scholarly journals Reflection-driven magnetohydrodynamic turbulence in the solar atmosphere and solar wind

2019 ◽  
Vol 85 (4) ◽  
Author(s):  
Benjamin D. G. Chandran ◽  
Jean C. Perez
Keyword(s):  
Solar Wind ◽  
Heating Rate ◽  
Three Dimensional ◽  
Power Spectra ◽  
Inertial Range ◽  
Magnetic Flux Tube ◽  
Analytic Model ◽  
Mhd Turbulence ◽  
Background Magnetic Field ◽  
Turbulent Heating

We present three-dimensional direct numerical simulations and an analytic model of reflection-driven magnetohydrodynamic (MHD) turbulence in the solar wind. Our simulations describe transverse, non-compressive MHD fluctuations within a narrow magnetic flux tube that extends from the photosphere, through the chromosphere and corona and out to a heliocentric distance  $r$ of 21 solar radii  $(R_{\odot })$ . We launch outward-propagating ‘ $\boldsymbol{z}^{+}$ fluctuations’ into the simulation domain by imposing a randomly evolving photospheric velocity field. As these fluctuations propagate away from the Sun, they undergo partial reflection, producing inward-propagating ‘ $\boldsymbol{z}^{-}$ fluctuations’. Counter-propagating fluctuations subsequently interact, causing fluctuation energy to cascade to small scales and dissipate. Our analytic model incorporates dynamic alignment, allows for strongly or weakly turbulent nonlinear interactions and divides the $\boldsymbol{z}^{+}$ fluctuations into two populations with different characteristic radial correlation lengths. The inertial-range power spectra of $\boldsymbol{z}^{+}$ and $\boldsymbol{z}^{-}$ fluctuations in our simulations evolve toward a $k_{\bot }^{-3/2}$ scaling at $r>10R_{\odot }$ , where $k_{\bot }$ is the wave-vector component perpendicular to the background magnetic field. In two of our simulations, the $\boldsymbol{z}^{+}$ power spectra are much flatter between the coronal base and $r\simeq 4R_{\odot }$ . We argue that these spectral scalings are caused by: (i) high-pass filtering in the upper chromosphere; (ii) the anomalous coherence of inertial-range $\boldsymbol{z}^{-}$ fluctuations in a reference frame propagating outwards with the $\boldsymbol{z}^{+}$ fluctuations; and (iii) the change in the sign of the radial derivative of the Alfvén speed at $r=r_{\text{m}}\simeq 1.7R_{\odot }$ , which disrupts this anomalous coherence between $r=r_{\text{m}}$ and $r\simeq 2r_{\text{m}}$ . At $r>1.3R_{\odot }$ , the turbulent heating rate in our simulations is comparable to the turbulent heating rate in a previously developed solar-wind model that agreed with a number of observational constraints, consistent with the hypothesis that MHD turbulence accounts for much of the heating of the fast solar wind.

Strong MHD helical turbulence and the nonlinear dynamo effect

1976 ◽  
Vol 77 (2) ◽  
pp. 321-354 ◽  
Author(s):  
A. Pouquet ◽  
U. Frisch ◽  
J. Léorat
Keyword(s):  
Large Scale ◽  
Magnetic Energy ◽  
Three Dimensional ◽  
Power Laws ◽  
Inertial Range ◽  
Small Scale ◽  
Mhd Turbulence ◽  
Inverse Cascade ◽  
Small Scales ◽  
Dynamo Effect

