1
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Grošelj D, Hakobyan H, Beloborodov AM, Sironi L, Philippov A. Radiative Particle-in-Cell Simulations of Turbulent Comptonization in Magnetized Black-Hole Coronae. PHYSICAL REVIEW LETTERS 2024; 132:085202. [PMID: 38457737 DOI: 10.1103/physrevlett.132.085202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/26/2023] [Revised: 09/30/2023] [Accepted: 01/24/2024] [Indexed: 03/10/2024]
Abstract
We report results from the first radiative particle-in-cell simulations of strong Alfvénic turbulence in plasmas of moderate optical depth. The simulations are performed in a local 3D periodic box and self-consistently follow the evolution of radiation as it interacts with a turbulent electron-positron plasma via Compton scattering. We focus on the conditions expected in magnetized coronae of accreting black holes and obtain an emission spectrum consistent with the observed hard state of Cyg X-1. Most of the turbulence power is transferred directly to the photons via bulk Comptonization, shaping the peak of the emission around 100 keV. The rest is released into nonthermal particles, which generate the MeV spectral tail. The method presented here shows promising potential for ab initio modeling of various astrophysical sources and opens a window into a new regime of kinetic plasma turbulence.
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Affiliation(s)
- Daniel Grošelj
- Centre for mathematical Plasma Astrophysics, Department of Mathematics, KU Leuven, B-3001 Leuven, Belgium
- Department of Astronomy and Columbia Astrophysics Laboratory, Columbia University, New York, New York 10027, USA
| | - Hayk Hakobyan
- Computational Sciences Department, Princeton Plasma Physics Laboratory, Princeton, New Jersey 08540, USA
- Department of Physics and Columbia Astrophysics Laboratory, Columbia University, New York, New York 10027, USA
| | - Andrei M Beloborodov
- Department of Physics and Columbia Astrophysics Laboratory, Columbia University, New York, New York 10027, USA
- Max Planck Institute for Astrophysics, D-85741 Garching, Germany
| | - Lorenzo Sironi
- Department of Astronomy and Columbia Astrophysics Laboratory, Columbia University, New York, New York 10027, USA
| | - Alexander Philippov
- Department of Physics, University of Maryland, College Park, Maryland 20742, USA
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2
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Li TC, Liu YH, Qi Y, Zhou M. Extended Magnetic Reconnection in Kinetic Plasma Turbulence. PHYSICAL REVIEW LETTERS 2023; 131:085201. [PMID: 37683145 DOI: 10.1103/physrevlett.131.085201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/06/2022] [Revised: 06/02/2023] [Accepted: 07/18/2023] [Indexed: 09/10/2023]
Abstract
Magnetic reconnection and plasma turbulence are ubiquitous processes important for laboratory, space, and astrophysical plasmas. Reconnection has been suggested to play an important role in the energetics and dynamics of turbulence by observations, simulations, and theory for two decades. The fundamental properties of reconnection at kinetic scales, essential to understanding the general problem of reconnection in magnetized turbulence, remain largely unknown at present. Here, we present an application of the magnetic flux transport method that can accurately identify reconnection in turbulence to a three-dimensional simulation. Contrary to ideas that reconnection in turbulence would be patchy and unpredictable, highly extended reconnection X lines, on the same order of magnitude as the system size, form at kinetic scales. Extended X lines develop through bidirectional reconnection spreading. They satisfy critical balance characteristic of turbulence, which predicts the X-line extent at a given scale. These results present a picture of fundamentally extended reconnection in kinetic-scale turbulence.
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Affiliation(s)
- Tak Chu Li
- Department of Physics and Astronomy, Dartmouth College, Hanover, New Hampshire 03755, USA
| | - Yi-Hsin Liu
- Department of Physics and Astronomy, Dartmouth College, Hanover, New Hampshire 03755, USA
| | - Yi Qi
- Laboratory for Atmospheric and Space Physics, University of Colorado Boulder, Boulder, Colorado 80303, USA
| | - Muni Zhou
- School of Natural Sciences, Institute for Advanced Study, Princeton, New Jersey 08544, USA
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3
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Lemoine M. First-Principles Fermi Acceleration in Magnetized Turbulence. PHYSICAL REVIEW LETTERS 2022; 129:215101. [PMID: 36461966 DOI: 10.1103/physrevlett.129.215101] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/08/2022] [Revised: 09/02/2022] [Accepted: 09/29/2022] [Indexed: 06/17/2023]
Abstract
This Letter provides a concrete implementation of Fermi's model of particle acceleration in magnetohydrodynamic (MHD) turbulence, connecting the rate of energization to the gradients of the velocity of magnetic field lines, which it characterizes within a multifractal picture of turbulence intermittency. It then derives a transport equation in momentum space for the distribution function. This description is shown to be substantiated by a large-scale numerical simulation of strong MHD turbulence. The present general framework can be used to model particle acceleration in a variety of environments.
