On the ion-inertial-range density-power spectra in solar wind 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.

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

10.5194/angeo-2018-129 ◽

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.

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

Journal of Plasma Physics ◽

10.1017/s0022377819000540 ◽

2019 ◽

Vol 85 (4) ◽

Cited By ~ 13

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.

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The small amplitude of density turbulence in the inner solar wind

Nonlinear Processes in Geophysics ◽

10.5194/npg-10-113-2003 ◽

2003 ◽

Vol 10 (1/2) ◽

pp. 113-120 ◽

Cited By ~ 4

Author(s):

S. R. Spangler

Keyword(s):

Solar Wind ◽

Spatial Scales ◽

Power Spectra ◽

Solar Wind Plasma ◽

Density Fluctuations ◽

Long Baseline ◽

Interferometer Phase ◽

The Mean ◽

Pass Through ◽

Rms Amplitude

Abstract. Very Long Baseline Interferometer (VLBI) observations were made of radio sources close to the Sun, whose lines of sight pass through the inner solar wind (impact parameters 16-26 RE). Power spectra were analyzed of the interferometer phase fluctuations due to the solar wind plasma. These power spectra provide information on the level of plasma density fluctuations on spatial scales of roughly one hundred to several thousand kilometers. By specifying an outer scale to the turbulence spectrum, we can estimate the root-mean-square (rms) amplitude of the density fluctuations. The data indicate that the rms fluctuation in density is only about 10% of the mean density. This value is low, and consistent with extrapolated estimates from more distant parts of the solar wind. Physical speculations based on this result are presented.

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What can Hall-MHD simulations tell us about the transition region in the solar wind proton density spectrum?

10.5194/egusphere-egu2020-2440 ◽

2020 ◽

Author(s):

Victor Montagud-Camps ◽

František Němec ◽

Jana Šafránková ◽

Zdeněk Němeček ◽

Roland Grappin ◽

...

Keyword(s):

Solar Wind ◽

Transition Region ◽

Spectral Index ◽

Density Fluctuations ◽

Power Density Spectrum ◽

Proton Density ◽

Density Spectrum ◽

Significant Difference ◽

Field Fluctuations ◽

Hall Mhd

Similarly to the power density spectrum of magnetic field fluctuations in the solar wind, the spectrum of density fluctuations also shows multiple spectral slopes. Both of them present a spectral index varying between &#8211;3/2 and &#8211;5/3 in the inertial range and close to &#8211;2.8 between the proton and electron gyrofrequencies.Despite these similarities, the spectrum of density fluctuations has a significant difference with respect to the magnetic and velocity fluctuations spectra: it shows a transition region between the inertial and the kinetic ranges with spectral index typically around &#8211;1.We have combined the results of compressible Hall-MHD numerical simulations and measurements of the BMSW instrument onboard Spektr-R satellite to study the possible causes of the flattening in the density spectrum. Both numerical and experimental approaches point towards an important role played by Kinetic Alfv&#233;n Waves.

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Turbulent spectra in the solar wind plasma

Journal of Plasma Physics ◽

10.1017/s0022377809990237 ◽

2009 ◽

Vol 76 (2) ◽

pp. 183-191 ◽

Cited By ~ 4

Author(s):

DASTGEER SHAIKH ◽

G. P. ZANK

Keyword(s):

Solar Wind ◽

Three Dimensional ◽

Solar Wind Plasma ◽

Density Fluctuations ◽

Magnetized Plasma ◽

Density Spectrum ◽

Turbulent Spectrum ◽

Extended Length ◽

Turbulent Spectra ◽

Magnetohydrodynamic Fluid

AbstractObservations of interstellar scintillations at radio wavelengths reveal a Kolmogorov-like scaling of the electron density spectrum with a spectral slope of −5/3 over six decades in wavenumber space. A similar turbulent density spectrum in the solar wind plasma has been reported. The energy transfer process in the magnetized solar wind plasma over such extended length scales remains an unresolved paradox of modern turbulence theories, raising the especially intriguing question of how a compressible magnetized solar wind exhibits a turbulent spectrum that is a characteristic of an incompressible hydrodynamic fluid. To address these questions, we have undertaken three-dimensional time-dependent numerical simulations of a compressible magnetohydrodynamic fluid describing super-Alfvénic, supersonic and strongly magnetized plasma. It is shown that the observed Kolmogorov-like (−5/3) spectrum can develop in the solar wind plasma by supersonic plasma motions that dissipate into highly subsonic motion that passively convect density fluctuations.

