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Found 28 entries in the Bibliography.
Showing entries from 1 through 28
| 2021 |
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Small-scale Magnetic Flux Ropes with Field-aligned Flows via the PSP In Situ Observations Magnetic flux rope, formed by the helical magnetic field lines, can sometimes maintain its shape while carrying significant plasma flow that is aligned with the local magnetic field. We report the existence of such structures and static flux ropes by applying the Grad-Shafranov-based algorithm to the Parker Solar Probe in situ measurements in the first five encounters. These structures are detected at heliocentric distances, ranging from 0.13 to 0.66 au, in a 4-month time period. We find that flux ropes with field-aligned fl ... Chen, Yu; Hu, Qiang; Zhao, Lingling; Kasper, Justin; Huang, Jia; Published by: \apj Published on: jun YEAR: 2021 DOI: 10.3847/1538-4357/abfd30 Parker Data Used; Solar wind; Astronomy data analysis; interplanetary turbulence; Solar magnetic reconnection; Solar magnetic fields; 1534; 1858; 830; 1504; 1503; Astrophysics - Solar and Stellar Astrophysics; Physics - Space Physics |
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Anisotropy of Solar Wind Turbulence in the Inner Heliosphere at Kinetic Scales: PSP Observations The anisotropy of solar wind turbulence is a critical issue in understanding the physics of energy transfer between scales and energy conversion between fields and particles in the heliosphere. Using the measurement of Parker Solar Probe (PSP), we present an observation of the anisotropy at kinetic scales in the slow, Alfv\ enic, solar wind in the inner heliosphere. The magnetic compressibility behaves as expected for kinetic Alfv\ enic turbulence below the ion scale. A steepened transition range is found between the inertia ... Duan, Die; He, Jiansen; Bowen, Trevor; Woodham, Lloyd; Wang, Tieyan; Chen, Christopher; Mallet, Alfred; Bale, Stuart; Published by: \apjl Published on: jul YEAR: 2021 DOI: 10.3847/2041-8213/ac07ac Parker Data Used; Solar wind; interplanetary turbulence; Alfven waves; 1534; 830; 23; Physics - Space Physics; Astrophysics - Solar and Stellar Astrophysics |
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Various forms of exact laws governing magnetohydrodynamic (MHD) turbulence have been derived either in the incompressibility limit, or for isothermal compressible flows. Here we propose a more general method that allows us to obtain such laws for any turbulent isentropic flow (i.e., constant entropy). We demonstrate that the known MHD exact laws (incompressible and isothermal) and the new (polytropic) one can be obtained as specific cases of the general law when the corresponding closure equation is stated. We also recover a ... Published by: \apj Published on: jul YEAR: 2021 DOI: 10.3847/1538-4357/ac0337 Solar wind; Solar Physics; Parker Data Used; Magnetohydrodynamics; Plasma astrophysics; Plasma physics; interplanetary turbulence; 1534; 1476; 1964; 1261; 2089; 830; Physics - Plasma Physics; Physics - Fluid Dynamics |
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Turbulent Generation of Magnetic Switchbacks in the Alfv\ enic Solar Wind One of the most important early results from the Parker Solar Probe (PSP) is the ubiquitous presence of magnetic switchbacks, whose origin is under debate. Using a three-dimensional direct numerical simulation of the equations of compressible magnetohydrodynamics from the corona to 40 solar radii, we investigate whether magnetic switchbacks emerge from granulation-driven Alfv\ en waves and turbulence in the solar wind. The simulated solar wind is an Alfv\ enic slow-solar- wind stream with a radial profile consistent with var ... Shoda, Munehito; Chandran, Benjamin; Cranmer, Steven; Published by: \apj Published on: jul YEAR: 2021 DOI: 10.3847/1538-4357/abfdbc Space plasmas; Solar wind; interplanetary turbulence; Parker Data Used; Magnetohydrodynamical simulations; Alfven waves; 1544; 1534; 830; 1966; 23; Astrophysics - Solar and Stellar Astrophysics; Physics - Plasma Physics |
