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Cassak PA, Barbhuiya MH, Liang H, Argall MR. Quantifying Energy Conversion in Higher-Order Phase Space Density Moments in Plasmas. PHYSICAL REVIEW LETTERS 2023; 130:085201. [PMID: 36898122 DOI: 10.1103/physrevlett.130.085201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/05/2022] [Revised: 01/09/2023] [Accepted: 01/24/2023] [Indexed: 06/18/2023]
Abstract
Weakly collisional and collisionless plasmas are typically far from local thermodynamic equilibrium (LTE), and understanding energy conversion in such systems is a forefront research problem. The standard approach is to investigate changes in internal (thermal) energy and density, but this omits energy conversion that changes any higher-order moments of the phase space density. In this Letter, we calculate from first principles the energy conversion associated with all higher moments of the phase space density for systems not in LTE. Particle-in-cell simulations of collisionless magnetic reconnection reveal that energy conversion associated with higher-order moments can be locally significant. The results may be useful in numerous plasma settings, such as reconnection, turbulence, shocks, and wave-particle interactions in heliospheric, planetary, and astrophysical plasmas.
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Affiliation(s)
- Paul A Cassak
- Department of Physics and Astronomy and the Center for KINETIC Plasma Physics, West Virginia University, Morgantown, West Virginia 26506, USA
| | - M Hasan Barbhuiya
- Department of Physics and Astronomy and the Center for KINETIC Plasma Physics, West Virginia University, Morgantown, West Virginia 26506, USA
| | - Haoming Liang
- Center for Space Plasma and Aeronomic Research, University of Alabama in Huntsville, Huntsville, Alabama 35899, USA
| | - Matthew R Argall
- Space Science Center, Institute for the Study of Earth, Oceans, and Space, University of New Hampshire, Durham, New Hampshire 03824, USA
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Liang H, Cassak PA, Swisdak M, Servidio S. Estimating Effective Collision Frequency and Kinetic Entropy Uncertainty in Particle-in-Cell Simulations. ACTA ACUST UNITED AC 2020. [DOI: 10.1088/1742-6596/1620/1/012009] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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3
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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: 13] [Impact Index Per Article: 2.6] [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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4
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Kawazura Y, Barnes M, Schekochihin AA. Thermal disequilibration of ions and electrons by collisionless plasma turbulence. Proc Natl Acad Sci U S A 2019; 116:771-776. [PMID: 30598448 PMCID: PMC6338852 DOI: 10.1073/pnas.1812491116] [Citation(s) in RCA: 66] [Impact Index Per Article: 13.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/04/2022] Open
Abstract
Does overall thermal equilibrium exist between ions and electrons in a weakly collisional, magnetized, turbulent plasma? And, if not, how is thermal energy partitioned between ions and electrons? This is a fundamental question in plasma physics, the answer to which is also crucial for predicting the properties of far-distant astronomical objects such as accretion disks around black holes. In the context of disks, this question was posed nearly two decades ago and has since generated a sizeable literature. Here we provide the answer for the case in which energy is injected into the plasma via Alfvénic turbulence: Collisionless turbulent heating typically acts to disequilibrate the ion and electron temperatures. Numerical simulations using a hybrid fluid-gyrokinetic model indicate that the ion-electron heating-rate ratio is an increasing function of the thermal-to-magnetic energy ratio, [Formula: see text]: It ranges from [Formula: see text] at [Formula: see text] to at least 30 for [Formula: see text] This energy partition is approximately insensitive to the ion-to-electron temperature ratio [Formula: see text] Thus, in the absence of other equilibrating mechanisms, a collisionless plasma system heated via Alfvénic turbulence will tend toward a nonequilibrium state in which one of the species is significantly hotter than the other, i.e., hotter ions at high [Formula: see text] and hotter electrons at low [Formula: see text] Spectra of electromagnetic fields and the ion distribution function in 5D phase space exhibit an interesting new magnetically dominated regime at high [Formula: see text] and a tendency for the ion heating to be mediated by nonlinear phase mixing ("entropy cascade") when [Formula: see text] and by linear phase mixing (Landau damping) when [Formula: see text].