To understand the turbulent generation of large-scale magnetic fields and to advance beyond purely kinematic approaches to the dynamo effect like that introduced by Steenbeck, Krause & Radler (1966)’ a new nonlinear theory is developed for three-dimensional, homogeneous, isotropic, incompressible MHD turbulence with helicity, i.e. not statistically invariant under plane reflexions. For this, techniques introduced for ordinary turbulence in recent years by Kraichnan (1971 a)’ Orszag (1970, 1976) and others are generalized to MHD; in particular we make use of the eddy-damped quasi-normal Markovian approximation. The resulting closed equations for the evolution of the kinetic and magnetic energy and helicity spectra are studied both theoretically and numerically in situations with high Reynolds number and unit magnetic Prandtl number.Interactions between widely separated scales are much more important than for non-magnetic turbulence. Large-scale magnetic energy brings to equipartition small-scale kinetic and magnetic excitation (energy or helicity) by the ‘Alfvén effect’; the small-scale ‘residual’ helicity, which is the difference between a purely kinetic and a purely magnetic helical term, induces growth of large-scale magnetic energy and helicity by the ‘helicity effect’. In the absence of helicity an inertial range occurs with a cascade of energy to small scales; to lowest order it is a −3/2 power law with equipartition of kinetic and magnetic energy spectra as in Kraichnan (1965) but there are −2 corrections (and possibly higher ones) leading to a slight excess of magnetic energy. When kinetic energy is continuously injected, an initial seed of magnetic field will grow to approximate equipartition, at least in the small scales. If in addition kinetic helicity is injected, an inverse cascade of magnetic helicity is obtained leading to the appearance of magnetic energy and helicity in ever-increasing scales (in fact, limited by the size of the system). This inverse cascade, predicted by Frischet al.(1975), results from a competition between the helicity and Alféh effects and yields an inertial range with approximately — 1 and — 2 power laws for magnetic energy and helicity. When kinetic helicity is injected at the scale linjand the rate$\tilde{\epsilon}^V$(per unit mass), the time of build-up of magnetic energy with scaleL[Gt ] linjis$t \approx L(|\tilde{\epsilon}^V|l^2_{\rm inj})^{-1/3}.$

scholarly journals On the ion-inertial range density power spectra in solar wind turbulence

2018 ◽  
Author(s):  
Rudolf A. Treumann ◽  
Wolfgang Baumjohann ◽  
Yasuhito Narita
Keyword(s):  
Solar Wind ◽  
Solar Wind Velocity ◽  
Power Spectra ◽  
Inertial Range ◽  
Pressure Balance ◽  
Density Spectrum ◽  
Magnetic Turbulence ◽  
Power Spectral ◽  
Velocity Turbulence ◽  
Range Density

Abstract. De-magnetised ions in the ion inertial range of quasi-neutral plasmas respond to Kolmogorov inertial range velocity turbulence power spectra via the spectrum of the velocity turbulence related random mean square induction electric field. Maintenance of electrical quasi-neutrality in this field causes deformation in the power spectral density of the density turbulence. Experimentally confirmed Kolmogorov inertial range spectra in solar wind velocity turbulence and observations of density power spectra suggest that the observed unexplained scale-limited occasional bumps in the density power spectrum may be caused by this electric ion response. Magnetic power spectra react passively to the density spectrum by warranting pressure balance. This effect still neglects contribution of Hall currents and is restricted to the ion inertial range scale. It occurs under certain conditions only. While both density and magnetic turbulence spectra in the range of ion inertial scales deviate from Kolmogorov, the velocity turbulence preserves its Kolmogorov inertial range shape in this process to which spectral advection turns out to be secondary.

scholarly journals Three-dimensional Hybrid Simulation Results of a Variable Magnetic Helicity Signature at Proton Kinetic Scales

2022 ◽  
Vol 924 (2) ◽  
pp. 41
Author(s):  
Bernard J. Vasquez ◽  
Sergei A. Markovskii ◽  
Charles W. Smith
Keyword(s):  
Magnetic Field ◽  
Solar Wind ◽  
Physical Quantity ◽  
Large Scale ◽  
Three Dimensional ◽  
Turbulent Energy ◽  
Magnetic Helicity ◽  
Intrinsic Variability ◽  
Background Magnetic Field ◽  
Simulation Results