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Domains of Magnetic Pressure Balance in Parker Solar Probe Observations of the Solar Wind

The Astrophysical Journal ◽

10.3847/1538-4357/ac2ee3 ◽

2021 ◽

Vol 923 (2) ◽

pp. 158

Author(s):

David Ruffolo ◽

Nawin Ngampoopun ◽

Yash R. Bhora ◽

Panisara Thepthong ◽

Peera Pongkitiwanichakul ◽

...

Keyword(s):

Magnetic Field ◽

Solar Wind ◽

Density Fluctuations ◽

Magnetic Pressure ◽

Inverse Association ◽

The Sun ◽

Thin Domains ◽

Pressure Balance ◽

Filling Fraction ◽

The Mean

Abstract The Parker Solar Probe (PSP) spacecraft is performing the first in situ exploration of the solar wind within 0.2 au of the Sun. Initial observations confirmed the Alfvénic nature of aligned fluctuations of the magnetic field B and velocity V in solar wind plasma close to the Sun, in domains of nearly constant magnetic field magnitude ∣ B ∣, i.e., approximate magnetic pressure balance. Such domains are interrupted by particularly strong fluctuations, including but not limited to radial field (polarity) reversals, known as switchbacks. It has been proposed that nonlinear Kelvin–Helmholtz instabilities form near magnetic boundaries in the nascent solar wind leading to extensive shear-driven dynamics, strong turbulent fluctuations including switchbacks, and mixing layers that involve domains of approximate magnetic pressure balance. In this work we identify and analyze various aspects of such domains using data from the first five PSP solar encounters. The filling fraction of domains, a measure of Alfvénicity, varies from median values of 90% within 0.2 au to 38% outside 0.9 au, with strong fluctuations. We find an inverse association between the mean domain duration and plasma β. We examine whether the mean domain duration is also related to the crossing time of spatial structures frozen into the solar wind flow for extreme cases of the aspect ratio. Our results are inconsistent with long, thin domains aligned along the radial or Parker spiral direction, and compatible with isotropic domains, which is consistent with prior observations of isotropic density fluctuations or flocculae in the solar wind.

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Structure in the Solar Corona from Radio Scintillation Measurements

International Astronomical Union Colloquium ◽

10.1017/s0252921100030013 ◽

1996 ◽

Vol 154 ◽

pp. 97-104

Author(s):

Richard Woo

Keyword(s):

Solar Wind ◽

Wind Speed ◽

Recent Progress ◽

Solar Wind Speed ◽

Source Region ◽

Density Fluctuations ◽

The Sun ◽

Fine Scale ◽

Radio Scintillation ◽

Electron Density Fluctuations

AbstractSince the 1950s, a wide variety of radio observations based on scattering by electron density fluctuations in the solar wind has provided much of our information on density fluctuations and solar wind speed near the source region of the solar wind. This paper reviews recent progress in the understanding of the nature of these density fluctuations and their relationship to features on the Sun. The results include the first measurements of fine-scale structure within coronal streamers and evidence for structure in solar wind speed in the inner corona.

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Turbulence in stratified atmospheres: implications for the intracluster medium

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/staa711 ◽

2020 ◽

Vol 493 (4) ◽

pp. 5838-5853 ◽

Cited By ~ 2

Author(s):

Rajsekhar Mohapatra ◽

Christoph Federrath ◽

Prateek Sharma

Keyword(s):

Power Spectrum ◽

Radial Profile ◽

Power Spectra ◽

Density Fluctuations ◽

Total Power ◽

Intracluster Medium ◽

Stratified Turbulence ◽

Density Spectrum ◽

Velocity Fluctuations ◽

Hydrodynamical Simulations

ABSTRACT The gas motions in the intracluster medium (ICM) are governed by turbulence. However, since the ICM has a radial profile with the centre being denser than the outskirts, ICM turbulence is stratified. Stratified turbulence is fundamentally different from Kolmogorov (isotropic, homogeneous) turbulence; kinetic energy not only cascades from large to small scales, but it is also converted into buoyancy potential energy. To understand the density and velocity fluctuations in the ICM, we conduct high-resolution (10242 × 1536 grid points) hydrodynamical simulations of subsonic turbulence (with rms Mach number $\mathcal {M}\approx 0.25$) and different levels of stratification, quantified by the Richardson number Ri, from Ri = 0 (no stratification) to Ri = 13 (strong stratification). We quantify the density, pressure, and velocity fields for varying stratification because observational studies often use surface brightness fluctuations to infer the turbulent gas velocities of the ICM. We find that the standard deviation of the logarithmic density fluctuations (σs), where s = ln (ρ/ < ρ($z$) >), increases with Ri. For weakly stratified subsonic turbulence (Ri ≲ 10, $\mathcal {M}\lt 1$), we derive a new σs–$\mathcal {M}$–Ri relation, $\sigma _\mathrm{ s}^2=\ln (1+b^2\mathcal {M}^4+0.09\mathcal {M}^2 \mathrm{Ri} H_\mathrm{ P}/H_\mathrm{ S})$, where b = 1/3–1 is the turbulence driving parameter, and HP and HS are the pressure and entropy scale heights, respectively. We further find that the power spectrum of density fluctuations, P(ρk/ < ρ >), increases in magnitude with increasing Ri. Its slope in k-space flattens with increasing Ri before steepening again for Ri ≳ 1. In contrast to the density spectrum, the velocity power spectrum is invariant to changes in the stratification. Thus, we find that the ratio between density and velocity power spectra strongly depends on Ri, with the total power in density and velocity fluctuations described by our σs–$\mathcal {M}$–Ri relation. Pressure fluctuations, on the other hand, are independent of stratification and only depend on $\mathcal {M}$.

