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Richard L, Sorriso-Valvo L, Yordanova E, Graham DB, Khotyaintsev YV. Turbulence in Magnetic Reconnection Jets from Injection to Sub-Ion Scales. PHYSICAL REVIEW LETTERS 2024; 132:105201. [PMID: 38518330 DOI: 10.1103/physrevlett.132.105201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/16/2023] [Revised: 10/02/2023] [Accepted: 02/05/2024] [Indexed: 03/24/2024]
Abstract
We investigate turbulence in magnetic reconnection jets in the Earth's magnetotail using data from the Magnetospheric Multiscale spacecraft. We show that signatures of a limited inertial range are observed in many reconnection jets. The observed turbulence develops on the timescale of a few ion gyroperiods, resulting in intermittent multifractal energy cascade from the characteristic scale of the jet down to the ion scales. We show that at sub-ion scales, the fluctuations are close to monofractal and predominantly kinetic Alfvén waves. The observed energy transfer rate across the inertial range is ∼10^{8} J kg^{-1} s^{-1}, which is the largest reported for space plasmas so far.
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Affiliation(s)
- Louis Richard
- Swedish Institute of Space Physics, Uppsala 751 21, Sweden and Department of Physics and Astronomy, Space and Plasma Physics, Uppsala University, Uppsala 751 20, Sweden
| | - Luca Sorriso-Valvo
- CNR/ISTP-Istituto per la Scienza e la Tecnologia dei Plasmi, 70126 Bari, Italy; Space and Plasma Physics, School of Electrical Engineering and Computer Science, KTH Royal Institute of Technology, Stockholm 114 28, Sweden; and Swedish Institute of Space Physics, Uppsala 751 21, Sweden
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2
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Manzini D, Sahraoui F, Califano F, Ferrand R. Local energy transfer and dissipation in incompressible Hall magnetohydrodynamic turbulence: The coarse-graining approach. Phys Rev E 2022; 106:035202. [PMID: 36266803 DOI: 10.1103/physreve.106.035202] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/27/2022] [Accepted: 07/27/2022] [Indexed: 06/16/2023]
Abstract
We derive the coarse-graining (CG) equations of incompressible Hall magnetohydrodynamic (HMHD) turbulence to investigate the local (in space) energy transfer rate as a function of the filtering scale ℓ. First, the CG equations are space averaged to obtain the analytical expression of the mean cascade rate. Its application to three-dimensional simulations of (weakly compressible) HMHD shows a cascade rate consistent with the value of the mean dissipation rate in the simulations and with the classical estimates based on the "third-order" law. Furthermore, we developed an anisotropic version of CG that allows us to study the magnitude of the cascade rate along different directions with respect to the mean magnetic field. Its implementation on the numerical data with moderate background magnetic field shows a weaker cascade along the magnetic field than in the perpendicular plane, while an isotropic cascade is recovered in the absence of a background field. The strength of the CG approach is further revealed when considering the local-in-space energy transfer, which is shown theoretically and numerically to match at a given position x, when locally averaged over a neighboring region, the (quasi-)local dissipation. Prospects of exploiting this model to investigate local dissipation in spacecraft data are discussed.
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Affiliation(s)
- D Manzini
- Laboratoire de Physique des Plasmas (LPP), CNRS, École Polytechnique, Sorbonne Université, Université Paris-Saclay, Observatoire de Paris, 91120 Palaiseau, France
- Dipartimento di Fisica E. Fermi, University of Pisa, 56127 Pisa, Italy
| | - F Sahraoui
- Laboratoire de Physique des Plasmas (LPP), CNRS, École Polytechnique, Sorbonne Université, Université Paris-Saclay, Observatoire de Paris, 91120 Palaiseau, France
| | - F Califano
- Dipartimento di Fisica E. Fermi, University of Pisa, 56127 Pisa, Italy
| | - R Ferrand
- Laboratoire de Physique des Plasmas (LPP), CNRS, École Polytechnique, Sorbonne Université, Université Paris-Saclay, Observatoire de Paris, 91120 Palaiseau, France
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Simon P, Sahraoui F. Exact law for compressible pressure-anisotropic magnetohydrodynamic turbulence: Toward linking energy cascade and instabilities. Phys Rev E 2022; 105:055111. [PMID: 35706285 DOI: 10.1103/physreve.105.055111] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/02/2021] [Accepted: 05/04/2022] [Indexed: 06/15/2023]
Abstract
We derive an exact law for compressible pressure-anisotropic magnetohydrodynamic turbulence. For a gyrotropic pressure tensor, we study the double-adiabatic case and show the presence of new flux and source terms in the exact law, reminiscent of the plasma instability conditions due to pressure anisotropy. The Hall term is shown to bring ion-scale corrections to the exact law without affecting explicitly the pressure terms. In the pressure isotropy limit we recover all known results obtained for isothermal and polytropic closures. The incompressible limit of the gyrotropic system leads to a generalization of the Politano and Pouquet's law where a new incompressible source term is revealed and reflects exchanges of the magnetic and kinetic energies with the no-longer-conserved internal energy. We highlight the possibilities offered by the new laws to investigate potential links between turbulence cascade and instabilities widely observed in laboratory and astrophysical plasmas.