Abstract Three-dimensional hybrid kinetic simulations are conducted with particle protons and warm fluid electrons. Alfvénic fluctuations initialized at large scales and with wavevectors that are highly oblique with respect to the background magnetic field evolve into a turbulent energy cascade that dissipates at proton kinetic scales. Accompanying the proton scales is a spectral magnetic helicity signature with a peak in magnitude. A series of simulation runs are made with different large-scale cross helicity and different initial fluctuation phases and wavevector configurations. From the simulations a so-called total magnetic helicity peak is evaluated by summing contributions at a wavenumber perpendicular to the background magnetic field. The total is then compared with the reduced magnetic helicity calculated along spacecraft-like trajectories through the simulation box. The reduced combines the helicity from different perpendicular wavenumbers and depends on the sampling direction. The total is then the better physical quantity to characterize the turbulence. On average the ratio of reduced to total is 0.45. The total magnetic helicity and the reduced magnetic helicity show intrinsic variability based on initial fluctuation conditions. This variability can contribute to the scatter found in the observed distribution of solar wind reduced magnetic helicity as a function of cross helicity.

scholarly journals MHD Turbulence in the Solar Wind and Interplanetary Dynamo Effects

1993 ◽  
Vol 157 ◽  
pp. 51-57
Author(s):  
E. Marsch ◽  
C.-Y. Tu
Keyword(s):  
Magnetic Field ◽  
Solar Wind ◽  
Electric Fields ◽  
Power Spectra ◽  
Dynamo Theory ◽  
Mhd Turbulence ◽  
Correlation Studies ◽  
Negative Results ◽  
Alpha Effect ◽  
The Mean

From the fluctuations of the velocity and magnetic field observed in different kinds of solar wind the fluctuating electric fields are derived, and their power spectra are constructed and analysed. The mean electromotive force ɛ generated by the turbulent motions depends upon the nature of the fluctuations. Simple dynamo theory predicts a linear relationship between ɛ and the mean magnetic field B0. Correlation studies carried out to establish the alpha effect in the solar wind have given negative results.

scholarly journals Ion parallel viscosity and anisotropy in MHD turbulence

1996 ◽  
Vol 56 (3) ◽  
pp. 641-657 ◽  
Author(s):  
Sean Oughton
Keyword(s):  
Large Scale ◽  
Three Dimensional ◽  
Nonlinear Process ◽  
Mhd Equations ◽  
Mhd Turbulence ◽  
Viscosity Term ◽  
Anisotropy Effect ◽  
Background Magnetic Field ◽  
Linear And Nonlinear ◽  
Almost All

We report on results from direct numerical simulation of the incompressible three- dimensional magnetohydrodynamic (MHD) equations, modified to incorporate viscous dissipation via the strongly anisotropic ion-parallel viscosity term. Both linear and nonlinear cases are considered, all with a strong background magnetic field. It is found that spectral anisotropy develops in almost all cases, but that the contribution from effects associated with the ion-parallel viscosity is relatively weak compared with the previously reported nonlinear process. Furthermore, and in contrast to this earlier work, it is suggested that when B0 is large, the anisotropy will develop and persist for many large-scale turnover times even for non-dissipative runs. Resistive dissipation is found to dominate over viscous even when the resistivity is several orders of magnitude smaller than the ion parallel viscosity. A variance anisotropy effect and anisotropy dependence on the polarization of the fluctuations are also observed.

scholarly journals Scaling laws in Hall-inertial range turbulence

2019 ◽  
Author(s):  
Yasuhito Narita ◽  
Wolfgang Baumjohann ◽  
Rudolf A. Treumann
Keyword(s):  
Magnetic Field ◽  
Electric Field ◽  
Scaling Laws ◽  
Magnetic Energy ◽  
Spatial Scales ◽  
Electric Energy ◽  
Power Spectra ◽  
Inertial Range ◽  
Energy Spectra ◽  
Mhd Turbulence