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Large Amplitude Switchback Turbulence: Possible Magnetic Velocity Alignment Structures Switchbacks are widely acknowledged phenomena observed by the Parker Solar Probe and appear to occur in patches. Previous studies focused on the fluctuations at the magnetic reversals. However, the nature of the fluctuations inside the switchbacks remains unknown. Here we utilize the magnetic field data and plasma data measured by the Parker Solar Probe in the first four encounters. We investigate the fluctuations in the switchback intervals of 100 s with $B_R 0$ at every instant and compare them to the fluctuations in the n ... Wu, Honghong; Tu, Chuanyi; Wang, Xin; Yang, Liping; Published by: The Astrophysical Journal Published on: 06/2021 YEAR: 2021 DOI: 10.3847/1538-4357/abec6c Parker Data Used; Solar wind; interplanetary turbulence; 1534; 830; Astrophysics - Solar and Stellar Astrophysics; Physics - Plasma Physics; Physics - Space Physics |
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Flux Ropes, Turbulence, and Collisionless Perpendicular Shock Waves: High Plasma Beta Case With the onset of solar maximum and the expected increased prevalence of interplanetary shock waves, Parker Solar Probe is likely to observe numerous shocks in the next few years. An outstanding question that has received surprisingly little attention has been how turbulence interacts with collisionless shock waves. Turbulence in the supersonic solar wind is described frequently as a superposition of a majority 2D and a minority slab component. We formulate a collisional perpendicular shock-turbulence transmission problem in ... Zank, G.; Nakanotani, M.; Zhao, L.; Du, S.; Adhikari, L.; Che, H.; le Roux, J.; Published by: The Astrophysical Journal Published on: 06/2021 YEAR: 2021 DOI: 10.3847/1538-4357/abf7c8 Interplanetary shocks; interplanetary turbulence; 829; 830; Parker Data Used |
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The first radial alignment between Parker Solar Probe and Solar Orbiter spacecraft is used to investigate the evolution of solar wind turbulence in the inner heliosphere. Assuming ballistic propagation, two 1.5 hr intervals are tentatively identified as providing measurements of the same plasma parcels traveling from 0.1 to 1 au. Using magnetic field measurements from both spacecraft, the properties of turbulence in the two intervals are assessed. Magnetic spectral density, flatness, and high-order moment scaling laws are ca ... Telloni, Daniele; Sorriso-Valvo, Luca; Woodham, Lloyd; Panasenco, Olga; Velli, Marco; Carbone, Francesco; Zank, Gary; Bruno, Roberto; Perrone, Denise; Nakanotani, Masaru; Shi, Chen; Amicis, Raffaella; De Marco, Rossana; Jagarlamudi, Vamsee; Steinvall, Konrad; Marino, Raffaele; Adhikari, Laxman; Zhao, Lingling; Liang, Haoming; Tenerani, Anna; Laker, Ronan; Horbury, Timothy; Bale, Stuart; Pulupa, Marc; Malaspina, David; MacDowall, Robert; Goetz, Keith; de Wit, Thierry; Harvey, Peter; Kasper, Justin; Korreck, Kelly; Larson, Davin; Case, Anthony; Stevens, Michael; Whittlesey, Phyllis; Livi, Roberto; Owen, Christopher; Livi, Stefano; Louarn, Philippe; Antonucci, Ester; Romoli, Marco; Brien, Helen; Evans, Vincent; Angelini, Virginia; Published by: The Astrophysical Journal Published on: 05/2021 YEAR: 2021 DOI: 10.3847/2041-8213/abf7d1 Parker Data Used; Magnetohydrodynamics; Alfven waves; Space plasmas; interplanetary turbulence; Solar wind; 1964; 23; 1544; 830; 1534 |
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The Parker Solar Probe (PSP) routinely observes magnetic field deflections in the solar wind at distances less than 0.3 au from the Sun. These deflections are related to structures commonly called "switchbacks" (SBs), whose origins and characteristic properties are currently debated. Here, we use a database of visually selected SB intervals—and regions of solar wind plasma measured just before and after each SB—to examine plasma parameters, turbulent spectra from inertial to dissipation scales, and intermittency ... Martinovic, Mihailo; Klein, Kristopher; Huang, Jia; Chandran, Benjamin; Kasper, Justin; Lichko, Emily; Bowen, Trevor; Chen, Christopher; Matteini, Lorenzo; Stevens, Michael; Case, Anthony; Bale, Stuart; Published by: The Astrophysical Journal Published on: 05/2021 YEAR: 2021 DOI: 10.3847/1538-4357/abebe5 Parker Data Used; Space plasmas; interplanetary turbulence; Solar wind; 1544; 830; 1534; Astrophysics - Solar and Stellar Astrophysics; Physics - Space Physics |