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Affiliation(s)
- P Simon
- Laboratoire de Physique des Plasmas (LPP), CNRS, Observatoire de Paris, Sorbonne Université, Université Paris-Saclay, École polytechnique, Institut Polytechnique de Paris, 91128 Palaiseau, France
| | - F Sahraoui
- Laboratoire de Physique des Plasmas (LPP), CNRS, Observatoire de Paris, Sorbonne Université, Université Paris-Saclay, École polytechnique, Institut Polytechnique de Paris, 91128 Palaiseau, France
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Parashar TN, Matthaeus WH. Observations of cross scale energy transfer in the inner heliosphere by Parker Solar Probe. REVIEWS OF MODERN PLASMA PHYSICS 2022; 6:41. [PMCID: PMC9684259 DOI: 10.1007/s41614-022-00097-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/03/2022] [Accepted: 10/02/2022] [Indexed: 11/27/2022]
Abstract
The solar wind, a continuous flow of plasma from the sun, not only shapes the near Earth space environment but also serves as a natural laboratory to study plasma turbulence in conditions that are not achievable in the lab. Starting with the Mariners, for more than five decades, multiple space missions have enabled in-depth studies of solar wind turbulence. Parker Solar Probe (PSP) was launched to explore the origins and evolution of the solar wind. With its state-of-the-art instrumentation and unprecedented close approaches to the sun, PSP is starting a new era of inner heliospheric exploration. In this review we discuss observations of turbulent energy flow across scales in the inner heliosphere as observed by PSP. After providing a quick theoretical overview and a quick recap of turbulence before PSP, we discuss in detail the observations of energy at various scales on its journey from the largest scales to the internal degrees of freedom of the plasma. We conclude with some open ended questions, many of which we hope that PSP will help answer.
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Affiliation(s)
- Tulasi N. Parashar
- grid.267827.e0000 0001 2292 3111School of Chemical and Physical Sciences, Victoria University of Wellington, Gate 7, Kelburn Parade, Kelburn, Wellington, 6012 New Zealand ,grid.33489.350000 0001 0454 4791Department of Physics and Astronomy, University of Delaware, Sharp Laboratory, Newark, Delaware 19711 USA
| | - William H. Matthaeus
- grid.33489.350000 0001 0454 4791Department of Physics and Astronomy, University of Delaware, Sharp Laboratory, Newark, Delaware 19711 USA
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Compressible Turbulence in the Interstellar Medium: New Insights from a High-resolution Supersonic Turbulence Simulation. ACTA ACUST UNITED AC 2020. [DOI: 10.3847/1538-4357/abb76e] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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Morad AM, Maize SMA, Nowaya AA, Rammah YS. Stability Analysis of Magnetohydrodynamics Waves in Compressible Turbulent Plasma. JOURNAL OF NANOFLUIDS 2020. [DOI: 10.1166/jon.2020.1740] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
Abstract
Here, the solitary waves propagation in the cold plasma and their stability conditions are studied. The governing equations are expanded by using the reductive perturbation method with taken under the influence of the magnetic field under consideration. A new nonlinear wave equation
is obtained that reconciles the derivative nonlinear Schrdinger equation with a modified form. By considering the magnetic field is constant along the x-direction, the complete set of equations is obtained, and the stable solitary waves are observed. A compariso between the soliton
solutions of the modified nonlinear Schrdinger evolution equation (MNLS) and the solutions of the compressible magnetohydrodynamic (MHD) equations has been performed. It is shown that stable solitons can be created in such nonrelativistic fluids in the presence of the magnetic field. The modulation
instability for a one-dimensional MNLS equation is carried as well. The regions of stability and instability fo the present system are well determined.
