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At least 487 records · Page 27
All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

Simultaneous observations of VLF ground transmitter signals on the DE 1 and COSMOC 1809 satellites: Detection of a magnetospheric caustic and a duct

Khabarovsk transmitter signals (15.0 kHz, 48 deg N, 135 deg E) were observed on the high-altitude (approximately 15000 km) Dynamic Explorer 1 (DE 1) and the low-altitude (approximately 960) km COSMOS 1809 satellites during a 9-day period in August 1989. On 7 out of 9 days the linear wave receiver (LWR) on the DE 1 satellite also detected signals from the Alpha transmitter (11.9-15.6 kHz) in Russia and an Omega transmitter (10.2-13.6 kHz) in Australia, as well as natural VLF emissions such as hiss, chorus, whistlers, and wideband impulsive signals. On two days, August 23 and 27, 1989, observations of the Khabarovsk transmitter signals were simultaneously carried out at high altitude on thre DE 1 satellite and at low altitude on the COSMOS 1809 satellite. Analysis of data from these 2 days has led to several new results on the propagation of whistler mode signals in the Earth's magnetosphere. New evidence was found of previously reported propagation phenomena, such as (1) confinement of transmitter signals in the conjugate hemisphere at ionospheric heights (approximately 1000 km), (2) observation of direct multipath propagation on both DE 1 and COSMOS 1809, (3) detection of ionospheric irregularities of is less than or equal to 100 km scale size with a few percent enhancement in electron density. We also report the first direct detection of a magnetospheric dust at L = 2.94 which was believed to be responsible for the ducted propagation of Khabarovsk signals observed in the COSMOS 1809 satellite. Our study also indicates that duct end points can extend down to at least approximately 1000 km. The peak electric and magnetic fields of ducted Khabarovsk transmitter signals at approximately 1000 km were 520 micro V/m and 36 pT respectively. Estimated field strengths of these signals inside the dust at the geomagnetic equator were 57 micro V/m and 12 pT for electric and magnetic field respectively. The results of two-dimensional ray tracing simulations were consistent with the observations of the nonducted whistler-mode propagation of Khabarovsk (15 kHz) and Alpha (11.9 kHz) signals from the transmitter location to the DE 1 and COSMOS 1809 satellites. Our results have direct implications for the question of accessibility of waves injected from the ground to various regions of the ionosphere and the magnetosphere.

Chmyrev, V. M.↗
NASA NTRS2001

Plasma Waves Observed in the Cusp Turbulent Boundary Layer: An Analysis of High Time Resolution Wave and Particle Measurements from the Polar Spacecraft

The boundary layer located in the cusp and adjacent to the magnetopause is a region that is quite turbulent and abundant with waves. The Polar spacecraft's orbit and sophisticated instrumentation are ideal for studying this region of space. Our analysis of the waveform data obtained in this turbulent boundary layer shows broadband magnetic noise extending up to a few kilohertz (but less than the electron cyclotron frequency); sinusoidal bursts (a few tenths of a second) of whistler mode waves at around a few tens of hertz, a few hundreds of hertz, and just below the electron cyclotron frequency; and bipolar pulses, interpreted as electron phase-space holes. In addition, bursts of electron cyclotron harmonic waves are occasionally observed with magnetic components. We show evidence of broadband electrostatic bursts covering a range of approx. 3 to approx. 25 kHz (near but less than the plasma frequency) occurring in packets modulated at the frequency of some of the whistler mode waves. On the basis of high time resolution particle data from the Polar HYDRA instrument, we show that these bursts are consistent with generation by the resistive medium instability. The most likely source of the whistler mode waves is the magnetic reconnection site closest to the spacecraft, since the waves are observed propagating both toward and away from the Earth, are bursty, which is often the case with reconnection, and do not fit on the theoretical cold plasma dispersion relation curve.