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Subproton-scale Intermittency in Near-Sun Solar Wind Turbulence Observed by the Parker Solar Probe High time-resolution solar wind magnetic field data are employed to study statistics describing intermittency near the first perihelion (∼35.6 R⊙) of the Parker Solar Probe mission. A merged data set employing two instruments on the FIELDS suite enables broadband estimation of higher-order moments of magnetic field increments, with five orders established with reliable accuracy. The duration, cadence, and low noise level of the data permit evaluation of scale dependence of the observed intermittency from the i ... Chhiber, Rohit; Matthaeus, William; Bowen, Trevor; Bale, Stuart; Published by: The Astrophysical Journal Published on: 04/2021 YEAR: 2021 DOI: 10.3847/2041-8213/abf04e Parker Data Used; Solar wind; interplanetary turbulence; Magnetohydrodynamics; Space plasmas; 1534; 830; 1964; 1544; Physics - Space Physics; Astrophysics - Solar and Stellar Astrophysics; Physics - Geophysics; Physics - Plasma Physics |
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Identification of Active Magnetic Reconnection Using Magnetic Flux Transport in Plasma Turbulence Magnetic reconnection has been suggested to play an important role in the dynamics and energetics of plasma turbulence by spacecraft observations, simulations, and theory over the past two decades, and recently, by magnetosheath observations of MMS. A new method based on magnetic flux transport (MFT) has been developed to identify reconnection activity in turbulent plasmas. This method is applied to a gyrokinetic simulation of two-dimensional (2D) plasma turbulence. Results on the identification of three active reconnection ... Li, Tak; Liu, Yi-Hsin; Qi, Yi; Published by: The Astrophysical Journal Published on: 03/2021 YEAR: 2021 DOI: 10.3847/2041-8213/abea0b Solar magnetic reconnection; Space plasmas; interplanetary turbulence; 1504; 1544; 830 |
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The scaling of the turbulent spectra provides a key measurement that allows us to discriminate between different theoretical predictions of turbulence. In the solar wind, this has driven a large number of studies dedicated to this issue using in situ data from various orbiting spacecraft. While a semblance of consensus exists regarding the scaling in the magnetohydrodynamic (MHD) and dispersive ranges, the precise scaling in the transition range and the actual physical mechanisms that control it remain open questions. Using ... Huang, S; Sahraoui, F.; Andrés, N.; Hadid, L.; Yuan, Z.; He, J.; Zhao, J.; Galtier, S.; Zhang, J.; Deng, X.; Jiang, K.; Yu, L.; Xu, S.; Xiong, Q; Wei, Y; de Wit, Dudok; Bale, S.; Kasper, J.; Published by: The Astrophysical Journal Published on: 03/2021 YEAR: 2021 DOI: 10.3847/2041-8213/abdaaf Parker Data Used; Solar wind; interplanetary turbulence; Solar coronal heating; 1534; 830; 1989; Physics - Space Physics; Astrophysics - Solar and Stellar Astrophysics |
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Harmonic Radio Emission in Randomly Inhomogeneous Plasma In the present paper, we describe a theoretical model of the generation of harmonic emissions of type III solar radio bursts. The goal of our study is to fully take into account the most efficient physical processes involved in the generation of harmonic electromagnetic emission via nonlinear coupling of Langmuir waves in randomly inhomogeneous plasma of solar wind ( $l+l^\prime \to t$ ). We revisit the conventional mechanism of coalescence of primarily generated and back-scattered Langmuir waves in quasihomogeneous plasma. ... Tkachenko, Anna; Krasnoselskikh, Vladimir; Voshchepynets, Andrii; Published by: The Astrophysical Journal Published on: 02/2021 YEAR: 2021 DOI: 10.3847/1538-4357/abd2bd Parker Data Used; Solar wind; interplanetary turbulence; Solar Coronal Waves; 1534; 830; 1995; Physics - Plasma Physics; Astrophysics - Solar and Stellar Astrophysics; Physics - Space Physics |
