Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “SOLAR WIND”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Solar Models in Light of New High Metallicity Measurements from Solar Wind Data

We study the impact of new metallicity measurements, from solar wind data, on the solar model. The “solar modeling problem” refers to the persisting discrepancy between helioseismological observations and predictions of solar models computed implementing state-of-the-art photospheric abundances. We critically reassess the problem, in particular considering the new set of abundances of von Steiger and Zurbuchen, determined through the in situ collection of solar wind samples from polar coronal holes. This new set of abundances indicates a solar metallicity Z{sub ⊙}⩾0.0196±0.0014, significantly higher than the currently established value. The new values hint at an abundance of volatile elements (i.e., C, N, O, Ne) close to previous results of Grevesse and Sauval, whereas the abundance of refractory elements (i.e., Mg, Si, S, Fe) is considerably increased. Using the Linear Solar Model formalism, we determine the variation of helioseismological observables in response to the changes in elemental abundances, in order to explore the consistency of these new measurements with constraints from helioseismology. We find that for observables that are particularly sensitive to the abundance of volatile elements, in particular the radius of the convective zone boundary (CZB) and the sound speed around the radius of CZB, improved agreement over previous models is obtained. Conversely, the high abundance of refractories correlates with a higher core temperature, resulting in an overproduction of neutrinos and a huge increase in the surface helium abundance. We conclude that the “solar modeling problem” remains unsolved.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

A study of density modulation index in the inner heliospheric solar wind during solar cycle 23

The ratio of the rms electron density fluctuations to the background density in the solar wind (density modulation index, ε {sub N} ≡ ΔN/N) is of vital importance for understanding several problems in heliospheric physics related to solar wind turbulence. In this paper, we have investigated the behavior of ε {sub N} in the inner heliosphere from 0.26 to 0.82 AU. The density fluctuations ΔN have been deduced using extensive ground-based observations of interplanetary scintillation at 327 MHz, which probe spatial scales of a few hundred kilometers. The background densities (N) have been derived using near-Earth observations from the Advanced Composition Explorer. Our analysis reveals that 0.001 ≲ ε {sub N} ≲ 0.02 and does not vary appreciably with heliocentric distance. We also find that ε {sub N} declines by 8% from 1998 to 2008. We discuss the impact of these findings on problems ranging from our understanding of Forbush decreases to the behavior of the solar wind dynamic pressure over the recent peculiar solar minimum at the end of cycle 23.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

THE NEW HORIZONS SOLAR WIND AROUND PLUTO (SWAP) OBSERVATIONS OF THE SOLAR WIND FROM 11–33 au

The Solar Wind Around Pluto (SWAP) instrument on National Aeronautics and Space Administration's New Horizons Pluto mission has collected solar wind observations en route from Earth to Pluto, and these observations continue beyond Pluto. Few missions have explored the solar wind in the outer heliosphere making this dataset a critical addition to the field. We created a forward model of SWAP count rates, which includes a comprehensive instrument response function based on laboratory and flight calibrations. By fitting the count rates with this model, the proton density (n), speed (V), and temperature (T) parameters are determined. Comparisons between SWAP parameters and both propagated 1 au observations and prior Voyager 2 observations indicate consistency in both the range and mean wind values. These comparisons as well as our additional findings confirm that small and midsized solar wind structures are worn down with increasing distance due to dynamic interaction of parcels of wind with different speed. For instance, the T–V relationship steepens, as the range in V is limited more than the range in T with distance. At times the T–V correlation clearly breaks down beyond 20 au, which may indicate wind currently expanding and cooling may have an elevated T reflecting prior heating and compression in the inner heliosphere. The power of wind parameters at shorter periodicities decreases with distance as the longer periodicities strengthen. The solar rotation periodicity is present in temperature beyond 20 au indicating the observed parcel temperature may reflect not only current heating or cooling, but also heating occurring closer to the Sun.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Observation and modeling of geocoronal charge exchange X-ray emission during solar wind gusts

