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Nayak I, Teixeira FL, Na DY, Kumar M, Omelchenko YA. Accelerating particle-in-cell kinetic plasma simulations via reduced-order modeling of space-charge dynamics using dynamic mode decomposition. Phys Rev E 2024; 109:065307. [PMID: 39020909 DOI: 10.1103/physreve.109.065307] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/28/2023] [Accepted: 04/30/2024] [Indexed: 07/20/2024]
Abstract
We present a data-driven reduced-order modeling of the space-charge dynamics for electromagnetic particle-in-cell (EMPIC) plasma simulations based on dynamic mode decomposition (DMD). The dynamics of the charged particles in kinetic plasma simulations such as EMPIC is manifested through the plasma current density defined along the edges of the spatial mesh. We showcase the efficacy of DMD in modeling the time evolution of current density through a low-dimensional feature space. Not only do such DMD-based predictive reduced-order models help accelerate EMPIC simulations, they also have the potential to facilitate investigative analysis and control applications. We demonstrate the proposed DMD-EMPIC scheme for reduced-order modeling of current density and speedup in EMPIC simulations involving electron beam under the influence of magnetic field, virtual cathode oscillations, and backward wave oscillator.
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Zhang LQ, Wang C, Baumjohann W, Wang RS, Wang JY, Burch JL, Khotyaintsev YV. First observation of fluid-like eddy-dominant bursty bulk flow turbulence in the Earth's tail plasma sheet. Sci Rep 2023; 13:19201. [PMID: 37932297 PMCID: PMC10628178 DOI: 10.1038/s41598-023-45867-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/19/2023] [Accepted: 10/25/2023] [Indexed: 11/08/2023] Open
Abstract
Turbulence is a ubiquitous phenomenon in neutral and conductive fluids. According to classical theory, turbulence is a rotating flow containing vortices of different scales. Eddies play a fundamental role in the nonlinear cascade of kinetic energy at different scales in turbulent flow. In conductive fluids, the Alfvénic/kinetic Alfvénic wave (AW/KAW) is the new "cell" of magnetohydrodynamic (MHD) turbulence (frozen-in condition). Wave energy, which has equal kinetic and magnetic energy, is redistributed among multiple-scale Fourier modes and transferred from the large MHD scale to the small kinetic scale through the collision of counter-propagating Alfvénic wave packages propagating along the magnetic field line. Fluid-like eddy-dominant plasma flow turbulence has never been found in space since the launch of the first satellite in 1957. In this paper, we report the first observation of eddy-dominant turbulence within magnetic reconnection-generated fast flow in the Earth's tail plasma sheet by the Magnetospheric Multiscale Spacecraft (MMS). In eddy-dominant turbulent reconnection jet, ions dominate the flow field while electrons dominate current and magnetic fluctuations. Our findings shed new light on the nonlinear kinetic and magnetic energy cascade in MHD turbulence.
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Affiliation(s)
- L Q Zhang
- State Key Laboratory of Space Weather, National Space Science Center, Chinese Academy of Sciences, Beijing, 100080, China
| | - Chi Wang
- State Key Laboratory of Space Weather, National Space Science Center, Chinese Academy of Sciences, Beijing, 100080, China.
| | - W Baumjohann
- Space Research Institute, Austrian Academy of Sciences, 8042, Graz, Austria
| | - R S Wang
- CAS KCAS Key Laboratory of Geospace Environment, Department of Geophysics and Planetary Science, University of Science and Technology of China, Hefei, 230026, China
| | - J Y Wang
- Information Engineering College, Central University for Nationalities, Beijing, 100081, China
| | - James L Burch
- Southwest Research Institute San Antonio, San Antonio, TX, 78238, USA
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Zhou M, Liu Z, Loureiro NF. Electron heating in kinetic-Alfvén-wave turbulence. Proc Natl Acad Sci U S A 2023; 120:e2220927120. [PMID: 37252951 PMCID: PMC10265953 DOI: 10.1073/pnas.2220927120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2022] [Accepted: 04/23/2023] [Indexed: 06/01/2023] Open
Abstract
We report analytical and numerical investigations of subion-scale turbulence in low-beta plasmas using a rigorous reduced kinetic model. We show that efficient electron heating occurs and is primarily due to Landau damping of kinetic Alfvén waves, as opposed to Ohmic dissipation. This collisionless damping is facilitated by the local weakening of advective nonlinearities and the ensuing unimpeded phase mixing near intermittent current sheets, where free energy concentrates. The linearly damped energy of electromagnetic fluctuations at each scale explains the steepening of their energy spectrum with respect to a fluid model where such damping is excluded (i.e., a model that imposes an isothermal electron closure). The use of a Hermite polynomial representation to express the velocity-space dependence of the electron distribution function enables us to obtain an analytical, lowest-order solution for the Hermite moments of the distribution, which is borne out by numerical simulations.