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Affiliation(s)
- Martin Lemoine
- Institut d'Astrophysique de Paris, CNRS-Sorbonne Université, 98 bis boulevard Arago, F-75014 Paris, France
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4
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Adhikari S, Parashar TN, Shay MA, Matthaeus WH, Pyakurel PS, Fordin S, Stawarz JE, Eastwood JP. Energy transfer in reconnection and turbulence. Phys Rev E 2022; 104:065206. [PMID: 35030942 DOI: 10.1103/physreve.104.065206] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/03/2021] [Accepted: 12/03/2021] [Indexed: 11/07/2022]
Abstract
Reconnection and turbulence are two of the most commonly observed dynamical processes in plasmas, but their relationship is still not fully understood. Using 2.5D kinetic particle-in-cell simulations of both strong turbulence and reconnection, we compare the cross-scale transfer of energy in the two systems by analyzing the generalization of the von Kármán Howarth equations for Hall magnetohydrodynamics, a formulation that subsumes the third-order law for steady energy transfer rates. Even though the large scale features are quite different, the finding is that the decomposition of the energy transfer is structurally very similar in the two cases. In the reconnection case, the time evolution of the energy transfer also exhibits a correlation with the reconnection rate. These results provide explicit evidence that reconnection dynamics fundamentally involves turbulence-like energy transfer.
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Affiliation(s)
- S Adhikari
- Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716, USA
| | - T N Parashar
- Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716, USA.,School of Chemical and Physical Sciences, Victoria University of Wellington, Wellington 6012, New Zealand
| | - M A Shay
- Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716, USA.,Bartol Research Institute, Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716, USA
| | - W H Matthaeus
- Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716, USA.,Bartol Research Institute, Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716, USA
| | - P S Pyakurel
- Space Sciences Laboratory, University of California, Berkeley, Berkeley, California 94720, USA
| | - S Fordin
- Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716, USA
| | - J E Stawarz
- Department of Physics, Imperial College London, SW7 2AZ, United Kingdom
| | - J P Eastwood
- Department of Physics, Imperial College London, SW7 2AZ, United Kingdom
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5
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Pyakurel PS, Shay MA, Drake JF, Phan TD, Cassak PA, Verniero JL. Faster Form of Electron Magnetic Reconnection with a Finite Length X-Line. PHYSICAL REVIEW LETTERS 2021; 127:155101. [PMID: 34677989 DOI: 10.1103/physrevlett.127.155101] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/30/2021] [Accepted: 09/13/2021] [Indexed: 06/13/2023]
Abstract
Observations in Earth's turbulent magnetosheath downstream of a quasiparallel bow shock reveal a prevalence of electron-scale current sheets favorable for electron-only reconnection where ions are not coupled to the reconnecting magnetic fields. In small-scale turbulence, magnetic structures associated with intense current sheets are limited in all dimensions. And since the coupling of ions are constrained by a minimum length scale, the dynamics of electron reconnection is likely to be 3D. Here, both 2D and 3D kinetic particle-in-cell simulations are used to investigate electron-only reconnection, focusing on the reconnection rate and associated electron flows. A new form of 3D electron-only reconnection spontaneously develops where the magnetic X-line is localized in the out-of-plane (z) direction. The consequence is an enhancement of the reconnection rate compared with two dimensions, which results from differential mass flux out of the diffusion region along z, enabling a faster inflow velocity and thus a larger reconnection rate. This outflow along z is due to the magnetic tension force in z just as the conventional exhaust tension force, allowing particles to leave the diffusion region efficiently along z unlike the 2D configuration.
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Affiliation(s)
- P S Pyakurel
- Space Sciences Laboratory, University of California, Berkeley, California 94720, USA
| | - M A Shay
- University of Delaware, Newark, Delaware 19716, USA
| | - J F Drake
- Department of Physics and the Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
| | - T D Phan
- Space Sciences Laboratory, University of California, Berkeley, California 94720, USA
| | - P A Cassak
- Department of Physics and Astronomy and Center for KINETIC Plasma Physics, West Virginia University, Morgantown, West Virginia 26506, USA
| | - J L Verniero
- Space Sciences Laboratory, University of California, Berkeley, California 94720, USA
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6
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Ni L, Ji H, Murphy NA, Jara-Almonte J. Magnetic reconnection in partially ionized plasmas. Proc Math Phys Eng Sci 2020; 476:20190867. [PMID: 32398944 DOI: 10.1098/rspa.2019.0867] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2019] [Accepted: 03/11/2020] [Indexed: 11/12/2022] Open
Abstract
Magnetic reconnection has been intensively studied in fully ionized plasmas. However, plasmas are often partially ionized in astrophysical environments. The interactions between the neutral particles and ionized plasmas might strongly affect the reconnection mechanisms. We review magnetic reconnection in partially ionized plasmas in different environments from theoretical, numerical, observational and experimental points of view. We focus on mechanisms which make magnetic reconnection fast enough to compare with observations, especially on the reconnection events in the low solar atmosphere. The heating mechanisms and the related observational evidence of the reconnection process in the partially ionized low solar atmosphere are also discussed. We describe magnetic reconnection in weakly ionized astrophysical environments, including the interstellar medium and protostellar discs. We present recent achievements about fast reconnection in laboratory experiments for partially ionized plasmas.