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Affiliation(s)
- Yohei Kawazura
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3PU, United Kingdom;
| | - Michael Barnes
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3PU, United Kingdom
- Culham Centre for Fusion Energy, Culham Science Centre, Abingdon OX14 3DB, United Kingdom
| | - Alexander A Schekochihin
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3PU, United Kingdom
- Merton College, Oxford OX1 4JD, United Kingdom
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Servidio S, Chasapis A, Matthaeus WH, Perrone D, Valentini F, Parashar TN, Veltri P, Gershman D, Russell CT, Giles B, Fuselier SA, Phan TD, Burch J. Magnetospheric Multiscale Observation of Plasma Velocity-Space Cascade: Hermite Representation and Theory. PHYSICAL REVIEW LETTERS 2017; 119:205101. [PMID: 29219385 DOI: 10.1103/physrevlett.119.205101] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/12/2017] [Indexed: 06/07/2023]
Abstract
Plasma turbulence is investigated using unprecedented high-resolution ion velocity distribution measurements by the Magnetospheric Multiscale mission (MMS) in the Earth's magnetosheath. This novel observation of a highly structured particle distribution suggests a cascadelike process in velocity space. Complex velocity space structure is investigated using a three-dimensional Hermite transform, revealing, for the first time in observational data, a power-law distribution of moments. In analogy to hydrodynamics, a Kolmogorov approach leads directly to a range of predictions for this phase-space transport. The scaling theory is found to be in agreement with observations. The combined use of state-of-the-art MMS data sets, novel implementation of a Hermite transform method, and scaling theory of the velocity cascade opens new pathways to the understanding of plasma turbulence and the crucial velocity space features that lead to dissipation in plasmas.
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Affiliation(s)
- S Servidio
- Dipartimento di Fisica, Università della Calabria, I-87036 Cosenza, Italy
| | - A Chasapis
- 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
| | - D Perrone
- European Space Agency, ESAC, 28692 Madrid, Spain
| | - F Valentini
- Dipartimento di Fisica, Università della Calabria, I-87036 Cosenza, Italy
| | - T N Parashar
- Bartol Research Institute and Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716, USA
| | - P Veltri
- Dipartimento di Fisica, Università della Calabria, I-87036 Cosenza, Italy
| | - D Gershman
- NASA Goddard Space Flight Center, Greenbelt, Maryland 20771, USA
| | - C T Russell
- University of California at Los Angeles, Los Angeles, California 90095, USA
| | - B Giles
- NASA Goddard Space Flight Center, Greenbelt, Maryland 20771, USA
| | - S A Fuselier
- Southwest Research Institute, San Antonio, Texas 78238, USA
- University of Texas at San Antonio, San Antonio, Texas 78249, USA
| | - T D Phan
- University of California, Berkeley, California 94720, USA
| | - J Burch
- Southwest Research Institute, San Antonio, Texas 78238, USA
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7
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Kawamori E, Chen J, Lin C, Lee Z. Ring-averaged ion velocity distribution function probe for laboratory magnetized plasma experiment. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2017; 88:103507. [PMID: 29092513 DOI: 10.1063/1.4986589] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Ring-averaged velocity distribution function of ions at a fixed guiding center position is a fundamental quantity in the gyrokinetic plasma physics. We have developed a diagnostic tool for the ring averaged velocity distribution function of ions for laboratory plasma experiments, which is named as the ring-averaged ion distribution function probe (RIDFP). The RIDFP is a set of ion collectors for different velocities. It is designed to be immersed in magnetized plasmas and achieves momentum selection of incoming ions by the selection of the ion Larmor radii. To nullify the influence of the sheath potential surrounding the RIDFP on the orbits of the incoming ions, the electrostatic potential of the RIDFP body is automatically adjusted to coincide with the space potential of the target plasma with the use of an emissive probe and a voltage follower. The developed RIDFP successfully measured the equilibrium ring-averaged velocity distribution function of a laboratory magnetized plasma, which was in accordance with the Maxwellian distribution having an ion temperature of 0.2 eV.