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The random walk of magnetic field lines is an important ingredient in understanding how the connectivity of the magnetic field affects the spatial transport and diffusion of charged particles. As solar energetic particles propagate away from near-solar sources, they interact with the fluctuating magnetic field, which modifies their distributions. We develop a formalism in which the differential equation describing the field line random walk contains both effects due to localized magnetic displacements and a non-stochastic co ... Chhiber, Rohit; Ruffolo, David; Matthaeus, William; Usmanov, Arcadi; Tooprakai, Paisan; Chuychai, Piyanate; Goldstein, Melvyn; Published by: The Astrophysical Journal Published on: 02/2021 YEAR: 2021 DOI: 10.3847/1538-4357/abd7f0 Parker Data Used; Solar energetic particles; interplanetary turbulence; interplanetary magnetic fields; Solar wind; 1491; 830; 824; 1534; Physics - Space Physics; Astrophysics - Solar and Stellar Astrophysics; Physics - Plasma Physics |
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Three-dimensional Simulations of the Inhomogeneous Low Solar Wind Magyar, N.; Nakariakov, V.~M.; Published by: \apj Published on: 01/2021 YEAR: 2021 DOI: 10.3847/1538-4357/abd02f Fast solar wind; interplanetary turbulence; Magnetohydrodynamical simulations; Solar Coronal Waves; 1872; 830; 1966; 1995; Astrophysics - Solar and Stellar Astrophysics |
| 2020 |
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Magnetohydrodynamic Turbulent Evolution of a Magnetic Cloud in the Outer Heliosphere Telloni, Daniele; Zhao, Lingling; Zank, Gary; Liang, Haoming; Nakanotani, Masaru; Adhikari, Laxman; Carbone, Francesco; Amicis, Raffaella; Perrone, Denise; Bruno, Roberto; Dasso, Sergio; Published by: \apjl Published on: 12/2020 YEAR: 2020 DOI: 10.3847/2041-8213/abcb03 Parker Data Used; Magnetohydrodynamics; interplanetary turbulence; Solar coronal mass ejections; interplanetary magnetic fields; Heliosphere; Solar wind; Solar magnetic reconnection; 1964; 830; 310; 824; 711; 1534; 1504 |
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Energy Supply for Heating the Slow Solar Wind Observed by Parker Solar Probe between 0.17 and 0.7 au Energy supply sources for the heating process in the slow solar wind remain unknown. The Parker Solar Probe (PSP) mission provides a good opportunity to study this issue. Recently, PSP observations have found that the slow solar wind experiences stronger heating inside 0.24 au. Here for the first time we measure in the slow solar wind the radial gradient of the low-frequency breaks on the magnetic trace power spectra and evaluate the associated energy supply rate. We find that the energy supply rate is consistent with the ob ... Wu, Honghong; Tu, Chuanyi; Wang, Xin; He, Jiansen; Yang, Liping; Published by: The Astrophysical Journal Published on: 11/2020 YEAR: 2020 DOI: 10.3847/2041-8213/abc5b6 Parker Data Used; Slow solar wind; interplanetary turbulence; Solar coronal heating |
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On the Scaling Properties of Magnetic-field Fluctuations through the Inner Heliosphere Although the interplanetary magnetic-field variability has been extensively investigated in situ using data from several space missions, newly launched missions providing high-resolution measures and approaching the Sun offer the possibility to study the multiscale variability in the innermost\ solar\ system. Here, using\ Parker\ Solar\ Probe\ measurements, we investigate the scaling properties of\ solar\ wind magnetic-field fluctuations at different heliocentric distances. The resu ... Alberti, Tommaso; Laurenza, Monica; Consolini, Giuseppe; Milillo, Anna; Marcucci, Maria; Carbone, Vincenzo; Bale, Stuart; Published by: The Astrophysical Journal Published on: 10/2020 YEAR: 2020 DOI: 10.3847/1538-4357/abb3d2 Chaos; interplanetary magnetic fields; interplanetary turbulence; Parker Data Used; parker solar probe; Solar Probe Plus; Solar wind; Time series analysis |