Solar wind charge exchange (SWCX) X-rays are emitted when highly charged solar wind ions such as O{sup 7{sup +}} collide with neutral gas, including the Earth's tenuous outer atmosphere (exosphere or geocorona) and hydrogen and helium from the local interstellar medium drifting through the heliosphere. This geocoronal and heliospheric emission comprises a significant and varying fraction of the soft X-ray background (SXRB) and is seen in every X-ray observation, with the intensity dependent on solar wind conditions and observation geometry. Under the right conditions, geocoronal emission can increase the apparent SXRB by roughly an order of magnitude for an hour or more. In this work, we study a dozen occasions when the near-Earth solar wind flux was exceptionally high. These gusts of wind lead to abrupt changes in SWCX X-ray emission around Earth, which may or may not be seen by X-ray observatories depending on their line of sight. Using detailed three-dimensional magnetohydrodynamical simulations of the solar wind's interaction with the Earth's magnetosphere, and element abundances and ionization states measured by ACE, we model the time-dependent brightness of major geocoronal SWCX emission lines during those gusts and compare with changes in the X-ray background measured by the Chandra X-ray Observatory. We find reasonably good agreement between model and observation, with measured geocoronal line brightnesses averaged over 1 hr of up to 136 photons s{sup –1} cm{sup –2} sr{sup –1} in the O VII Kα triplet around 564 eV.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

On Alfvénic turbulence of solar wind streams observed by Solar Orbiter during March 2022 perihelion and their source regions

It has been recently accepted that the standard classification of the solar wind solely according to flow speed is outdated, and particular interest has been devoted to the study of the origin and evolution of so-called Alfvénic slow solar wind streams and to what extent such streams resemble or differ from fast wind. In March 2022, Solar Orbiter completed its first nominal phase perihelion passage. During this interval, it observed several Alfvénic streams, allowing for characterization of fluctuations in three slow wind intervals (AS1-AS3) and comparison with a fast wind stream (F) at almost the same heliocentric distance. This work makes use of Solar Orbiter plasma parameters from the Solar Wind Analyzer (SWA) and magnetic field measurements from the magnetometer (MAG). The magnetic connectivity to the solar sources of selected solar wind intervals was reconstructed using a ballistic extrapolation based on measured solar wind speed down to the (spherical) source surface at 2.5 R s below which a potential field extrapolation was used to map back to the Sun. The source regions were identified using SDO/AIA observations. A spectral analysis of in situ measured magnetic field and velocity fluctuations was performed to characterize correlations, Alfvénicity, normalized cross-helicity, and residual energy in the frequency domain as well as intermittency of the fluctuations and spectral energy transfer rate estimated via mixed third-order moments. A machine learning technique was used to separate proton core, proton beam, and alpha particles and to study v − b correlations for the different ion populations in order to evaluate the role played by each population in determining the Alfvénic content of solar wind fluctuations. The comparison between fast wind and Alfvénic slow wind intervals highlights the differences between the two solar wind regimes: The fast wind is characterized by larger amplitude fluctuations, and magnetic and velocity fluctuations are closer to equipartition of energy. In fact the Alfvénic slow wind streams appear to be on a spectrum of wind types, with AS1, originating from open field lines neighboring active regions and displaying similarities with the fast wind in terms of fluctuation amplitude and turbulence characteristics, but not with respect to the alpha particles and proton beams. The other two slow streams differed both in their sources as well as plasma characteristics, with AS2 coming from the expansion of a narrow coronal hole corridor and AS3 from a region straddling a pseudostreamer. The latter displayed the coldest and highest density but the slowest stream with the smallest fluctuation amplitude and greatest magnetic energy excess. It also showed the largest scatter in proton beam speeds and the greatest difference in speed between proton beam and alpha particles. This study shows how the old fast–slow solar wind dichotomy, already called into question by the observations of slower Alfvénic solar wind streams, should further be refined, as the Alfvénic slow wind, originating in different solar wind regions, show significant differences in density, temperature, and proton and alpha-particle properties in the inner heliosphere. The observations presented here provide the starting point for a better understanding of the origin and evolution of different solar wind streams as well as the evolving turbulence contained within.