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Affiliation(s)
- Eiichirou Kawamori
- Institute of Space and Plasma Sciences, National Cheng Kung University, Tainan 70101, Taiwan
| | - Jinting Chen
- Institute of Space and Plasma Sciences, National Cheng Kung University, Tainan 70101, Taiwan
| | - Chiahsuan Lin
- Institute of Space and Plasma Sciences, National Cheng Kung University, Tainan 70101, Taiwan
| | - Zongmau Lee
- Institute of Space and Plasma Sciences, National Cheng Kung University, Tainan 70101, Taiwan
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8
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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: 7] [Impact Index Per Article: 1.0] [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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9
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Howes GG. A prospectus on kinetic heliophysics. PHYSICS OF PLASMAS 2017; 24:055907. [PMID: 29104421 PMCID: PMC5648573 DOI: 10.1063/1.4983993] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/14/2017] [Accepted: 05/01/2017] [Indexed: 05/29/2023]
Abstract
Under the low density and high temperature conditions typical of heliospheric plasmas, the macroscopic evolution of the heliosphere is strongly affected by the kinetic plasma physics governing fundamental microphysical mechanisms. Kinetic turbulence, collisionless magnetic reconnection, particle acceleration, and kinetic instabilities are four poorly understood, grand-challenge problems that lie at the new frontier of kinetic heliophysics. The increasing availability of high cadence and high phase-space resolution measurements of particle velocity distributions by current and upcoming spacecraft missions and of massively parallel nonlinear kinetic simulations of weakly collisional heliospheric plasmas provides the opportunity to transform our understanding of these kinetic mechanisms through the full utilization of the information contained in the particle velocity distributions. Several major considerations for future investigations of kinetic heliophysics are examined. Turbulent dissipation followed by particle heating is highlighted as an inherently two-step process in weakly collisional plasmas, distinct from the more familiar case in fluid theory. Concerted efforts must be made to tackle the big-data challenge of visualizing the high-dimensional (3D-3V) phase space of kinetic plasma theory through physics-based reductions. Furthermore, the development of innovative analysis methods that utilize full velocity-space measurements, such as the field-particle correlation technique, will enable us to gain deeper insight into these four grand-challenge problems of kinetic heliophysics. A systems approach to tackle the multi-scale problem of heliophysics through a rigorous connection between the kinetic physics at microscales and the self-consistent evolution of the heliosphere at macroscales will propel the field of kinetic heliophysics into the future.
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Affiliation(s)
- Gregory G Howes
- Department of Physics and Astronomy, University of Iowa, Iowa City, Iowa 52242, USA
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10
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Waelbroeck FL. Models for Sub-Alfvénic Magnetodynamics of Fusion Plasmas. FUSION SCIENCE AND TECHNOLOGY 2017. [DOI: 10.13182/fst11-a11692] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Affiliation(s)
- F. L. Waelbroeck
- Institute for Fusion Studies, University of Texas, Austin, Texas 78712
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11
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Howes GG. A dynamical model of plasma turbulence in the solar wind. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2015; 373:20140145. [PMID: 25848075 PMCID: PMC4394677 DOI: 10.1098/rsta.2014.0145] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 02/05/2015] [Indexed: 06/01/2023]
Abstract
A dynamical approach, rather than the usual statistical approach, is taken to explore the physical mechanisms underlying the nonlinear transfer of energy, the damping of the turbulent fluctuations, and the development of coherent structures in kinetic plasma turbulence. It is argued that the linear and nonlinear dynamics of Alfvén waves are responsible, at a very fundamental level, for some of the key qualitative features of plasma turbulence that distinguish it from hydrodynamic turbulence, including the anisotropic cascade of energy and the development of current sheets at small scales. The first dynamical model of kinetic turbulence in the weakly collisional solar wind plasma that combines self-consistently the physics of Alfvén waves with the development of small-scale current sheets is presented and its physical implications are discussed. This model leads to a simplified perspective on the nature of turbulence in a weakly collisional plasma: the nonlinear interactions responsible for the turbulent cascade of energy and the formation of current sheets are essentially fluid in nature, while the collisionless damping of the turbulent fluctuations and the energy injection by kinetic instabilities are essentially kinetic in nature.