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Affiliation(s)
- Lei Ni
- Yunnan Observatories, Chinese Academy of Sciences, PO Box 110, Kunming, Yunnan 650216, People's Republic of China.,Center for Astronomical Mega-Science, Chinese Academy of Sciences, 20A Datun Road, Chaoyang District, Beijing 100012, People's Republic of China
| | - Hantao Ji
- Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544, USA.,Princeton Plasma Physics Laboratory, Princeton, NJ 08543, USA
| | - Nicholas A Murphy
- Center for Astrophysics
- Harvard and Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA
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7
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Jafari A, Vishniac E, Vaikundaraman V. Statistical analysis of stochastic magnetic fields. Phys Rev E 2020; 101:022122. [PMID: 32168717 DOI: 10.1103/physreve.101.022122] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/06/2019] [Accepted: 01/28/2020] [Indexed: 11/07/2022]
Abstract
Previous work has introduced scale-split energy density ψ_{l,L}(x,t)=1/2B_{l}·B_{L} for vector field B(x,t) coarse grained at scales l and L, in order to quantify the field stochasticity or spatial complexity. In this formalism, the L_{p} norms S_{p}(t)=1/2||1-B[over ̂]_{l}·B[over ̂]_{L}||_{p}, pth-order stochasticity level, and E_{p}(t)=1/2||B_{l}B_{L}||_{p}, pth order mean cross energy density, are used to analyze the evolution of the stochastic field B(x,t). Application to turbulent magnetic fields leads to the prediction that turbulence in general tends to tangle an initially smooth magnetic field increasing the magnetic stochasticity level, ∂_{t}S_{p}>0. An increasing magnetic stochasticity in turn leads to disalignments of the coarse-grained fields B_{d} at smaller scales, d≪L, thus they average to weaker fields B_{L} at larger scales upon coarse graining, i.e., ∂_{t}E_{p}<0. Magnetic field resists the tangling effect of the turbulence by means of magnetic tension force. This can lead at some point to a sudden slippage between the field and fluid, decreasing the stochasticity ∂_{t}S_{p}<0 and increasing the energy ∂_{t}E_{p}>0 by aligning small-scale fields B_{d}. Thus the maxima (minima) of magnetic stochasticity are expected to approximately coincide with the minima (maxima) of cross energy density, occurrence of which corresponds to slippage of the magnetic field through the fluid. In this formalism, magnetic reconnection and field-fluid slippage both correspond to T_{p}=∂_{t}S_{p}=0and∂_{t}T_{2}<0. Previous work has also linked field-fluid slippage to magnetic reconnection invoking totally different approaches. In this paper, (a) we test these theoretical predictions numerically using a homogeneous, incompressible magnetohydrodynamic (MHD) simulation. Apart from expected small-scale deviations, possibly due to, e.g., intermittency and strong field annihilation, the theoretically predicted global relationship between stochasticity and cross energy is observed in different subvolumes of the simulation box. This indicate ubiquitous local field-fluid slippage and reconnection events in MHD turbulence. In addition, (b) we show that the conditions T_{p}=∂_{t}S_{p}=0and∂_{t}T_{p}<0 lead to sudden increases in kinetic stochasticity level, i.e., τ_{p}=∂_{t}s_{p}(t)>0 with s_{p}(t)=1/2||1-u[over ̂]_{l}.u[over ̂]_{L}||_{p}, which may correspond to fluid jets spontaneously driven by sudden field-fluid slippage-magnetic reconnection. Otherwise, they may correspond only to field-fluid slippage without energy dissipation. This picture, therefore, suggests defining reconnection as field-fluid slippage (changes in S_{p}) accompanied with magnetic energy dissipation (changes in E_{p}). All in all, these provide a statistical approach to the reconnection in terms of the time evolution of magnetic and kinetic stochasticities, S_{p} and s_{p}, their time derivatives, T_{p}=∂_{t}S_{p}, τ_{p}=∂_{t}s_{p}, and corresponding cross energies, E_{p}, e_{p}(t)=1/2||u_{l}u_{L}||_{p}. Furthermore, (c) we introduce the scale-split magnetic helicity based on which we discuss the energy or stochasticity relaxation of turbulent magnetic fields-a generalized Taylor relaxation. Finally, (d) we construct and numerically test a toy model, which resembles a classical version of quantum mean field Ising model for magnetized fluids, in order to illustrate how turbulent energy can affect magnetic stochasticity in the weak field regime.