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The Origin of Switchbacks in the Solar Corona: Linear Theory The origin, structure, and propagation characteristics of a switchback are compelling questions posed by Parker Solar Probe (PSP) observations of velocity spikes and magnetic field reversals. By assuming interchange reconnection between coronal loop and open magnetic field, we show that this results in the generation of upward (into the heliosphere) and downward complex structures propagating at the fast magnetosonic speed (i.e., the Alfvén speed in the low plasma beta corona) that can have an arbitrary radial magnetic fiel ... Zank, G.; Nakanotani, M.; Zhao, L.-L.; Adhikari, L.; Kasper, J.; Published by: The Astrophysical Journal Published on: 10/2020 YEAR: 2020 DOI: 10.3847/1538-4357/abb828 Parker Data Used; Active Solar Corona; Solar Coronal Waves; interplanetary turbulence |
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Zank, G.~P.; Nakanotani, M.; Zhao, L.; Adhikari, L.; Telloni, D.; Published by: \apj Published on: 09/2020 YEAR: 2020 DOI: 10.3847/1538-4357/abad30 |
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Turbulence, a ubiquitous phenomenon in interplanetary space, is crucial for the energy conversion of space plasma at multiple scales. This work focuses on the propagation, polarization, and wave composition properties of the\ solar\ wind turbulence within 0.3 au, and its variation with heliocentric distance at magnetohydrodynamic scales (from 10 s to 1000 s in the spacecraft frame). We present the probability density function of propagation wavevectors (PDF (k(parallel to),k)) for\ solar\ wind turbulen ... Zhu, Xingyu; He, Jiansen; Verscharen, Daniel; Duan, Die; Bale, Stuart; Published by: The Astrophysical Journal Published on: 09/2020 YEAR: 2020 DOI: 10.3847/2041-8213/abb23e Alfv\ en waves; Heliosphere; interplanetary turbulence; Parker Data Used; parker solar probe; Slow solar wind; Solar Probe Plus |
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Cross Helicity of the 2018 November Magnetic Cloud Observed by the Parker Solar Probe Magnetic clouds are large-scale transient structures in the solar wind with low plasma-beta, low-amplitude magnetic field fluctuations, and twisted field lines with both ends often connected to the Sun. Their inertial-range turbulent properties have not been examined in detail. In this Letter, we analyze the normalized cross helicity, sigma(c), and residual energy, sigma(r), of plasma fluctuations in the 2018 November magnetic cloud observed at 0.25.au by the Parker Solar Probe. A low value of |sigma(c)| was present in th ... Good, S.; Kilpua, E.; Ala-Lahti, M.; Osmane, A.; Bale, S.; Zhao, L.-L.; Published by: The Astrophysical Journal Published on: 09/2020 YEAR: 2020 DOI: 10.3847/2041-8213/abb021 interplanetary magnetic fields; interplanetary turbulence; Parker Data Used; parker solar probe; Solar coronal mass ejections; Solar Probe Plus; Solar wind |
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Spectral Features in Field-aligned Solar Wind Turbulence from Parker Solar Probe Observations Parker Solar Probe (PSP) observed a large variety of Alfv\ enic fluctuations in the fast and slow solar wind flow during its two perihelia. The properties of Alfv\ enic solar wind turbulence have been studied for decades in the near-Earth environment. A spectral index of -5/3 or -2 for magnetic field fluctuations has been observed using spacecraft measurements, which can be explained by turbulence theories of nearly incompressible magnetohydrodynamics (NI MHD) or critical balance. In this study, a rigorous search of field ... Zhao, L.-L.; Zank, G.; Adhikari, L.; Nakanotani, M.; Telloni, D.; Carbone, F.; Published by: The Astrophysical Journal Published on: 08/2020 YEAR: 2020 DOI: 10.3847/1538-4357/ab9b7e interplanetary turbulence; Parker Data Used; parker solar probe; Solar Probe Plus; Solar wind; Spectral index |
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Small-scale Magnetic Flux Ropes in the First Two Parker Solar Probe Encounters Small-scale magnetic flux ropes (SFRs) are a type of structure in the solar wind that possess helical magnetic field lines. In a recent report we presented the radial variations of the properties of SFRs from 0.29 to 8 au using in situ measurements from the Helios, Advanced Composition Explorer/WIND (ACE/Wind), Ulysses, and Voyager spacecrafts. With the launch of the Parker Solar Probe (PSP), we extend our previous investigation further into the inner heliosphere. We apply a Grad–Shafranov-based algorithm to identify SFRs ... Chen, Yu; Hu, Qiang; Zhao, Lingling; Kasper, Justin; Bale, Stuart; Korreck, Kelly; Case, Anthony; Stevens, Michael; Bonnell, John; Goetz, Keith; Harvey, Peter; Klein, Kristopher; Larson, Davin; Livi, Roberto; MacDowall, Robert; Malaspina, David; Pulupa, Marc; Whittlesey, Phyllis; Published by: The Astrophysical Journal Published on: YEAR: 2020 DOI: 10.3847/1538-4357/abb820 Solar wind; interplanetary turbulence; Magnetohydrodynamics; Astronomy data analysis; Astronomy databases; Parker Data Used |