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Sub-ion scale measurements of compressible turbulence in the solar wind MMS Observations

10.5194/egusphere-egu2020-6815 ◽

2020 ◽

Author(s):

Owen Roberts ◽

Rumi Nakamura ◽

Yasuhito Narita ◽

Justin Holmes ◽

Zoltan Voros ◽

...

Keyword(s):

Magnetic Field ◽

Solar Wind ◽

Power Spectrum ◽

Electron Density ◽

Field Measurements ◽

Small Region ◽

Density Fluctuations ◽

Compressible Turbulence ◽

Density Spectrum ◽

Spacecraft Potential

Compressible plasma turbulence is investigated at sub ion scales using both the Fast Plasma Investigation instrument on the Magnetospheric MultiScale mission as well as using calibrated spacecraft potential. The data from FPI allow inertial and a small region of sub-ion scales to be investigated before the instrumental noise becomes significant near 3Hz. In this work we give a detailed description of the spacecraft potential and how it is calibrated such that it can be used the measure the electron density. The key advantage of using the calibrated spacecraft potential is that a much higher time resolution is possible when compared to the direct measurement. This allows a measurement down to 40Hz for a measurement of the electron density. This is an improvement of an additional decade in scale. Using a one hour interval of solar wind burst mode data the power spectrum of the density fluctuations is measured from the inertial range to the sub ion range. At inertial scales the density spectrum shows similarities with the magnetic field power spectrum with a characteristic Kolmogorov like power law. In between the ion inertial and kinetic scales there is a brief flattening in the spectra before steepening in the sub ion range to a spectral index comparable to the trace magnetic field fluctuations. The morphology if the density spectra can be explained by either a cascade of Alfv\'en waves and slow waves at large scales and kinetic Alfv\'en waves at sub ion scales, or by the presence of the hall effect. Using electric field measurements the two hypotheses are tested.

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Rapid density fluctuations in the solar wind

Annales Geophysicae ◽

10.5194/angeo-23-3765-2005 ◽

2005 ◽

Vol 23 (12) ◽

pp. 3765-3773 ◽

Cited By ~ 71

Author(s):

P. J. Kellogg ◽

T. S. Horbury

Keyword(s):

Solar Wind ◽

Electron Density ◽

Acoustic Waves ◽

Density Fluctuations ◽

Magnetic Fluctuations ◽

Pressure Balance ◽

Ion Acoustic Waves ◽

Ion Density ◽

Ion Acoustic ◽

Electron Density Fluctuations

Abstract. Electron density fluctuations (up to 2.5 Hz) in the solar wind have been studied, using the EFW experiment on the Cluster spacecraft, which measures density through measurements of the biased probe potentials relative to the spacecraft. The density fluctuation spectra obtained from the EFW probe potential variations are compared to earlier, OGO 5, measurements of ion density fluctuations and ISEE measurements of electron density fluctuations, and are consistent with them. The electric fields corresponding to the electron density fluctuations are extremely small compared with what would be obtained if the electron fluctuations were not cancelled out by nearly equal ion density fluctuations. This is consistent with the nature of ion acoustic waves. In agreement with ISEE work, the fluctuations are proportional to the ambient density. Correlation with magnetic fluctuations is weak, essentially nonexistent during part of the period studied. This might be expected as magnetic fluctuations are known to be nearly incompressible, but even the correlation with fluctuations in the magnitude of B is very small. However, many structures which apparently are pressure balance structures are found. Pressure balance structures are the nearly perpendicular propagation limit of ion acoustic waves. As ion acoustic waves are strongly damped in plasmas like the solar wind at least if the plasma is taken as Maxwellian, it has always been a puzzle as to why they are found there. We speculate that these waves are created by mode conversion from magnetic fluctuations, and may represent part of the dissipation process for these.

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