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Affiliation(s)
- Amir Jafari
- Department of Physics & Astronomy, Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Ethan Vishniac
- Department of Physics & Astronomy, Johns Hopkins University, Baltimore, Maryland 21218, USA
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8
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Jafari A, Vishniac E, Vaikundaraman V. Magnetic stochasticity and diffusion. Phys Rev E 2019; 100:043205. [PMID: 31770890 DOI: 10.1103/physreve.100.043205] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/09/2019] [Indexed: 11/07/2022]
Abstract
We develop a quantitative relationship between magnetic diffusion and the level of randomness, or stochasticity, of the diffusing magnetic field in a magnetized medium. A general mathematical formulation of magnetic stochasticity in turbulence has been developed in previous work in terms of the L_{p} norm S_{p}(t)=1/2∥1-B[over ̂]_{l}·B[over ̂]_{L}∥_{p}, pth-order magnetic stochasticity of the stochastic field B(x,t), based on the coarse-grained fields B_{l} and B_{L} at different scales l≠L. For laminar flows, the stochasticity level becomes the level of field self-entanglement or spatial complexity. In this paper, we establish a connection between magnetic stochasticity S_{p}(t) and magnetic diffusion in magnetohydrodynamic (MHD) turbulence and use a homogeneous, incompressible MHD simulation to test this prediction. Our results agree with the well-known fact that magnetic diffusion in turbulent media follows the superlinear Richardson dispersion scheme. This is intimately related to stochastic magnetic reconnection in which superlinear Richardson diffusion broadens the matter outflow width and accelerates the reconnection process.
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Affiliation(s)
- Amir Jafari
- Department of Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Ethan Vishniac
- Department of Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Vignesh Vaikundaraman
- Department of Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21218, USA
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9
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Jafari A, Vishniac E. Topology and stochasticity of turbulent magnetic fields. Phys Rev E 2019; 100:013201. [PMID: 31499931 DOI: 10.1103/physreve.100.013201] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/07/2019] [Indexed: 11/07/2022]
Abstract
We present a mathematical formalism for the topology and stochasticity of vector fields based on renormalization group methodology. The concept of a scale-split energy density, ψ_{l,L}=B_{l}·B_{L}/2 for vector field B(x,t) renormalized at scales l and L, is introduced in order to quantify the notion of the field topological deformation, topology change, and stochasticity level. In particular, for magnetic fields, it is shown that the evolution of the field topology is directly related to the field-fluid slippage, which has already been linked to magnetic reconnection in previous work. The magnitude and direction of stochastic magnetic fields, shown to be governed, respectively, by the parallel and vertical components of the renormalized induction equation with respect to the magnetic field, can be studied separately by dividing ψ_{l,L} into two (3+1)-dimensional scalar fields. The velocity field can be approached in a similar way. Magnetic reconnection can then be defined in terms of the extrema of the L_{p} norms of these scalar fields. This formulation in fact clarifies different definitions of magnetic reconnection, which vaguely rely on the magnetic field topology, stochasticity, and energy conversion. Our results support the well-founded yet partly overlooked picture in which magnetic reconnection in turbulent fluids occurs on a wide range of scales as a result of nonlinearities at large scales (turbulence inertial range) and nonidealities at small scales (dissipative range). Lagrangian particle trajectories, as well as magnetic field lines, are stochastic in turbulent magnetized media in the limit of small resistivity and viscosity. The magnetic field tends to reduce its stochasticity induced by the turbulent flow by slipping through the fluid, which may accelerate fluid particles. This suggests that reconnection is a relaxation process by which the magnetic field lowers both its topological entanglements induced by turbulence and its energy level.