magnetohydrodynamics (MHD)↗
DOE OSTI2014

The dynamic character of the polar solar wind

The Solar and Heliospheric Observatory (SOHO) Large Angle and Spectrometric Coronagraph C2 and Solar Terrestrial Relations Observatory (STEREO) COR2A coronagraph images, when analyzed using correlation tracking techniques, show a surprising result in places ordinarily thought of as 'quiet' solar wind above the poles in coronal hole regions. Instead of the static well-ordered flow and gradual acceleration normally expected, coronagraph images show outflow in polar coronal holes consisting of a mixture of intermittent slow and fast patches of material. We compare measurements of this highly variable solar wind from C2 and COR2A images and show that both coronagraphs measure essentially the same structures. Measurements of the mean velocity as a function of height of these structures are compared with mass flux determinations of the solar wind outflow in the large polar coronal hole regions and give similar results.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

A STATISTICAL SURVEY OF DYNAMIC PRESSURE PULSES IN THE SOLAR WIND BASED ON WIND OBSERVATIONS

Solar wind dynamic pressure pulse (DPP) structures, across which the dynamic pressure changes abruptly over timescales from a few seconds to several minutes, are often observed in the near-Earth space environment. The space weather effects of DPPs on the magnetosphere–ionosphere coupling system have been widely investigated in the last two decades. In this study, we perform a statistical survey on the properties of DPPs near 1 AU based on nearly 20 years of observations from the WIND spacecraft. It is found that only a tiny fraction of DPPs (around 4.2%) can be regarded as interplanetary shocks. For most DPPs, the total pressure (the sum of the thermal pressure and magnetic pressure) remains in equilibrium, but there also exists a small fraction of DPPs that are not pressure-balanced. The overwhelming majority of DPPs are associated with solar wind disturbances, including coronal mass ejection-related flows, corotating interaction regions, as well as complex ejecta. The annual variations of the averaged occurrence rate of DPPs are roughly in phase with the solar activity during solar cycle 23, and during the rising phase of solar cycle 24.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Solar wind magnetic fluctuations and electron non-thermal temperature anisotropy: survey of Wind-SWE-VEIS observations

The solar wind electron velocity distribution function (eVDF) exhibits a variety of non-thermal features that deviate from thermal equilibrium. These deviations from equilibrium provide a local source for electromagnetic fluctuation emissions, including the commonly observed electron whistler-cyclotron and firehose instabilities. We present a systematic analysis of Wind-SWE-VEIS observations of solar wind electron plasma and associated Wind-MFI observed magnetic fluctuations. For the first time using the full solar wind electron distribution and its moments, without separation of the various electron components, we show clear evidence that the temperature anisotropy threshold of the parallel electron cyclotron anisotropic instability bounds solar wind electrons during slow solar wind periods. We also demonstrate that during periods of slow solar wind, collisions—while infrequent—are the dominant mechanism by which solar wind electrons are constrained, leading to isotropization. During fast solar wind periods, magnetic fluctuations and solar wind anisotropies are enhanced above the parallel whistler anisotropic threshold boundary and collisional effects are significantly reduced. Preliminary calculations further show that the oblique electron whistler mirror anisotropic instability bounds both the slow and fast solar wind. Regardless of speed, the solar wind electron thermal anisotropy appears globally bounded by the parallel electron firehose instability for anisotropies T{sub e⊥}/T{sub e||}<1. Our results indicate that collisions, while infrequent, play a necessary role in regulating the solar wind eVDFs. In striking contrast to solar wind ions, solar wind electron plasma, when considered globally as a single eVDF, is only marginally stable with respect to parallel propagating instabilities.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Turbulent Transport in a Three-dimensional Solar Wind