Pickett, J. S.↗
NASA NTRS2012

Magnetic and Electric Field Polarizations of Oblique Magnetospheric Chorus Waves

A theory was developed to explain the properties of the chorus magnetic and electric field components in the case of an arbitrary propagation angle. The new theory shows that a whistler wave has circularly polarized magnetic fields for oblique propagation. This theoretical result is verified by GEOTAIL observations. The wave electric field polarization plane is not orthogonal to the wave vector, and in general is highly elliptically polarized. A special case of the whistler wave called the Gendrin mode is also discussed. This will help to construct a detailed and realistic picture of wave interaction with magnetosphere electrons. It is the purpose of this innovation to study the magnetic and electric polarization properties of chorus at all frequencies, and at all angles of propagation. Even though general expressions for electromagnetic wave polarization in anisotropic plasma are derived in many textbooks, to the knowledge of the innovators, a detailed analysis for oblique whistler wave mode is lacking. Knowledge of the polarization properties is critical for theoretical calculations of resonant wave-particle interactions.

Verkhoglyadova, Olga↗
NASA NTRS2016

Banded Structures in Electron Pitch Angle Diffusion Coefficients from Resonant Wave Particle Interactions

Electron pitch angle (D (alpha)) and momentum (D(pp)) diffusion coefficients have been calculated due to resonant interactions with electrostatic electron cyclotron harmonic (ECH) and whistler mode chorus waves. Calculations have been performed at two spatial locations L = 4.6 and 6.8 for electron energies 10 keV. Landau (n = 0) resonance and cyclotron harmonic resonances n = +/-1, +/-2,...+/-5 have been included in the calculations. It is found that diffusion coefficient versus pitch angle (alpha) profiles show large dips and oscillations or banded structures. The structures are more pronounced for ECH and lower band chorus (LBC) and particularly at location 4.6. Calculations of diffusion coefficients have also been performed for individual resonances. It is noticed that the main contribution of ECH waves in pitch angle diffusion coefficient is due to resonances n = +1 and n = +2. A major contribution to momentum diffusion coefficients appears from n = +2. However, the banded structures in D alpha and Dpp coefficients appear only in the profile of diffusion coefficients for n = +2. The contribution of other resonances to diffusion coefficients is found to be, in general, quite small or even negligible. For LBC and upper band chorus waves, the banded structures appear only in Landau resonance. The Dpp diffusion coefficient for ECH waves is one to two orders smaller than D alpha coefficients. For chorus waves, Dpp coefficients are about an order of magnitude smaller than D alpha coefficients for the case n does not = 0. In case of Landau resonance, the values of Dpp coefficient are generally larger than the values of D alpha coefficients particularly at lower energies. As an aid to the interpretation of results, we have also determined the resonant frequencies. For ECH waves, resonant frequencies have been estimated for wave normal angle 89 deg and harmonic resonances n = +1, +2, and +3, whereas for whistler mode waves, the frequencies have been calculated for angle 10 deg and Landau resonance. Further, in ECH waves, the banded structures appear for electron energies (is) greater than1 keV, and for whistler mode chorus waves, structures appear for energies greater than 2 keV at L = 4.6 and above 200 eV for L = 6.8. The results obtained in the present work will be helpful in the study of diffusion curves and will have important consequences for diffuse aurora and pancake distributions.

diffusion↗
NASA NTRS2016

Ionosphere-Magnetosphere Energy Interplay in the Regions of Diffuse Aurora

Both electron cyclotron harmonic (ECH) waves and whistler mode chorus waves resonate with electrons of the Earths plasma sheet in the energy range from tens of eV to several keV and produce the electron diffuse aurora at ionospheric altitudes. Interaction of these superthermal electrons with the neutral atmosphere leads to the production of secondary electrons (E500600 eV) and, as a result, leads to the activation of lower energy superthermal electron spectra that can escape back to the magnetosphere and contribute to the thermal electron energy deposition processes in the magnetospheric plasma. The ECH and whistler mode chorus waves, however, can also interact with the secondary electrons that are coming from both of the magnetically conjugated ionospheres after they have been produced by initially precipitated high-energy electrons that came from the plasma sheet. After their degradation and subsequent reflection in magnetically conjugate atmospheric regions, both the secondary electrons and the precipitating electrons with high (E600 eV) initial energies will travel back through the loss cone, become trapped in the magnetosphere, and redistribute the energy content of the magnetosphere-ionosphere system. Thus, scattering of the secondary electrons by ECH and whistler mode chorus waves leads to an increase of the fraction of superthermal electron energy deposited into the core magnetospheric plasma.

