations. The investigation was focused on describing MHD turbulence in a current-carrying bounded magnetofluid. A cylindrical geometry with a square cross-section was considered, with the walls being rigid perfect conductors with free-slip boundary conditions. A uniform magnetic field and the electric current density both point in the z-direction. Initial conditions are specified which feature small amounts of random noise expressed as Fourier modes. Linearized equations are defined for tracing the movement to equlibrium conditions or other temporal development. The model is further refined with nonlinear equations to examine the effects of the appearance of disruptions. Comparisons are drawn between solutions obtained with linear and nonlinear equations, with an eye to the associated physical realities.

Dahlburg, J. P.↗

NASA NTRS1985

An interplanetary magnetic field ensemble at 1 AU

A method for calculation ensemble averages from magnetic field data is described. A data set comprising approximately 16 months of nearly continuous ISEE-3 magnetic field data is used in this study. Individual subintervals of this data, ranging from 15 hours to 15.6 days comprise the ensemble. The sole condition for including each subinterval in the averages is the degree to which it represents a weakly time-stationary process. Averages obtained by this method are appropriate for a turbulence description of the interplanetary medium. The ensemble average correlation length obtained from all subintervals is found to be 4.9 x 10 to the 11th cm. The average value of the variances of the magnetic field components are in the approximate ratio 8:9:10, where the third component is the local mean field direction. The correlation lengths and variances are found to have a systematic variation with subinterval duration, reflecting the important role of low-frequency fluctuations in the interplanetary medium.

Matthaeus, W. H.↗

NASA NTRS1985

Rapid magnetic reconnection caused by finite amplitude fluctuations

The nonlinear dynamics of the magnetohydrodynamic sheet pinch have been investigated as an unforced initial value problem for large scale Reynolds numbers up to 1000. Reconnection is triggered by adding to the sheet pinch a small but finite level of broadband random perturbations. Effects of turbulence in the solutions include the production of reconnected magnetic islands at rates that are insensitive to resistivity at early times. This is explained by noting that electric field fluctuations near the X point produce irregularities in the vector potential, sometimes taking the form of 'magnetic bubbles', which allow rapid change of field topology.

Matthaeus, W. H.↗

NASA NTRS1984

Particle-acceleration by turbulent magnetohydrodynamic reconnection

Test particles in a two dimensional, turbulent MHD simulation are found to undergo significant acceleration. The magnetic field configuration is a periodic sheet pinch which undergoes reconnection. The test particles are trapped in the reconnection region for times of order an Alfven transit time in the large electric fields that characterize the turbulent reconnection process at the relatively large magnetic Reynolds number used in the simulation. The maximum speed attained by these particles is consistent with an analytic estimate which depends on the reconnection electric field, the Alfven speed, and the ratio of Larmor period to the Alfven transit time.

Matthaeus, W. H.↗

NASA NTRS1984

Particle acceleration by turbulent magnetohydro-dynamic reconnection

Test particles in a two dimensional, turbulent MHD simulation are found to undergo significant acceleration. The magnetic field configuration is a periodic sheet pinch which undergoes reconnection. The test particles are trapped in the reconnection region for times of order an Alfven transit time in the large electric fields that characterize the turbulent reconnection process at the relatively large magnetic Reynolds number used in the simulation. The maximum speed attained by these particles is consistent with an analytic estimate which depends on the reconnection electric field, the Alfven speed, and the ratio of Larmor period to the Alfven transit time.

Matthaeus, W. H.↗

NASA NTRS1984

Power spectral signatures of interplanetary corotating and transient flows

Studies of the time behavior of the galactic cosmic ray intensity have concluded that long term decreases in the intensity are generally associated with systems of interplanetary flows that contain flare generated shock waves, magnetic clouds and other transient phenomena. The magnetic field power spectral signatures of such flow systems are compared to power spectra obtained during times when the solar wind is dominated by stable corotating streams that do not usually produce long-lived reduction in the cosmic ray intensity. The spectral signatures of these two types of regimes (transient and corotating) are distinct. However, the distinguishing features are not the same throughout the heliosphere. In data collected beyond 1 AU the primary differences are in the power spectra of the magnitude of the magnetic field rather than in the power in the field components. Consequently, decreases in cosmic ray intensity are very likely due to magnetic mirror forces and gradient drifts rather than to small angle scattering due to cyclotron wave-particle interactions. Previously announced in STAR as N84-18131

Goldstein, M. L.↗

NASA NTRS1984

Power spectral signatures of interplanetary corotating and transient flows

Studies of the time behavior of the galactic cosmic ray intensity have concluded that long term decreases in the intensity are generally associated with systems of interplanetary flows that contain flare generated shock waves, magnetic clouds and other transient phenomena. The magnetic field power spectral signatures of such flow systems are compared to power spectra obtained during times when the solar wind is dominated by stable corotating streams that do not usually produce long-lived reduction in the cosmic ray intensity. The spectral signatures of these two types of regimes (transient and corotating) are distinct. However, the distinguishing features are not the same throughout the heliosphere. In data collected beyond 1 AU the primary differences are in the power spectra of the magnitude of the magnetic field rather than in the power in the field components. Consequently, decreases in cosmic ray intensity are very likely due to magnetic mirror forces and gradient drifts rather than to small angle scattering due to cyclotron wave-particle interactions.

Goldstein, M. L.↗

NASA NTRS1984

Dynamic alignment and selective decay in MHD

Under some circumstances, incompressible magnetohydrodynamic turbulence will evolve toward a state in which the velocity fields and magnetic fields are aligned or anti-aligned. We propose a mechanism for this effect and illustrate with numerical computations. Under some other circumstances, the energy appears to decay selectively toward a minimum energy state in which the kinetic energy has disappeared. It has not been possible so far to identify a boundary in the phase space which divides the two regimes.

Matthaeus, W. H.↗

NASA NTRS1983

Large amplitude MHD waves upstream of the Jovian bow shock

Observations of large amplitude MHD waves upstream of Jupiter's bow shock are analyzed. The waves are found to be right circularly polarized in the solar wind frame, which suggests that they are propagating in the fast magnetosonic mode. A complete spectral and minimum variance eigenvalue analysis of the data was performed. The power spectrum of the magnetic fluctuations contains several peaks. The fluctuations at 2.3 MHz have a direction of minimum variance anti-parallel to the direction of the average magnetic field. Several harmonics at 6, 9, and 12 MHz are also present. The direction of minimum variance of these fluctuations lies at approximately 40 deg to the magnetic field. It is argued that these fluctuations are waves excited by protons reflected off the Jovian bow shock. The inferred speed of the reflected protons is about two times the solar wind speed in the solar wind frame. A linear instability analysis is presented that suggests an explanation for many of the observed features of the observations. The fluctuations apparently contain a significant fraction of magnetic energy that is linearly polarized and in the Alfven mode.

Goldstein, M. L.↗