Turbulence in the solar wind can play essential roles in the heating of coronal and solar wind plasma and the acceleration of the solar wind and energetic particles. Turbulence sources are not well understood and thought to be partly enhanced by interaction with the large-scale inhomogeneity of the solar wind and the interplanetary magnetic field and/or transported from the solar corona. To investigate the interaction with background inhomogeneity and the turbulence sources, we have developed a new 3D MHD model that includes the transport and dissipation of turbulence using the theoretical model of Zank et al. We solve for the temporal and spatial evolution of three moments or variables, the energy in the forward and backward fluctuating modes and the residual energy and their three corresponding correlation lengths. The transport model is coupled to our 3D model of the inhomogeneous solar wind. We present results of the coupled solar wind-turbulence model assuming a simple tilted dipole magnetic configuration that mimics solar minimum conditions, together with several comparative intermediate cases. By considering eight possible solar wind and turbulence source configurations, we show that the large-scale solar wind and IMF inhomogeneity and the strength of the turbulence sources significantly affect the distribution of turbulence in the heliosphere within 6 au. We compare the predicted turbulence distribution results from a complete solar minimum model with in situ measurements made by the Helios and Ulysses spacecraft, finding that the synthetic profiles of the turbulence intensities show reasonable agreement with observations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Nature and Scalings of Density Fluctuations of Compressible Magnetohydrodynamic Turbulence with Applications to the Solar Wind

Abstract The solar wind is a magnetized and turbulent plasma. Its turbulence is often dominated by Alfvénic fluctuations and often deemed as nearly incompressible far away from the Sun, as shown by in situ measurements near 1 au. However, for solar wind closer to the Sun, the plasma β decreases (often lower than unity) while the turbulent Mach number M t increases (can approach unity, e.g., transonic fluctuations). These conditions could produce significantly more compressible effects, characterized by enhanced density fluctuations, as seen by several space missions. In this paper, a series of 3D MHD simulations of turbulence are carried out to understand the properties of compressible turbulence, particularly the generation of density fluctuations. We find that, over a broad range of parameter space in plasma β , cross helicity, and polytropic index, the turbulent density fluctuations scale linearly as a function of M t , with the scaling coefficients showing weak dependence on parameters. Furthermore, through detailed spatiotemporal analysis, we show that the density fluctuations are dominated by low-frequency nonlinear structures, rather than compressible MHD eigenwaves. These results could be important for understanding how compressible turbulence contributes to solar wind heating near the Sun.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Cyclotron breaking: a mechanism for parallel ion cyclotron waves to heat the fast solar wind

The Parker Solar Probe mission has observed near-continuous power in parallel ion cyclotron waves (PICWs) in the young, fast solar wind. These waves are unlikely to be directly produced by the turbulent cascade and are likely born of a local instability; yet, they are observed to both cool – and heat – the plasma. We propose that these observations can be self-consistently explained as the natural consequence of PICWs propagating in the inhomogeneous solar wind after they have been driven unstable. In this work, we argue that strong proton heating by a turbulent cascade of oblique ICWs will result in PICWs being driven unstable in a process known as quasi-linear focusing. Because the power in the turbulent cascade is concentrated at scales above the turbulent transition region, PICWs will be driven unstable within a range of wavenumbers parallel to the background magnetic field, 𝑘 ∥ , that is bounded from above by 𝑘$^{∗}_{∥P}$, corresponding to the start of the transition region. As unstable PICWs propagate away from the Sun to regions of lower proton density, their 𝑘 ∥ , multiplied by the proton inertial length 𝑑 p , increases. Eventually, 𝑘$^{∗}_{∥P}$ of the PICWs becomes larger than 𝑘$^{∗}_{∥P}$⁢𝑑 p and the waves damp, heating the solar wind. We call this effect ‘cyclotron breaking’, in analogy with ocean waves breaking on the shore. We then discuss the testable predictions of the theory, including a distinct heating signature in which PICWs cool fast protons and heat slow protons at any given heliocentric distance 𝑟. Finally, we conjecture that cyclotron breaking can lead to net heating by PICWs if the power emitted as PICWs decreases sufficiently rapidly with 𝑟 that local emission of PICWs is overwhelmed by the local damping of PICWs generated closer to the Sun.