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Affiliation(s)
- Amir Jafari
- Department of Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Ethan Vishniac
- Department of Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21218, USA
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10
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Kuzzay D, Alexandrova O, Matteini L. Local approach to the study of energy transfers in incompressible magnetohydrodynamic turbulence. Phys Rev E 2019; 99:053202. [PMID: 31212494 DOI: 10.1103/physreve.99.053202] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2018] [Indexed: 11/07/2022]
Abstract
We present a local approach to the study of scale-to-scale energy transfers in magnetohydrodynamic (MHD) turbulence. This approach is based on performing local averages of the physical fields, which amounts to filtering scales smaller than some parameter ℓ. A key step in this work is the derivation of a local Kármán-Howarth-Monin relation which provides a local form of Politano and Pouquet's 4/3 law, without any assumption of homogeneity or isotropy. Our approach is exact and nonrandom, and we show its connection to the usual statistical results of turbulence. Its implementation on data obtained via a three-dimensional direct numerical simulation of the forced incompressible MHD equations from the John Hopkins turbulence database constitutes the main part of our study. First, we show that the local Kármán-Howarth-Monin relation holds well. The space statistics of local cross-scale transfers are studied next, their means and standard deviations being maximum at inertial scales and their probability density functions (PDFs) displaying very wide tails. Events constituting the tails of the PDFs are shown to form structures of strong transfers, either positive or negative, which can be observed over the whole available range of scales. As ℓ is decreased, these structures become more and more localized in space while contributing to an increasing fraction of the mean energy cascade rate. Finally, we highlight their quasi-one-dimensional (filamentlike) or quasi-two-dimensional (sheetlike or ribbonlike) nature and show that they appear in areas of strong vorticity or electric current density.
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Affiliation(s)
- Denis Kuzzay
- LESIA, Observatoire de Paris, Université PSL, CNRS, Sorbonne Université, Université Paris Diderot, Sorbonne Paris Cité, 5 Place Jules Janssen, 92195 Meudon, France
| | - Olga Alexandrova
- LESIA, Observatoire de Paris, Université PSL, CNRS, Sorbonne Université, Université Paris Diderot, Sorbonne Paris Cité, 5 Place Jules Janssen, 92195 Meudon, France
| | - Lorenzo Matteini
- LESIA, Observatoire de Paris, Université PSL, CNRS, Sorbonne Université, Université Paris Diderot, Sorbonne Paris Cité, 5 Place Jules Janssen, 92195 Meudon, France
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11
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Abstract
The origin and maintenance of coherent magnetic fields in the Universe is reviewed with an emphasis on the possible challenges that arise in their theoretical understanding. We begin with the interesting possibility that magnetic fields originated at some level from the early universe. This could be during inflation, the electroweak, or the quark-hadron phase transitions. These mechanisms can give rise to fields which could be strong, but often with much smaller coherence scales than galactic scales. Their subsequent turbulent decay decreases their strength but increases their coherence. We then turn to astrophysical batteries which can generate seed magnetic fields. Here the coherence scale can be large, but the field strength is generally very small. These seed fields need to be further amplified and maintained by a dynamo to explain observed magnetic fields in galaxies. Basic ideas behind both small and large-scale turbulent dynamos are outlined. The small-scale dynamo may help to understand the first magnetization of young galaxies, while the large-scale dynamo is important for the generation of fields with scales larger than the stirring scale, as observed in nearby disk galaxies. The current theoretical challenges that turbulent dynamos encounter and their possible resolution are discussed.
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12
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Bian X, Aluie H. Decoupled Cascades of Kinetic and Magnetic Energy in Magnetohydrodynamic Turbulence. PHYSICAL REVIEW LETTERS 2019; 122:135101. [PMID: 31012636 DOI: 10.1103/physrevlett.122.135101] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/10/2018] [Revised: 01/08/2019] [Indexed: 06/09/2023]
Abstract
Magnetic energy (ME) and kinetic energy (KE) in ideal incompressible magnetohydrodynamics are not global invariants and, therefore, it has been justified to discuss only the cascade of their sum total energy. We provide a physical argument based on scale locality, along with compelling evidence that ME and KE budgets statistically decouple beyond a transitional "conversion" range. This arises because magnetic field-line stretching is a large-scale process which vanishes on average at intermediate and small scales within the inertial-inductive range, thereby allowing each of the mean ME and KE to cascade conservatively and at an equal rate, yielding a turbulent magnetic Prandtl number of unity over these scales.