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Affiliation(s)
- Muni Zhou
- Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, MA02139
- Department of Astrophysical Sciences, Princeton University, Princeton, NJ08544
- School of Natural Science, Institute for Advanced Study, Princeton, NJ08544
| | - Zhuo Liu
- Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, MA02139
| | - Nuno F. Loureiro
- Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, MA02139
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Verscharen D, Klein KG, Maruca BA. The multi-scale nature of the solar wind. LIVING REVIEWS IN SOLAR PHYSICS 2019; 16:5. [PMID: 31929769 PMCID: PMC6934245 DOI: 10.1007/s41116-019-0021-0] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/09/2019] [Accepted: 11/09/2019] [Indexed: 05/29/2023]
Abstract
The solar wind is a magnetized plasma and as such exhibits collective plasma behavior associated with its characteristic spatial and temporal scales. The characteristic length scales include the size of the heliosphere, the collisional mean free paths of all species, their inertial lengths, their gyration radii, and their Debye lengths. The characteristic timescales include the expansion time, the collision times, and the periods associated with gyration, waves, and oscillations. We review the past and present research into the multi-scale nature of the solar wind based on in-situ spacecraft measurements and plasma theory. We emphasize that couplings of processes across scales are important for the global dynamics and thermodynamics of the solar wind. We describe methods to measure in-situ properties of particles and fields. We then discuss the role of expansion effects, non-equilibrium distribution functions, collisions, waves, turbulence, and kinetic microinstabilities for the multi-scale plasma evolution.
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Affiliation(s)
- Daniel Verscharen
- Mullard Space Science Laboratory, University College London, Dorking, RH5 6NT UK
- Space Science Center, University of New Hampshire, Durham, NH 03824 USA
| | - Kristopher G. Klein
- Lunar and Planetary Laboratory and Department of Planetary Sciences, University of Arizona, Tucson, AZ 85719 USA
| | - Bennett A. Maruca
- Bartol Research Institute, Department of Physics and Astronomy, University of Delaware, Newark, DE 19716 USA
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Camporeale E, Sorriso-Valvo L, Califano F, Retinò A. Coherent Structures and Spectral Energy Transfer in Turbulent Plasma: A Space-Filter Approach. PHYSICAL REVIEW LETTERS 2018; 120:125101. [PMID: 29694094 DOI: 10.1103/physrevlett.120.125101] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/02/2017] [Revised: 02/15/2018] [Indexed: 06/08/2023]
Abstract
Plasma turbulence at scales of the order of the ion inertial length is mediated by several mechanisms, including linear wave damping, magnetic reconnection, the formation and dissipation of thin current sheets, and stochastic heating. It is now understood that the presence of localized coherent structures enhances the dissipation channels and the kinetic features of the plasma. However, no formal way of quantifying the relationship between scale-to-scale energy transfer and the presence of spatial structures has been presented so far. In the Letter we quantify such a relationship analyzing the results of a two-dimensional high-resolution Hall magnetohydrodynamic simulation. In particular, we employ the technique of space filtering to derive a spectral energy flux term which defines, in any point of the computational domain, the signed flux of spectral energy across a given wave number. The characterization of coherent structures is performed by means of a traditional two-dimensional wavelet transformation. By studying the correlation between the spectral energy flux and the wavelet amplitude, we demonstrate the strong relationship between scale-to-scale transfer and coherent structures. Furthermore, by conditioning one quantity with respect to the other, we are able for the first time to quantify the inhomogeneity of the turbulence cascade induced by topological structures in the magnetic field. Taking into account the low space-filling factor of coherent structures (i.e., they cover a small portion of space), it emerges that 80% of the spectral energy transfer (both in the direct and inverse cascade directions) is localized in about 50% of space, and 50% of the energy transfer is localized in only 25% of space.