Abstract. There is an increasing amount of observational evidence in space plasma for the breakdown of inertial-range spectra of magnetohydrodynamic (MHD) turbulence on spatial scales smaller than the ion inertial length. Magnetic energy spectra often exhibit a steepening, which is reminiscent of dissipation of turbulence energy, for example in wave-particle interactions. Electric energy spectra, on the other hand, tend to be flatter than those of MHD turbulence, which is indicative of a dispersive process converting magnetic into electric energy in electromagnetic wave excitation. Here we develop a model of the scaling laws and the power spectra for the Hall-inertial range in plasma turbulence. A phenomenological approach is taken. The Hall electric field attains an electrostatic component when the wave vectors are perpendicular to the mean magnetic field. The power spectra of Hall-turbulence are steep for the magnetic field with slope of −7/3 for compressible magnetic turbulence, they are flatter for the Hall electric field with slope −1/3. Our model for the Hall-turbulence serves as a likely candidate to explain the steepening of the magnetic energy spectra in the solar wind neither as indication of the dissipation range nor the dispersive range but as the Hall-inertial range. Our model also reproduces the shape of energy spectra in Kelvin-Helmholtz turbulence observed at the Earth magnetopause.

scholarly journals Scaling laws in Hall inertial-range turbulence

2019 ◽  
Vol 37 (5) ◽  
pp. 825-834 ◽  
Author(s):  
Yasuhito Narita ◽  
Wolfgang Baumjohann ◽  
Rudolf A. Treumann
Keyword(s):  
Magnetic Field ◽  
Electric Field ◽  
Scaling Laws ◽  
Magnetic Energy ◽  
Electric Energy ◽  
Power Spectra ◽  
Inertial Range ◽  
Energy Spectra ◽  
Mhd Turbulence ◽  
The Magnetic Field

Abstract. There is an increasing amount of observational evidence in space plasmas for the breakdown of inertial-range spectra of magnetohydrodynamic (MHD) turbulence on spatial scales smaller than the ion-inertial length. Magnetic energy spectra often exhibit a steepening, which is reminiscent of dissipation of turbulence energy, for example in wave–particle interactions. Electric energy spectra, on the other hand, tend to be flatter than those of MHD turbulence, which is indicative of a dispersive process converting magnetic into electric energy in electromagnetic wave excitation. Here we develop a model of the scaling laws and the power spectra for the Hall inertial range in plasma turbulence. In the present paper we consider a two-dimensional geometry with no wave vector component parallel to the magnetic field as is appropriate in Hall MHD. A phenomenological approach is taken. The Hall electric field attains an electrostatic component when the wave vectors are perpendicular to the mean magnetic field. The power spectra of Hall turbulence are steep for the magnetic field with a slope of -7/3 for compressible magnetic turbulence; they are flatter for the Hall electric field with a slope of -1/3. Our model for the Hall turbulence gives a possible explanation for the steepening of the magnetic energy spectra in the solar wind as an indication of neither the dissipation range nor the dispersive range but as the Hall inertial range. Our model also reproduces the shape of energy spectra in Kelvin–Helmholtz turbulence observed at the Earth's magnetopause.

Turbulent cascade in the solar wind on ion scales

2020 ◽  
Author(s):  
Petr Hellinger ◽  
Andrea Verdini ◽  
Simone Landi ◽  
Luca Franci ◽  
Emanuele Papini ◽  
...  
Keyword(s):  
Solar Wind ◽  
Numerical Simulations ◽  
Hall Effect ◽  
Power Spectra ◽  
Two Dimensional ◽  
Mhd Turbulence ◽  
Ion Heating ◽  
Simulation Results ◽  
Hall Mhd ◽  
Turbulent Cascade