Khazanov, G. V.↗
NASA NTRS2012

Lunar Precursor Effects in the Solar Wind and Terrestrial Magnetosphere

The two ARTEMIS probes observe significant precursor activity upstream from the Moon, when magnetically connected to the dayside lunar surface. The most common signature consists of high levels of whistler wave activity near half of the electron cyclotron frequency. This precursor activity extends to distances of many thousands of km, in both the solar wind and terrestrial magnetosphere. In the magnetosphere, electrons reflect from a combination of magnetic and electrostatic fields above the lunar surface, forming loss cone distributions. In the solar wind they generally form conics, as a result of reflection from an obstacle moving with respect to the plasma frame (just as at a shock). The anisotropy associated with these reflected electrons provides the free energy source for the whistlers, with cyclotron resonance conditions met between the reflected source population and Moonward-propagating waves. These waves can in turn affect incoming plasma, and we observe significant perpendicular electron heating and plasma density depletions in some cases. In the magnetosphere, we also observe broadband electrostatic modes driven by beams of secondary electrons and/or photoelectrons accelerated outward from the surface. We also occasionally see waves near the ion cyclotron frequency in the magnetosphere. These lower frequency waves, which may result from the presence of ions of lunar origin, modulate the whistlers described above, as well as the electrons. Taken together, our observations suggest that the presence of the Moon leads to the formation of an upstream region analogous in many ways to the terrestrial electron foreshock.

Magnetosphere↗
NASA NTRS2020

Ion-Scale Current Structures in Short Large-Amplitude Magnetic Structures

We investigate electric current structures in Short Large-Amplitude Magnetic Structures (SLAMS) in the terrestrial ion foreshock region observed by the Magnetospheric Multiscale mission. The structures with intense currents (|J|~1 𝜇𝐴/𝑚2) have scale lengths comparable to the local ion inertial length (di). One current structure type is a current sheet due to the magnetic field rotation of the SLAMS, and a subset of these current sheets can exhibit reconnection features including the electron outflow jet and X-line-type magnetic topology. The di-scale current sheet near the edge of a SLAMS propagates much more slowly than the overall SLAMS, suggesting that it may result from compression. The current structures also exist as magnetosonic whistler waves with fci < f < flh, where fci and flh are the ion cyclotron frequency and the lower- hybrid frequency, respectively.The field rotations in the current sheets and whistler waves generate comparable |J| and energy conversion rates. Electron heating is clearly observed in one whistler packet embedded in a larger-scale current sheet of the SLAMS, where the parallel electric field and the curvature drift opposite to the electric field energize electrons. The results give insight about the thin current structure generation and energy conversion at thin current structures in the shock transition region.

Shan Wang↗
NASA NTRS2020

The Formation of Electron Heat Flux in the Region of Diffuse Aurora

Whistler and electrostatic electron cyclotron harmonics waves are responsible for scattering and precipitating the energetic plasma sheet electrons that drive the diffuse aurora. These primary electrons with energies in the kiloelectron volt range, simultaneously precipitating in magnetically conjugate regions, produce the secondary electron population and can be reflected by the atmosphere back through the magnetosphere and precipitate into the conjugate region with additional follow‐up atmospheric backscatter. Primary, degraded, and secondary electrons can be trapped back into the magnetosphere as they travel back and forth between the two magnetically conjugate ionospheres and continuously delivering their energy to the cold plasma sheet electrons and form the electron thermal fluxes that deposit this energy at the upper ionospheric altitudes. We consider the formation of these heat fluxes focusing on the magnetosphere‐ionosphere energy interplay of the entire superthermal electron spectra from 1 eV up to 10 keV and discuss the efficiency of the different spectral energy intervals that contribute to the electron plasma heating at the magnetospheric altitudes. Our parametric studies at L = 6.8, with lower and upper band chorus whistler wave amplitudes of 10 pT and electron cyclotron harmonic wave amplitudes of 1 mVm−1, indicate the dominant role of the whistler mode in the formation of the electron heat flux coming from the magnetosphere to the ionosphere.