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Affiliation(s)
- Xin Bian
- Department of Mechanical Engineering, University of Rochester, Rochester, New York 14627, USA
| | - Hussein Aluie
- Department of Mechanical Engineering, University of Rochester, Rochester, New York 14627, USA
- Laboratory for Laser Energetics, University of Rochester, Rochester, New York 14627, USA
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13
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Ma ZW, Chen T, Zhang HW, Yu MY. Effective Resistivity in Collisionless Magnetic Reconnection. Sci Rep 2018; 8:10521. [PMID: 30002502 PMCID: PMC6043628 DOI: 10.1038/s41598-018-28851-7] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2018] [Accepted: 06/21/2018] [Indexed: 11/09/2022] Open
Abstract
An effective resistivity relevant to collisionless magnetic reconnection (MR) in plasma is presented. It is based on the argument that pitch angle scattering of electrons in the small electron diffusion region around the X line can lead to an effective, resistivity in collisionless plasma. The effective resistivity so obtained is in the form of a power law of the local plasma and magnetic field parameters. Its validity is confirmed by direct collisionless particle-in-cell (PIC) simulation. The result agrees very well with the resistivity (obtained from available data) of a large number of environments susceptible to MR: from the intergalactic and interstellar to solar and terrestrial to laboratory fusion plasmas. The scaling law can readily be incorporated into existing collisional magnetohydrodynamic simulation codes to investigate collisionless MR, as well as serve as a guide to ab initio theoretical investigations of the collisionless MR process.
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Affiliation(s)
- Z W Ma
- Institute for Fusion Theory and Simulation, Department of Physics, Zhejiang University, Hangzhou, 310027, China.
| | - T Chen
- Institute for Fusion Theory and Simulation, Department of Physics, Zhejiang University, Hangzhou, 310027, China
| | - H W Zhang
- Institute for Fusion Theory and Simulation, Department of Physics, Zhejiang University, Hangzhou, 310027, China
| | - M Y Yu
- Institute for Fusion Theory and Simulation, Department of Physics, Zhejiang University, Hangzhou, 310027, China
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14
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15
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Zhdankin V, Werner GR, Uzdensky DA, Begelman MC. Kinetic Turbulence in Relativistic Plasma: From Thermal Bath to Nonthermal Continuum. PHYSICAL REVIEW LETTERS 2017; 118:055103. [PMID: 28211730 DOI: 10.1103/physrevlett.118.055103] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/14/2016] [Indexed: 06/06/2023]
Abstract
We present results from particle-in-cell simulations of driven turbulence in magnetized, collisionless, and relativistic pair plasmas. We find that the fluctuations are consistent with the classical k_{⊥}^{-5/3} magnetic energy spectrum at fluid scales and a steeper k_{⊥}^{-4} spectrum at sub-Larmor scales, where k_{⊥} is the wave vector perpendicular to the mean field. We demonstrate the development of a nonthermal, power-law particle energy distribution f(E)∼E^{-α}, with an index α that decreases with increasing magnetization and increases with an increasing system size (relative to the characteristic Larmor radius). Our simulations indicate that turbulence can be a viable source of energetic particles in high-energy astrophysical systems, such as pulsar wind nebulae, if scalings asymptotically become insensitive to the system size.
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Affiliation(s)
- Vladimir Zhdankin
- JILA, University of Colorado and NIST, 440 UCB, Boulder, Colorado 80309, USA
| | - Gregory R Werner
- Center for Integrated Plasma Studies, Physics Department, University of Colorado, 390 UCB, Boulder, Colorado 80309, USA
| | - Dmitri A Uzdensky
- Center for Integrated Plasma Studies, Physics Department, University of Colorado, 390 UCB, Boulder, Colorado 80309, USA
- Institute for Advanced Study, Princeton, New Jersey 08540, USA
| | - Mitchell C Begelman
- JILA, University of Colorado and NIST, 440 UCB, Boulder, Colorado 80309, USA
- Department of Astrophysical and Planetary Sciences, 391 UCB, Boulder, Colorado 80309, USA
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16
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Zweibel EG, Yamada M. Perspectives on magnetic reconnection. Proc Math Phys Eng Sci 2016; 472:20160479. [PMID: 28119547 PMCID: PMC5247523 DOI: 10.1098/rspa.2016.0479] [Citation(s) in RCA: 54] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/14/2016] [Accepted: 10/31/2016] [Indexed: 11/12/2022] Open
Abstract
Magnetic reconnection is a topological rearrangement of magnetic field that occurs on time scales much faster than the global magnetic diffusion time. Since the field lines break on microscopic scales but energy is stored and the field is driven on macroscopic scales, reconnection is an inherently multi-scale process that often involves both magnetohydrodynamic (MHD) and kinetic phenomena. In this article, we begin with the MHD point of view and then describe the dynamics and energetics of reconnection using a two-fluid formulation. We also focus on the respective roles of global and local processes and how they are coupled. We conclude that the triggers for reconnection are mostly global, that the key energy conversion and dissipation processes are either local or global, and that the presence of a continuum of scales coupled from microscopic to macroscopic may be the most likely path to fast reconnection.