| 2019 |
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No Evidence for Critical Balance in Field-aligned Alfv\ enic Solar Wind Turbulence Telloni, Daniele; Carbone, Francesco; Bruno, Roberto; Sorriso-Valvo, Luca; Zank, Gary; Adhikari, Laxman; Hunana, Peter; Published by: \apj Published on: 12/2019 YEAR: 2019 DOI: 10.3847/1538-4357/ab517b Parker Data Used; interplanetary turbulence; Solar wind; Space plasmas; Alfven waves; Interplanetary medium; Magnetohydrodynamics; 830; 1534; 1544; 23; 825; 1964 |
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Ion Cyclotron Waves in Field-aligned Solar Wind Turbulence Telloni, Daniele; Carbone, Francesco; Bruno, Roberto; Zank, Gary; Sorriso-Valvo, Luca; Mancuso, Salvatore; Published by: \apjl Published on: 11/2019 YEAR: 2019 DOI: 10.3847/2041-8213/ab4c44 Parker Data Used; Magnetohydrodynamics; Space plasmas; Solar wind; interplanetary turbulence; Alfven waves; 1964; 1544; 1534; 830; 23 |
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The large-scale features of the solar wind are examined in order to predict small-scale features of turbulence in unexplored regions of the heliosphere. The strategy is to examine how system size, or effective Reynolds number Re, varies, and then how this quantity influences observable statistical properties, including intermittency properties of solar wind turbulence. The expectation based on similar hydrodynamics scalings is that the kurtosis, of the small-scale magnetic field increments, will increase with increasing R ... Parashar, T.; Cuesta, M.; Matthaeus, W.; Published by: The Astrophysical Journal Published on: 10/2019 YEAR: 2019 DOI: 10.3847/2041-8213/ab4a82 Heliosphere; interplanetary turbulence; parker solar probe; Physics - Space Physics; Plasma astrophysics; Solar Probe Plus; Solar wind; Space plasmas |
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Single-spacecraft Identification of Flux Tubes and Current Sheets in the Solar Wind A novel technique is presented for describing and visualizing the local topology of the magnetic field using single-spacecraft data in the solar wind. The approach merges two established techniques: the Grad-Shafranov (GS) reconstruction method, which provides a plausible regional two-dimensional magnetic field surrounding the spacecraft trajectory, and the Partial Variance of Increments (PVI) technique that identifies coherent magnetic structures, such as current sheets. When applied to one month of Wind magnetic field d ... Pecora, Francesco; Greco, Antonella; Hu, Qiang; Servidio, Sergio; Chasapis, Alexandros; Matthaeus, William; Published by: The Astrophysical Journal Published on: 08/2019 YEAR: 2019 DOI: 10.3847/2041-8213/ab32d9 interplanetary turbulence; magnetic fields; parker solar probe; Solar Probe Plus; Solar wind |
| 2018 |
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Solar wind turbulence within high-speed streams is reviewed from the point of view of embedded single nonlinear Alfv\ en wave cycles, discontinuities, magnetic decreases (MDs), and shocks. For comparison and guidance, cometary plasma turbulence is also briefly reviewed. It is demonstrated that cometary nonlinear magnetosonic waves phase-steepen, with a right-hand circular polarized foreshortened front and an elongated, compressive trailing edge. The former part is a form of "wave breaking" and the latter that of "period d ... Tsurutani, Bruce; Lakhina, Gurbax; Sen, Abhijit; Hellinger, Petr; Glassmeier, Karl-Heinz; Mannucci, Anthony; Published by: Journal of Geophysical Research: Space Physics Published on: 01/2018 YEAR: 2018 DOI: 10.1002/jgra.v123.410.1002/2017JA024203 Alfv\ en waves; discontinuities; interplanetary turbulence; magnetic decreases; parker solar probe; period doubling; Solar Probe Plus; wave phase-steepening |
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