plasma heating↗
DOE OSTI2015

INERTIAL RANGE TURBULENCE OF FAST AND SLOW SOLAR WIND AT 0.72 AU AND SOLAR MINIMUM

We investigate Venus Express observations of magnetic field fluctuations performed systematically in the solar wind at 0.72 Astronomical Units (AU), between 2007 and 2009, during the deep minimum of solar cycle 24. The power spectral densities (PSDs) of the magnetic field components have been computed for time intervals that satisfy the data integrity criteria and have been grouped according to the type of wind, fast and slow, defined for speeds larger and smaller, respectively, than 450 km s{sup −1}. The PSDs show higher levels of power for the fast wind than for the slow. The spectral slopes estimated for all PSDs in the frequency range 0.005–0.1 Hz exhibit a normal distribution. The average value of the trace of the spectral matrix is −1.60 for fast solar wind and −1.65 for slow wind. Compared to the corresponding average slopes at 1 AU, the PSDs are shallower at 0.72 AU for slow wind conditions suggesting a steepening of the solar wind spectra between Venus and Earth. No significant time variation trend is observed for the spectral behavior of both the slow and fast wind.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

On Kinetic Slow Modes, Fluid Slow Modes, and Pressure-balanced Structures in the Solar Wind

Observations in the solar wind suggest that the compressive component of inertial-range solar-wind turbulence is dominated by slow modes. The low collisionality of the solar wind allows for nonthermal features to survive, which suggests the requirement of a kinetic plasma description. The least-damped kinetic slow mode is associated with the ion-acoustic (IA) wave and a nonpropagating (NP) mode. We derive analytical expressions for the IA-wave dispersion relation in an anisotropic plasma in the framework of gyrokinetics and then compare them to fully kinetic numerical calculations, results from two-fluid theory, and magnetohydrodynamics (MHD). This comparison shows major discrepancies in the predicted wave phase speeds from MHD and kinetic theory at moderate to high β . MHD and kinetic theory also dictate that all plasma normal modes exhibit a unique signature in terms of their polarization. We quantify the relative amplitude of fluctuations in the three lowest particle velocity moments associated with IA and NP modes in the gyrokinetic limit and compare these predictions with MHD results and in situ observations of the solar-wind turbulence. The agreement between the observations of the wave polarization and our MHD predictions is better than the kinetic predictions, which suggests that the plasma behaves more like a fluid in the solar wind than expected.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Evolution of the Solar Wind Speed with Heliocentric Distance and Solar Cycle. Surprises from Ulysses and Unexpectedness from Observations of the Solar Corona

An extensive analysis of Ulysses observations of the solar wind speed V from 1990 to 2008 is undertaken. It is shown that the evolution of V with heliocentric distance r depends substantially on both the heliolatitude and the solar activity cycle. Deviations from the predicted Parker’s profile of V(r) are so considerable that cannot be explained by a scarcity of measurements or other technical effects. In particular, the expected smooth growth of the solar wind speed with r is typical only for the solar activity maximum and for low heliolatitudes (lower than ±40°), while at high latitudes, there are two V(r) branches: growing and falling. In the solar activity maximum, V increases toward the solar pole in the North hemisphere only; however, in the South hemisphere, it decreases with heliolatitude. In the minimum of solar activity, the profile of V(r) at low heliolatitudes has a local minimum between 2 and 5 AU. This result is confirmed by the corresponding data from other spacecraft (Voyager 1 and Pioneer 10). Unexpected spatial variations in V at low heliolatitudes can be explained by the impact of coronal hole flows on the V(r) profile since the flows incline to the ecliptic plane. To reproduce the impact of spatial variations of V in the polar corona on the behavior of V at low heliolatitudes, a stationary one-fluid ideal MHD-model is developed with account of recent results on imagery of the solar wind speed in the corona up to 5.5 solar radii obtained on the basis of combined observations from SOHO/UVCS, LASCO, and Mauna Loa.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

On the Relation between the In Situ Properties and the Coronal Sources of the Solar Wind