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Affiliation(s)
- Adel M. Morad
- Department of Mathematics and Computer Science, Menoufia University, Shebin-El Koom, 32511, Egypt
| | - S. M. A. Maize
- Physics Department, Faculty of Science, Menoufia University, Shebin El Koom, 32511, Egypt
| | - A. A. Nowaya
- Physics Department, Faculty of Science, Menoufia University, Shebin El Koom, 32511, Egypt
| | - Y. S. Rammah
- Physics Department, Faculty of Science, Menoufia University, Shebin El Koom, 32511, Egypt
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Banerjee S, Andrés N. Scale-to-scale energy transfer rate in compressible two-fluid plasma turbulence. Phys Rev E 2020; 101:043212. [PMID: 32422726 DOI: 10.1103/physreve.101.043212] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/06/2019] [Accepted: 04/01/2020] [Indexed: 11/07/2022]
Abstract
We derive the exact relation for the energy transfer in three-dimensional compressible two-fluid plasma turbulence. In the long-time limit, we obtain an exact law which expresses the scale-to-scale average energy flux rate in terms of two point increments of the fluid variables of each species, electric and magnetic field and current density, and puts a strong constraint on the turbulent dynamics. The incompressible single fluid and two-fluid limits and the compressible single fluid limit are recovered under appropriate assumption. In the single fluid limits, analyses are done with and without neglecting the electron mass thereby making the exact relation suitable for a broader range of application. In the compressible two-fluid regime, the total energy flux rate, unlike the single fluid case, is found to be unaltered by the presence of a background magnetic field. The exact relation provides a way to test whether a range of scales in a plasma is inertial or dissipative and is essential to understand the nonlinear nature of both space and dilute astrophysical plasmas.
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Affiliation(s)
- Supratik Banerjee
- Department of Physics, Indian Institute of Technology Kanpur, Kalyanpur 208016, Uttar Pradesh, India
| | - Nahuel Andrés
- Institute of Astronomy and Space Physics, Ciudad Universitaria, Buenos Aires 1428, Argentina and Physics Department, University of Buenos Aires, Ciudad Universitaria, Buenos Aires 1428, Argentina
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Andrés N, Sahraoui F, Galtier S, Hadid LZ, Ferrand R, Huang SY. Energy Cascade Rate Measured in a Collisionless Space Plasma with MMS Data and Compressible Hall Magnetohydrodynamic Turbulence Theory. PHYSICAL REVIEW LETTERS 2019; 123:245101. [PMID: 31922873 DOI: 10.1103/physrevlett.123.245101] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/09/2019] [Revised: 11/12/2019] [Indexed: 06/10/2023]
Abstract
The first complete estimation of the compressible energy cascade rate |ϵ_{C}| at magnetohydrodynamic (MHD) and subion scales is obtained in Earth's magnetosheath using Magnetospheric MultiScale spacecraft data and an exact law derived recently for compressible Hall MHD turbulence. A multispacecraft technique is used to compute the velocity and magnetic gradients, and then all the correlation functions involved in the exact relation. It is shown that when the density fluctuations are relatively small, |ϵ_{C}| identifies well with its incompressible analog |ϵ_{I}| at MHD scales but becomes much larger than |ϵ_{I}| at subion scales. For larger density fluctuations, |ϵ_{C}| is larger than |ϵ_{I}| at every scale with a value significantly higher than for smaller density fluctuations. Our study reveals also that for both small and large density fluctuations, the nonflux terms remain always negligible with respect to the flux terms and that the major contribution to |ϵ_{C}| at subion scales comes from the compressible Hall flux.