George V. Khazanov↗
DOE OSTI2014

A robust method for handling low density regions in hybrid simulations for collisionless plasmas

A robust method to handle vacuum and near vacuum regions in hybrid simulations for space and astrophysical plasmas is presented. The conventional hybrid simulation model dealing with kinetic ions and a massless charge-neutralizing electron fluid is known to be susceptible to numerical instability due to divergence of the whistler-mode wave dispersion, as well as division-by-density operation in regions of low density. Consequently, a pure vacuum region is not allowed to exist in the simulation domain unless some ad hoc technique is used. To resolve this difficulty, an alternative way to introduce finite electron inertia effect is proposed. Contrary to the conventional method, the proposed one introduces a correction to the electric field rather than the magnetic field. It is shown that the generalized Ohm's law correctly reduces to Laplace's equation in a vacuum which therefore does not involve any numerical problems. In addition, a variable ion-to-electron mass ratio is introduced to reduce the phase velocity of high frequency whistler waves at low density regions so that the stability condition is always satisfied. It is demonstrated that the proposed model is able to handle near vacuum regions generated as a result of nonlinear self-consistent development of the system, as well as pure vacuum regions set up at the initial condition, without losing the advantages of the standard hybrid code.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2012

Chorus wave amplification: A free electron laser in the Earth's magnetosphere

A new theoretical model for whistler-mode chorus amplification in the Earth's magnetosphere is presented. We derive, based on the free-electron laser mechanism in a high-gain amplifier, a new closed set of self-consistent relativistic equations that couple the Hamiltonian equations for particles with Maxwell's equations. We demonstrate that these equations predict, through a cubic equation, whistler amplification levels in good agreement with those observed in the Earth's magnetosphere.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

STEREO interplanetary shocks and foreshocks

We use STEREO data to study shocks driven by stream interactions and the waves associated with them. During the years of the extended solar minimum 2007-2010, stream interaction shocks have Mach numbers between 1.1-3.8 and {theta}{sub Bn}{approx}20-86 Degree-Sign . We find a variety of waves, including whistlers and low frequency fluctuations. Upstream whistler waves may be generated at the shock and upstream ultra low frequency (ULF) waves can be driven locally by ion instabilities. The downstream wave spectra can be formed by both, locally generated perturbations, and shock transmitted waves. We find that many quasiperpendicular shocks can be accompanied by ULF wave and ion foreshocks, which is in contrast to Earth's bow shock. Fluctuations downstream of quasi-parallel shocks tend to have larger amplitudes than waves downstream of quasi-perpendicular shocks. Proton foreshocks of shocks driven by stream interactions have extensions dr {<=}0.05 AU. This is smaller than foreshock extensions for ICME driven shocks. The difference in foreshock extensions is related to the fact that ICME driven shocks are formed closer to the Sun and therefore begin to accelerate particles very early in their existence, while stream interaction shocks form at {approx}1 AU and have been producing suprathermal particles for a shorter time.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Helicon waves in uniform plasmas. II. High m numbers

Helicons are whistler modes with azimuthal wave numbers. They have been studied in solids and plasmas where boundaries play a role. The present work shows that very similar modes exist in unbounded gaseous plasmas. Instead of boundaries, the antenna properties determine the topology of the wave packets. The simplest antenna is a magnetic loop which excites m = 0 or m = 1 helicons depending on whether the dipole moment is aligned parallel or perpendicular to the ambient background magnetic field B{sub 0}. While these low order helicons have been described by J. M. Urrutia and R. L. Stenzel [“Helicon modes in uniform plasmas. I. Low m modes,” Phys. Plasmas 22, 092111 (2015)], the present work focuses on high order modes up to m = 8. These are excited by antenna arrays forming magnetic multipoles. Their wave magnetic field has been measured in space and time in a large and uniform laboratory plasma free of boundary effects. The observed wave topology exhibits m pairs of unique field line spirals which may have inspired the name “helicon” to this mode. All field lines converge into these nested spirals which propagate like corkscrews along B{sub 0}. The field lines near the axis of helicons are perpendicular to B{sub 0} and circularly polarized as in parallel whistlers. Helical antennas couple to these transverse fields but not to the spiral fields of helicons. Using a circular antenna array of phased m = 0 loops, right or left rotating or non-rotating multipole antenna fields are generated. They excite m < 0 and m > 0 modes, showing that the plasma supports both modes equally well. The poor excitation of m < 0 modes is a characteristic of loops with dipole moment across B{sub 0}. The radiation efficiency of multipole antennas has been found to decrease with m.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