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Affiliation(s)
- Ellen G Zweibel
- Departments of Astronomy and Physics, University of Wisconsin-Madison, Madison, WI, USA; Princeton Plasma Physics Laboratory, Princeton University, Princeton, NJ, USA
| | - Masaaki Yamada
- Departments of Astronomy and Physics, University of Wisconsin-Madison, Madison, WI, USA; Princeton Plasma Physics Laboratory, Princeton University, Princeton, NJ, USA
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Servidio S, Haynes CT, Matthaeus WH, Burgess D, Carbone V, Veltri P. Explosive Particle Dispersion in Plasma Turbulence. PHYSICAL REVIEW LETTERS 2016; 117:095101. [PMID: 27610862 DOI: 10.1103/physrevlett.117.095101] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/05/2016] [Indexed: 06/06/2023]
Abstract
Particle dynamics are investigated in plasma turbulence, using self-consistent kinetic simulations, in two dimensions. In the steady state, the trajectories of single protons and proton pairs are studied, at different values of plasma β (ratio between kinetic and magnetic pressure). For single-particle displacements, results are consistent with fluids and magnetic field line dynamics, where particles undergo normal diffusion for very long times, with higher β's being more diffusive. In an intermediate time range, with separations lying in the inertial range, particles experience an explosive dispersion in time, consistent with the Richardson prediction. These results, obtained for the first time with a self-consistent kinetic model, are relevant for astrophysical and laboratory plasmas, where turbulence is crucial for heating, mixing, and acceleration processes.
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Affiliation(s)
- S Servidio
- Dipartimento di Fisica, Università della Calabria, I-87036 Cosenza, Italy
| | - C T Haynes
- School of Physics and Astronomy, Queen Mary University of London, Mile End Road, London E1 4NS, United Kingdom
| | - W H Matthaeus
- Bartol Research Institute and Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716, USA
| | - D Burgess
- School of Physics and Astronomy, Queen Mary University of London, Mile End Road, London E1 4NS, United Kingdom
| | - V Carbone
- Dipartimento di Fisica, Università della Calabria, I-87036 Cosenza, Italy
| | - P Veltri
- Dipartimento di Fisica, Università della Calabria, I-87036 Cosenza, Italy
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Subramanian K. The origin, evolution and signatures of primordial magnetic fields. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2016; 79:076901. [PMID: 27243368 DOI: 10.1088/0034-4885/79/7/076901] [Citation(s) in RCA: 43] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
The universe is magnetized on all scales probed so far. On the largest scales, galaxies and galaxy clusters host magnetic fields at the micro Gauss level coherent on scales up to ten kpc. Recent observational evidence suggests that even the intergalactic medium in voids could host a weak ∼ 10(-16) Gauss magnetic field, coherent on Mpc scales. An intriguing possibility is that these observed magnetic fields are a relic from the early universe, albeit one which has been subsequently amplified and maintained by a dynamo in collapsed objects. We review here the origin, evolution and signatures of primordial magnetic fields. After a brief summary of magnetohydrodynamics in the expanding universe, we turn to magnetic field generation during inflation and phase transitions. We trace the linear and nonlinear evolution of the generated primordial fields through the radiation era, including viscous effects. Sensitive observational signatures of primordial magnetic fields on the cosmic microwave background, including current constraints from Planck, are discussed. After recombination, primordial magnetic fields could strongly influence structure formation, especially on dwarf galaxy scales. The resulting signatures on reionization, the redshifted 21 cm line, weak lensing and the Lyman-α forest are outlined. Constraints from radio and γ-ray astronomy are summarized. Astrophysical batteries and the role of dynamos in reshaping the primordial field are briefly considered. The review ends with some final thoughts on primordial magnetic fields.
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Wu JH, Jia Q. The heterogeneous energy landscape expression of KWW relaxation. Sci Rep 2016; 6:20506. [PMID: 26879824 PMCID: PMC4754662 DOI: 10.1038/srep20506] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/01/2015] [Accepted: 01/05/2016] [Indexed: 11/09/2022] Open
Abstract
Here we show a heterogeneous energy landscape approach to describing the Kohlrausch-Williams-Watts (KWW) relaxation function. For a homogeneous dynamic process, the distribution of free energy landscape is first proposed, revealing the significance of rugged fluctuations. In view of the heterogeneous relaxation given in two dynamic phases and the transmission coefficient in a rate process, we obtain a general characteristic relaxation time distribution equation for the KWW function in a closed, analytic form. Analyses of numerical computation show excellent accuracy, both in time and frequency domains, in the convergent performance of the heterogeneous energy landscape expression and shunning the catastrophic truncations reported in the previous work. The stretched exponential β, closely associated to temperature and apparent correlation with one dynamic phase, reveals a threshold value of 1/2 defining different behavior of the probability density functions. Our work may contribute, for example, to in-depth comprehension of the dynamic mechanism of glass transition, which cannot be provided by existing approaches.