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Affiliation(s)
- E Camporeale
- Center for Mathematics and Computer Science (CWI), Amsterdam 1098 XG, The Netherlands
| | - L Sorriso-Valvo
- CNR-Nanotec-Unità di Cosenza, Ponte P. Bucci, cubo 31C, 87036 Rende, Italy
| | - F Califano
- Dipartimento di Fisica "E. Fermi," Università di Pisa, Largo B. Pontecorvo 3, I-56127 Pisa, Italy
| | - A Retinò
- Centre National de la Recherche Scientifique, LPP UMR 7648, Ecole Polytechnique, Universit Pierre et Marie Curie Paris VI, Observatoire de Paris, Route de Saclay Palaiseau 91128, France
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In Situ Observation of Intermittent Dissipation at Kinetic Scales in the Earth's Magnetosheath. ACTA ACUST UNITED AC 2018. [DOI: 10.3847/2041-8213/aaadf8] [Citation(s) in RCA: 42] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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Grošelj D, Mallet A, Loureiro NF, Jenko F. Fully Kinetic Simulation of 3D Kinetic Alfvén Turbulence. PHYSICAL REVIEW LETTERS 2018; 120:105101. [PMID: 29570310 DOI: 10.1103/physrevlett.120.105101] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/10/2017] [Revised: 01/25/2018] [Indexed: 06/08/2023]
Abstract
We present results from a three-dimensional particle-in-cell simulation of plasma turbulence, resembling the plasma conditions found at kinetic scales of the solar wind. The spectral properties of the turbulence in the subion range are consistent with theoretical expectations for kinetic Alfvén waves. Furthermore, we calculate the local anisotropy, defined by the relation k_{∥}(k_{⊥}), where k_{∥} is a characteristic wave number along the local mean magnetic field at perpendicular scale l_{⊥}∼1/k_{⊥}. The subion range anisotropy is scale dependent with k_{∥}<k_{⊥} and the ratio of linear to nonlinear time scales is of order unity, suggesting that the kinetic cascade is close to a state of critical balance. Our results compare favorably against a number of in situ solar wind observations and demonstrate-from first principles-the feasibility of plasma turbulence models based on a critically balanced cascade of kinetic Alfvén waves.
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Affiliation(s)
- Daniel Grošelj
- Max-Planck-Institut für Plasmaphysik, Boltzmannstraße 2, D-85748 Garching, Germany
| | - Alfred Mallet
- Space Science Center, University of New Hampshire, Durham, New Hampshire 03824, USA
| | - Nuno F Loureiro
- Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Frank Jenko
- Max-Planck-Institut für Plasmaphysik, Boltzmannstraße 2, D-85748 Garching, Germany
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Observational Evidence for Self-generation of Small-scale Magnetic Flux Ropes from Intermittent Solar Wind Turbulence. ACTA ACUST UNITED AC 2018. [DOI: 10.3847/2041-8213/aaa3d7] [Citation(s) in RCA: 54] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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Variability of the Magnetic Field Power Spectrum in the Solar Wind at Electron Scales. ACTA ACUST UNITED AC 2017. [DOI: 10.3847/1538-4357/aa93e5] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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Yang Y, Matthaeus WH, Parashar TN, Wu P, Wan M, Shi Y, Chen S, Roytershteyn V, Daughton W. Energy transfer channels and turbulence cascade in Vlasov-Maxwell turbulence. Phys Rev E 2017; 95:061201. [PMID: 28709288 DOI: 10.1103/physreve.95.061201] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/30/2017] [Indexed: 06/07/2023]
Abstract
Analysis of the Vlasov-Maxwell equations from the perspective of turbulence cascade clarifies the role of electromagnetic work, and reveals the importance of the pressure-strain relation in generating internal energy. Particle-in-cell simulation demonstrates the relative importance of the several energy exchange terms, indicating that the traceless pressure-strain interaction "Pi-D" is of particular importance for both electrons and protons. The Pi-D interaction and the second tensor invariants of the strain are highly localized in similar spatial regions, indicating that energy transfer occurs preferentially in coherent structures. The collisionless turbulence cascade may be fruitfully explored by study of these energy transfer channels, in addition to examining transfer across spatial scales.