Helicon waves in uniform plasmas. IV. Bessel beams, Gendrin beams, and helicons

Electromagnetic waves in the low frequency whistler mode regime are investigated experimentally and by digital data superposition. The radiation from a novel circular antenna array is shown to produce highly collimated helicon beams in a uniform unbounded plasma. The differences to Bessel beams in free space are remarked upon. Low divergence beams arise from the parallel group velocity of whistlers with phase velocity either along the guide field or at the Gendrin angle. Waves with angular momentum are produced by phasing the array in the circular direction. The differences in the field topologies for positive and negative modes numbers are shown. It is also shown that in uniform plasmas, the radial amplitude profile of the waves depends on the antenna field topology. Thus, there are no helicon “eigenmodes” with radial Bessel function profiles in uniform plasmas. It is pointed out that phase measurements in helicon devices indicate radial wave propagation which is inconsistent with helicon eigenmode theory based on paraxial wave propagation. Trivelpiece-Gould modes also exist in uniform unbounded plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

Trivelpiece-Gould modes in a uniform unbounded plasma

Trivelpiece-Gould (TG) modes originally described electrostatic surface waves on an axially magnetized cylindrical plasma column. Subsequent studies of electromagnetic waves in such plasma columns revealed two modes, a predominantly magnetic helicon mode (H) and the mixed magnetic and electrostatic Trivelpiece-Gould modes (TG). The latter are similar to whistler modes near the oblique cyclotron resonance in unbounded plasmas. The wave propagation in cylindrical geometry is assumed to be paraxial while the modes exhibit radial standing waves. The present work shows that TG modes also arise in a uniform plasma without radial standing waves. It is shown experimentally that oblique cyclotron resonance arises in large mode number helicons. Their azimuthal wave number far exceeds the axial wave number which creates whistlers near the oblique cyclotron resonance. Cyclotron damping absorbs the TG mode and can energize electrons in the center of a plasma column rather than the edge of conventional TG modes. The angular orbital field momentum can produce new perpendicular wave-particle interactions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2013

A second-order semi-implicit δf method for hybrid simulation

A second-order accurate semi-implicit Lorentz force ions, fluid electrons δf hybrid model has been developed using a “current closure” scheme. The model assumes quasi-neutrality and is fully electromagnetic. The implicit field solver improves numerical accuracy by separating the equilibrium terms in the presence of small perturbations. The equilibrium part of the generalized Ohm’s law is solved by direct matrix inversion along the direction of gradients for every Fourier mode in the other two directions, while the nonlinear part is solved iteratively. The simulation has been benchmarked on Alfvén waves, ion sound waves and whistler waves against analytical dispersion relation in a slab. In particular, the first-order and second-order schemes are compared by studying the numerical damping of whistler waves. The full evolution of the resistive tearing mode using the Harris sheet equilibrium is also investigated. The linear growth rate and mode structure are compared with the resistive MHD theory. Important tearing mode nonlinear phenomena such as the Rutherford regime and saturation are demonstrated. We also presented systematic study of Rutherford growth rates and saturation island width, which is consistent with previous MHD studies.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Physical processes in an electron current layer causing intense plasma heating and formation of x-lines