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Affiliation(s)
- N Andrés
- Laboratoire de Physique des Plasmas, École Polytechnique, CNRS, Sorbonne University, Observatoire de Paris, Univ. Paris-Sud, F-91128 Palaiseau Cedex, France
- Instituto de Astronomía y Física del Espacio, CONICET-UBA, Ciudad Universitaria, 1428, Buenos Aires, Argentina
- Departamento de Física, Facultad de Ciencias Exactas y Naturales, UBA, Ciudad Universitaria, 1428, Buenos Aires, Argentina
| | - F Sahraoui
- Laboratoire de Physique des Plasmas, École Polytechnique, CNRS, Sorbonne University, Observatoire de Paris, Univ. Paris-Sud, F-91128 Palaiseau Cedex, France
| | - S Galtier
- Laboratoire de Physique des Plasmas, École Polytechnique, CNRS, Sorbonne University, Observatoire de Paris, Univ. Paris-Sud, F-91128 Palaiseau Cedex, France
- Institut Universitaire de France (IUF), 2201 France
| | - L Z Hadid
- European Space Agency, ESTEC, 75231 Noordwijk, Netherlands
| | - R Ferrand
- Laboratoire de Physique des Plasmas, École Polytechnique, CNRS, Sorbonne University, Observatoire de Paris, Univ. Paris-Sud, F-91128 Palaiseau Cedex, France
| | - S Y Huang
- School of Electronic and Information, Wuhan University, 430072 Wuhan, China
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Banerjee S, Kritsuk AG. Energy transfer in compressible magnetohydrodynamic turbulence for isothermal self-gravitating fluids. Phys Rev E 2018; 97:023107. [PMID: 29548083 DOI: 10.1103/physreve.97.023107] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/03/2017] [Indexed: 06/08/2023]
Abstract
Three-dimensional, compressible, magnetohydrodynamic turbulence of an isothermal, self-gravitating fluid is analyzed using two-point statistics in the asymptotic limit of large Reynolds numbers (both kinetic and magnetic). Following an alternative formulation proposed by Banerjee and Galtier [Phys. Rev. E 93, 033120 (2016)2470-004510.1103/PhysRevE.93.033120; J. Phys. A: Math. Theor. 50, 015501 (2017)1751-811310.1088/1751-8113/50/1/015501], an exact relation has been derived for the total energy transfer. This approach results in a simpler relation expressed entirely in terms of mixed second-order structure functions. The kinetic, thermodynamic, magnetic, and gravitational contributions to the energy transfer rate can be easily separated in the present form. By construction, the new formalism includes such additional effects as global rotation, the Hall term in the induction equation, etc. The analysis shows that solid-body rotation cannot alter the energy flux rate of compressible turbulence. However, the contribution of a uniform background magnetic field to the flux is shown to be nontrivial unlike in the incompressible case. Finally, the compressible, turbulent energy flux rate does not vanish completely due to simple alignments, which leads to a zero turbulent energy flux rate in the incompressible case.
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Affiliation(s)
- Supratik Banerjee
- Universität zu Köln, Institut für Geophysik und Meteorologie, Pohligstrasse 3, 50969 Köln, Germany
| | - Alexei G Kritsuk
- University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093-0424, USA
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Andrés N, Galtier S, Sahraoui F. Exact law for homogeneous compressible Hall magnetohydrodynamics turbulence. Phys Rev E 2018; 97:013204. [PMID: 29448457 DOI: 10.1103/physreve.97.013204] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/28/2017] [Indexed: 06/08/2023]
Abstract
We derive an exact law for three-dimensional (3D) homogeneous compressible isothermal Hall magnetohydrodynamic turbulence, without the assumption of isotropy. The Hall current is shown to introduce new flux and source terms that act at the small scales (comparable or smaller than the ion skin depth) to significantly impact the turbulence dynamics. The law provides an accurate means to estimate the energy cascade rate over a broad range of scales covering the magnetohydrodynamic inertial range and the sub-ion dispersive range in 3D numerical simulations and in in situ spacecraft observations of compressible turbulence. This work is particularly relevant to astrophysical flows in which small-scale density fluctuations cannot be ignored such as the solar wind, planetary magnetospheres, and the interstellar medium.
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Affiliation(s)
- N Andrés
- LPP, CNRS, Ecole Polytechnique, UPMC Univ. Paris 06, Univ. Paris-Sud, Observatoire de Paris, Université Paris-Saclay, Sorbonne Universités, PSL Research University, F-91128 Palaiseau, France
| | - S Galtier
- LPP, CNRS, Ecole Polytechnique, UPMC Univ. Paris 06, Univ. Paris-Sud, Observatoire de Paris, Université Paris-Saclay, Sorbonne Universités, PSL Research University, F-91128 Palaiseau, France
- Département de Physique, Université Paris-Sud, Orsay, France
| | - F Sahraoui
- LPP, CNRS, Ecole Polytechnique, UPMC Univ. Paris 06, Univ. Paris-Sud, Observatoire de Paris, Université Paris-Saclay, Sorbonne Universités, PSL Research University, F-91128 Palaiseau, France
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