<p>Magnetic power spectra in the solar wind typically exhibit a transition, steepening, on characteristic ion scales. This transition is not yet fully understood. Two basic phenomena are usually suspected: Hall physics and dissipation. We investigate properties of this transition using numerical simulations.  We analyze results of two-dimensional hybrid simulations using a compressible version of von Kármán-Howarth equation for statistically homogeneous Hall MHD turbulence and compare these results to the predictions for the incompressible Hall MHD. The simulation results indicate that the transition between large, MHD and sub-ion scales is related to a combination of the Hall effect and ion heating/energization.</p>

scholarly journals On the ion-inertial-range density-power spectra in solar wind turbulence

2019 ◽  
Vol 37 (2) ◽  
pp. 183-199 ◽  
Author(s):  
Rudolf A. Treumann ◽  
Wolfgang Baumjohann ◽  
Yasuhito Narita
Keyword(s):  
Solar Wind ◽  
Source Region ◽  
Power Spectra ◽  
Density Fluctuations ◽  
Inertial Range ◽  
Wave Number ◽  
Mean Flow ◽  
Pressure Balance ◽  
Density Spectrum ◽  
Velocity Turbulence

Abstract. A model-independent first-principle first-order investigation of the shape of turbulent density-power spectra in the ion-inertial range of the solar wind at 1 AU is presented. Demagnetised ions in the ion-inertial range of quasi-neutral plasmas respond to Kolmogorov (K) or Iroshnikov–Kraichnan (IK) inertial-range velocity–turbulence power spectra via the spectrum of the velocity–turbulence-related random-mean-square induction–electric field. Maintenance of electrical quasi-neutrality by the ions causes deformations in the power spectral density of the turbulent density fluctuations. Assuming inertial-range K (IK) spectra in solar wind velocity turbulence and referring to observations of density-power spectra suggest that the occasionally observed scale-limited bumps in the density-power spectrum may be traced back to the electric ion response. Magnetic power spectra react passively to the density spectrum by warranting pressure balance. This approach still neglects contribution of Hall currents and is restricted to the ion-inertial-range scale. While both density and magnetic turbulence spectra in the affected range of ion-inertial scales deviate from K or IK power law shapes, the velocity turbulence preserves its inertial-range shape in the process to which spectral advection turns out to be secondary but may become observable under special external conditions. One such case observed by WIND is analysed. We discuss various aspects of this effect, including the affected wave-number scale range, dependence on the angle between mean flow velocity and wave numbers, and, for a radially expanding solar wind flow, assuming adiabatic expansion at fast solar wind speeds and a Parker dependence of the solar wind magnetic field on radius, also the presumable limitations on the radial location of the turbulent source region.

Nonlinear electromagnetic wave interactions in Hall–MHD plasmas

2010 ◽  
Vol 76 (6) ◽  
pp. 893-901
Author(s):  
DASTGEER SHAIKH ◽  
P. K. SHUKŁA
Keyword(s):  
Solar Wind ◽  
Electromagnetic Wave ◽  
Three Dimensional ◽  
Solar Wind Plasma ◽  
Inertial Range ◽  
High Time Resolution ◽  
Plasma Energy ◽  
Frequency Regime ◽  
Electromagnetic Wave Interactions ◽  
Hall Mhd

AbstractWe have developed a massively parallelized fully three-dimensional (3D) compressible Hall–magnetohydrodynamic (MHD) code to investigate inertial range electromagnetic wave cascades and dissipative processes in the regime, where characteristic length scales associated with plasma fluctuations are smaller than ion gyroradii. Such regime is ubiquitously present in the solar wind and many other collisionless space plasmas. Particularly, in the solar wind, the high time resolution databases depict a spectral break near the end of the 5/3 spectrum that corresponds to a high-frequency regime where the electromagnetic turbulent cascades cannot be explained by the usual MHD models. This refers to a second inertial range, where turbulent cascades follow a k−7/3 (where k is a wavenumber) spectrum in which the characteristic electromagnetic fluctuations evolve typically on kinetic Alfvén time scales. In this paper, we describe results from our 3D compressible Hall–MHD simulations that explain the observed k−7/3 spectrum in the solar wind plasma, energy cascade, anisotropy, and other spectral features.

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