We study the evolution of an electron current layer (ECL) through its several stages by means of three-dimensional particle-in-cell (PIC) simulations with ion to electron mass ratio M/m{sub e} = 400. An ECL evolves through the following stages: (i) Electrostatic (ES) current-driven instability (CDI) soon after its formation with half width w about 2 electron skin depth (d{sub e}), (ii) current disruption in the central part of the ECL by trapping of electrons and generation of anomalous resistivity, (iii) electron tearing instability (ETI) with significantly large growth rates in the lower end of the whistler frequency range, (iv) widening of the ECL and modulation of its width by the ETI, (v) gradual heating of electrons by the CDI-driven ES ion modes create the condition that the electrons become hotter than the ions, (vi) despite the reduced electron drift associated with the current disruption by the CDI, the enhanced electron temperature continues to favor a slow growth of the ion waves reaching nonlinear amplitudes, (vii) the nonlinear ion waves undergo modulation and collapse into localized density cavities containing spiky electric fields like in double layers (DLs), (viii) such spiky electric fields are very effective in further rapid heating of both electrons and ions. As predicted by the electron magnetohydrodynamic (EMHD) theories, the ETI growth rate maximizes at wave numbers in the range 0.4 < k{sub x}W < 0.8 where k{sub x} is the wave number parallel to the ECL magnetic field and w is the evolving half width of the ECL. The developing ETI generates in-plane currents that support out-of-plane magnetic fields around the emerging x-lines. The ETI and the spiky electrostatic structures are accompanied by fluctuations in the magnetic fields near and above the lower-hybrid (ion plasma) frequency, including the whistler frequency range. We compare our results with experimental results and satellite observation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

Kinetic theory of turbulence for parallel propagation revisited: Low-to-intermediate frequency regime

A previous paper [P. H. Yoon, “Kinetic theory of turbulence for parallel propagation revisited: Formal results,” Phys. Plasmas 22, 082309 (2015)] revisited the second-order nonlinear kinetic theory for turbulence propagating in directions parallel/anti-parallel to the ambient magnetic field, in which the original work according to Yoon and Fang [Phys. Plasmas 15, 122312 (2008)] was refined, following the paper by Gaelzer et al. [Phys. Plasmas 22, 032310 (2015)]. The main finding involved the dimensional correction pertaining to discrete-particle effects in Yoon and Fang's theory. However, the final result was presented in terms of formal linear and nonlinear susceptibility response functions. In the present paper, the formal equations are explicitly written down for the case of low-to-intermediate frequency regime by making use of approximate forms for the response functions. The resulting equations are sufficiently concrete so that they can readily be solved by numerical means or analyzed by theoretical means. The derived set of equations describe nonlinear interactions of quasi-parallel modes whose frequency range covers the Alfvén wave range to ion-cyclotron mode, but is sufficiently lower than the electron cyclotron mode. The application of the present formalism may range from the nonlinear evolution of whistler anisotropy instability in the high-beta regime, and the nonlinear interaction of electrons with whistler-range turbulence.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2012

DO OBLIQUE ALFVEN/ION-CYCLOTRON OR FAST-MODE/WHISTLER WAVES DOMINATE THE DISSIPATION OF SOLAR WIND TURBULENCE NEAR THE PROTON INERTIAL LENGTH?

To determine the wave modes prevailing in solar wind turbulence at kinetic scales, we study the magnetic polarization of small-scale fluctuations in the plane perpendicular to the data sampling direction (namely, the solar wind flow direction, V{sub SW}) and analyze its orientation with respect to the local background magnetic field B{sub 0,local}. As an example, we take only measurements made in an outward magnetic sector. When B{sub 0,local} is quasi-perpendicular to V{sub SW}, we find that the small-scale magnetic-field fluctuations, which have periods from about 1 to 3 s and are extracted from a wavelet decomposition of the original time series, show a polarization ellipse with right-handed orientation. This is consistent with a positive reduced magnetic helicity, as previously reported. Moreover, for the first time we find that the major axis of the ellipse is perpendicular to B{sub 0,local}, a property that is characteristic of an oblique Alfven wave rather than oblique whistler wave. For an oblique whistler wave, the major axis of the magnetic ellipse is expected to be aligned with B{sub 0,local}, thus indicating significant magnetic compressibility, and the polarization turns from right to left handedness as the wave propagation angle ({theta}{sub kB}) increases toward 90 Degree-Sign . Therefore, we conclude that the observation of a right-handed polarization ellipse with orientation perpendicular to B{sub 0,local} seems to indicate that oblique Alfven/ion-cyclotron waves rather than oblique fast-mode/whistler waves dominate in the 'dissipation' range near the break of solar wind turbulence spectra occurring around the proton inertial length.

79 ASTRONOMY AND ASTROPHYSICS↗