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Affiliation(s)
- Yan Yang
- State Key Laboratory for Turbulence and Complex Systems, Center for Applied Physics and Technology, College of Engineering, Peking University, Beijing 100871, China
- Bartol Research Institute and Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716, USA
| | - W H Matthaeus
- Bartol Research Institute and Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716, USA
| | - T N Parashar
- Bartol Research Institute and Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716, USA
| | - P Wu
- Bartol Research Institute and Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716, USA
- School of Mathematics and Physics, Queen's University Belfast, BT7 1NN, United Kingdom
| | - M Wan
- Department of Mechanics and Aerospace Engineering, South University of Science and Technology of China, Shenzhen, Guangdong 518055, China
| | - Y Shi
- State Key Laboratory for Turbulence and Complex Systems, Center for Applied Physics and Technology, College of Engineering, Peking University, Beijing 100871, China
| | - S Chen
- State Key Laboratory for Turbulence and Complex Systems, Center for Applied Physics and Technology, College of Engineering, Peking University, Beijing 100871, China
- Department of Mechanics and Aerospace Engineering, South University of Science and Technology of China, Shenzhen, Guangdong 518055, China
| | | | - W Daughton
- Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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Navarro AB, Teaca B, Told D, Groselj D, Crandall P, Jenko F. Structure of Plasma Heating in Gyrokinetic Alfvénic Turbulence. PHYSICAL REVIEW LETTERS 2016; 117:245101. [PMID: 28009188 DOI: 10.1103/physrevlett.117.245101] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/25/2016] [Indexed: 06/06/2023]
Abstract
We analyze plasma heating in weakly collisional kinetic Alfvén wave turbulence using high resolution gyrokinetic simulations spanning the range of scales between the ion and the electron gyroradii. Real space structures that have a higher than average heating rate are shown not to be confined to current sheets. This novel result is at odds with previous studies, which use the electromagnetic work in the local electron fluid frame, i.e., J·(E+v_{e}×B), as a proxy for turbulent dissipation to argue that heating follows the intermittent spatial structure of the electric current. Furthermore, we show that electrons are dominated by parallel heating while the ions prefer the perpendicular heating route. We comment on the implications of the results presented here.
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Affiliation(s)
- Alejandro Bañón Navarro
- Department of Physics and Astronomy, UCLA, 475 Portola Plaza, Los Angeles, California 90095-1547, USA
| | - Bogdan Teaca
- Applied Mathematics Research Centre, Coventry University, Coventry CV1 5FB, United Kingdom
| | - Daniel Told
- Department of Physics and Astronomy, UCLA, 475 Portola Plaza, Los Angeles, California 90095-1547, USA
| | - Daniel Groselj
- Department of Physics and Astronomy, UCLA, 475 Portola Plaza, Los Angeles, California 90095-1547, USA
- Max-Planck-Institut für Plasmaphysik, Boltzmannstraße 2, D-85748 Garching, Germany
| | - Paul Crandall
- Department of Physics and Astronomy, UCLA, 475 Portola Plaza, Los Angeles, California 90095-1547, USA
| | - Frank Jenko
- Department of Physics and Astronomy, UCLA, 475 Portola Plaza, Los Angeles, California 90095-1547, USA
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Gekelman W, De Haas T, Daughton W, Van Compernolle B, Intrator T, Vincena S. Pulsating Magnetic Reconnection Driven by Three-Dimensional Flux-Rope Interactions. PHYSICAL REVIEW LETTERS 2016; 116:235101. [PMID: 27341240 DOI: 10.1103/physrevlett.116.235101] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/18/2015] [Indexed: 06/06/2023]
Abstract
The dynamics of magnetic reconnection is investigated in a laboratory experiment consisting of two magnetic flux ropes, with currents slightly above the threshold for the kink instability. The evolution features periodic bursts of magnetic reconnection. To diagnose this complex evolution, volumetric three-dimensional data were acquired for both the magnetic and electric fields, allowing key field-line mapping quantities to be directly evaluated for the first time with experimental data. The ropes interact by rotating about each other and periodically bouncing at the kink frequency. During each reconnection event, the formation of a quasiseparatrix layer (QSL) is observed in the magnetic field between the flux ropes. Furthermore, a clear correlation is demonstrated between the quasiseparatrix layer and enhanced values of the quasipotential computed by integrating the parallel electric field along magnetic field lines. These results provide clear evidence that field lines passing through the quasiseparatrix layer are undergoing reconnection and give a direct measure of the nonlinear reconnection rate. The measurements suggest that the parallel electric field within the QSL is supported predominantly by electron pressure; however, resistivity may play a role.
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Affiliation(s)
- W Gekelman
- Department of Physics, University of California, Los Angeles, Los Angeles, California 90095, USA
| | - T De Haas
- Department of Physics, University of California, Los Angeles, Los Angeles, California 90095, USA
| | - W Daughton
- Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - B Van Compernolle
- Department of Physics, University of California, Los Angeles, Los Angeles, California 90095, USA
| | - T Intrator
- Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - S Vincena
- Department of Physics, University of California, Los Angeles, Los Angeles, California 90095, USA
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Passot T, Sulem PL. A MODEL FOR THE NON-UNIVERSAL POWER LAW OF THE SOLAR WIND SUB-ION-SCALE MAGNETIC SPECTRUM. ACTA ACUST UNITED AC 2015. [DOI: 10.1088/2041-8205/812/2/l37] [Citation(s) in RCA: 41] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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