We categorize the types of solar wind using a new classification scheme based on the location of the wind’s coronal source regions in the solar atmosphere and near-solar heliosphere. We first trace the solar wind measured by ACE/SWEPAM and SWICS from 1998 to 2011 at 1 au back to a 2.5R{sub s} solar surface using ballistic mapping at constant proton speed; then we map them back to their magnetic footpoints on the 1R{sub s} solar surface via the potential field source surface (PFSS) model. Coronal structures are identified using a classification scheme based on the pixel brightness in the SOHO or STEREO EUV Carrington images. The angular distances between each mapped solar wind footpoint to the different coronal structure pixels are calculated and used as a criterion to identify the type of solar wind source region. Depending on the proximity of the solar wind footpoints to a given coronal or heliospheric structure, we classify the solar wind into six types: active region (AR), AR-boundary, quiet Sun (QS), coronal hole (CH), CH-boundary, and helmet-streamer associated wind. The in situ properties of these six types of solar winds are then examined and compared, and their solar cycle dependences are also discussed.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

THE ORIGIN OF NON-MAXWELLIAN SOLAR WIND ELECTRON VELOCITY DISTRIBUTION FUNCTION: CONNECTION TO NANOFLARES IN THE SOLAR CORONA

The formation of the observed core-halo feature in the solar wind electron velocity distribution function is a long-time puzzle. In this Letter, based on the current knowledge of nanoflares, we show that the nanoflare-accelerated electron beams are likely to trigger a strong electron two-stream instability that generates kinetic Alfvén wave and whistler wave turbulence, as we demonstrated in a previous paper. We further show that the core-halo feature produced during the origin of kinetic turbulence is likely to originate in the inner corona and can be preserved as the solar wind escapes to space along open field lines. We formulate a set of equations to describe the heating processes observed in the simulation and show that the core-halo temperature ratio of the solar wind is insensitive to the initial conditions in the corona and is related to the core-halo density ratio of the solar wind and to the quasi-saturation property of the two-stream instability at the time when the exponential decay ends. This relation can be extended to the more general core-halo-strahl feature in the solar wind. The temperature ratio between the core and hot components is nearly independent of the heliospheric distance to the Sun. We show that the core-halo relative drift previously reported is a relic of the fully saturated two-stream instability. Our theoretical results are consistent with the observations while new tests for this model are provided.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

POWER SPECTRAL DENSITY OF FLUCTUATIONS OF BULK AND THERMAL SPEEDS IN THE SOLAR WIND

This paper analyzes solar wind power spectra of bulk and thermal speed fluctuations that are computed with a time resolution of 32 ms in the frequency range of 0.001–2 Hz. The analysis uses measurements of the Bright Monitor of the Solar Wind on board the Spektr-R spacecraft that are limited to 570 km s{sup 1} bulk speed. The statistics, based on more than 42,000 individual spectra, show that: (1) the spectra of bulk and thermal speeds can be fitted by two power-law segments; (2) despite their large variations, the parameters characterizing frequency spectrum fits computed on each particular time interval are very similar for both quantities; (3) the median slopes of the bulk and thermal speeds of the segment attributed to the MHD scale are 1.43 and 1.38, respectively, whereas they are 3.08 and 2.43 in the kinetic range; (4) the kinetic range slopes of bulk and thermal speed spectra become equal when either the ion density or magnetic field strength are high; (5) the break between MHD and kinetic scales seems to be controlled by the ion β parameter; (6) the best scaling parameter for bulk and thermal speed variations is a sum of the inertial length and proton thermal gyroradius; and (7) the above conclusions can be applied to the density variations if the background magnetic field is very low.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Electron temperature of the solar wind

Significance The problem of solar wind heating is one of the long-standing fundamental problems of space plasma physics. We propose that the electron component of the solar wind plasma is heated by electrons streaming from the hot solar corona and slowly losing their energy due to weak Coulomb collisions. Our first-principle kinetic derivation predicts the scaling of the solar wind electron temperature with the heliocentric distance, which is in good agreement with observations. Our theory reveals the role of the non-Maxwellian electron distribution function in the heating mechanism, and it may be valuable for interpreting the results of in situ satellite measurements.

79 ASTRONOMY AND ASTROPHYSICS↗