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Affiliation(s)
- J H Wu
- Peter Grünberg Research Center, Nanjing University of Posts and Telecommunications, Nanjing 210003, China.,Research Institute of Engineering and Technology, Korea University, Seoul 136-713, South Korea.,School of Life Sciences, Shandong University, Jinan 250100, China
| | - Q Jia
- Department of Management, Hohai University, Nanjing 211100, China
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Kanov K, Burns R, Lalescu C, Eyink G. The Johns Hopkins Turbulence Databases: An Open Simulation Laboratory for Turbulence Research. Comput Sci Eng 2015. [DOI: 10.1109/mcse.2015.103] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
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22
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Lazarian A, Eyink G, Vishniac E, Kowal G. Turbulent reconnection and its implications. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2015; 373:20140144. [PMID: 25848076 PMCID: PMC4394676 DOI: 10.1098/rsta.2014.0144] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 02/11/2015] [Indexed: 06/01/2023]
Abstract
Magnetic reconnection is a process of magnetic field topology change, which is one of the most fundamental processes happening in magnetized plasmas. In most astrophysical environments, the Reynolds numbers corresponding to plasma flows are large and therefore the transition to turbulence is inevitable. This turbulence, which can be pre-existing or driven by magnetic reconnection itself, must be taken into account for any theory of magnetic reconnection that attempts to describe the process in the aforementioned environments. This necessity is obvious as three-dimensional high-resolution numerical simulations show the transition to the turbulence state of initially laminar reconnecting magnetic fields. We discuss ideas of how turbulence can modify reconnection with the focus on the Lazarian & Vishniac (Lazarian & Vishniac 1999 Astrophys. J. 517, 700-718 (doi:10.1086/307233)) reconnection model. We present numerical evidence supporting the model and demonstrate that it is closely connected to the experimentally proven concept of Richardson dispersion/diffusion as well as to more recent advances in understanding of the Lagrangian dynamics of magnetized fluids. We point out that the generalized Ohm's law that accounts for turbulent motion predicts the subdominance of the microphysical plasma effects for reconnection for realistically turbulent media. We show that one of the most dramatic consequences of turbulence is the violation of the generally accepted notion of magnetic flux freezing. This notion is a cornerstone of most theories dealing with magnetized plasmas, and therefore its change induces fundamental shifts in accepted paradigms, for instance, turbulent reconnection entails reconnection diffusion process that is essential for understanding star formation. We argue that at sufficiently high Reynolds numbers the process of tearing reconnection should transfer to turbulent reconnection. We discuss flares that are predicted by turbulent reconnection and relate this process to solar flares and γ-ray bursts. With reference to experiments, we analyse solar observations in situ as measurements in the solar wind or heliospheric current sheet and show the correspondence of data with turbulent reconnection predictions. Finally, we discuss first-order Fermi acceleration of particles that is a natural consequence of the turbulent reconnection.
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Affiliation(s)
- A Lazarian
- Department of Astronomy, University of Wisconsin, 475 North Charter Street, Madison, WI 53706, USA
| | - G Eyink
- Department of Applied Mathematics and Statistics, The Johns Hopkins University, Baltimore, MD 21218, USA
| | - E Vishniac
- Department of Physics and Astronomy, McMaster University, 1280 Main Street West, Hamilton, Ontario, Canada L8S 4M1
| | - G Kowal
- Escola de Artes, Ciências e Humanidades, Universidade de São Paulo, Av. Arlindo Béttio, 1000-Ermelino Matarazzo, CEP 03828-000, São Paulo, Brazil
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Benveniste D, Drivas TD. Asymptotic results for backwards two-particle dispersion in a turbulent flow. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:041003. [PMID: 24827179 DOI: 10.1103/physreve.89.041003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/06/2014] [Indexed: 06/03/2023]
Abstract
We derive an exact equation governing two-particle backwards mean-squared dispersion for both deterministic and stochastic tracer particles in turbulent flows. For the deterministic trajectories, we probe the consequences of our formula for short times and arrive at approximate expressions for the mean-squared dispersion which involve second order structure functions of the velocity and acceleration fields. For the stochastic trajectories, we analytically compute an exact t3 contribution to the squared separation of stochastic paths. We argue that this contribution appears also for deterministic paths at long times and present direct numerical simulation results for incompressible Navier-Stokes flows to support this claim. We also numerically compute the probability distribution of particle separations for the deterministic paths and the stochastic paths and show their strong self-similar nature.
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Affiliation(s)
- Damien Benveniste
- Department of Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Theodore D Drivas
- Department of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore, Maryland 21218, USA
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