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Affiliation(s)
- G G Howes
- Department of Physics and Astronomy, University of Iowa, Iowa City, IA 52242, USA
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12
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Hatch DR, Jenko F, Bañón Navarro A, Bratanov V. Transition between saturation regimes of gyrokinetic turbulence. PHYSICAL REVIEW LETTERS 2013; 111:175001. [PMID: 24206497 DOI: 10.1103/physrevlett.111.175001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/18/2013] [Indexed: 06/02/2023]
Abstract
A gyrokinetic model of ion temperature gradient driven turbulence in magnetized plasmas is used to study the injection, nonlinear redistribution, and collisional dissipation of free energy in the saturated turbulent state over a broad range of driving gradients and collision frequencies. The dimensionless parameter L(T)/L(C), where L(T) is the ion temperature gradient scale length and L(C) is the collisional mean free path, is shown to parametrize a transition between a saturation regime dominated by nonlinear transfer of free energy to small perpendicular (to the magnetic field) scales and a regime dominated by dissipation at large scales in all phase space dimensions.
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Affiliation(s)
- D R Hatch
- Institute for Fusion Studies, University of Texas at Austin, Austin, Texas 78712, USA and Max Planck Institute for Plasma Physics, EURATOM Association, 85748 Garching, Germany
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13
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Kawamori E. Experimental verification of entropy cascade in two-dimensional electrostatic turbulence in magnetized plasma. PHYSICAL REVIEW LETTERS 2013; 110:095001. [PMID: 23496719 DOI: 10.1103/physrevlett.110.095001] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/17/2012] [Indexed: 06/01/2023]
Abstract
The wave number spectrum (one-dimensional spectrum) of electrostatic potential fluctuations at sub-Larmor scales was measured in two-dimensional (2D) electrostatic turbulence in laboratory magnetized plasma. The spectrum at scales k([perpendicular])ρ(i)>1, where k([perpendicular]) and ρ(i) are the fluctuation wave number perpendicular to the magnetic field and ion Larmor radius, respectively, supports the existence of the k(-10/3) inertial range of the entropy cascade induced by nonlinear phase mixing. This indicates agreement with a theoretical prediction [A. A. Schekochihin et al., Plasma Phys. Controlled Fusion 50, 124024 (2008)] and the result of a 2D gyrokinetic simulation [T. Tatsuno et al., Phys. Rev. Lett. 103, 015003 (2009)]. The cutoff wave numbers of the spectrum, above which the entropy cascade is smeared by collisions, observed in this experiment were consistent with those in the theory.
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Affiliation(s)
- Eiichirou Kawamori
- Institute of Space, Astrophysical and Plasma Sciences, National Cheng Kung University, Tainan 70101, Taiwan
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14
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Teaca B, Navarro AB, Jenko F, Brunner S, Villard L. Locality and universality in gyrokinetic turbulence. PHYSICAL REVIEW LETTERS 2012; 109:235003. [PMID: 23368214 DOI: 10.1103/physrevlett.109.235003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/18/2012] [Indexed: 06/01/2023]
Abstract
The nature of nonlinear interactions in gyrokinetic turbulence, driven by the ion-temperature gradient instability, is investigated using direct numerical simulations in toroidal flux tube geometry. To account for the level of separation existing between scales involved in an energetic interaction, the degree of locality of the free energy scale flux is analyzed employing Kraichnan's infrared (IR) and ultraviolet locality functions. Because of the nontrivial dissipative nature of gyrokinetic turbulence, an asymptotic level for the locality exponents, indicative of a universal dynamical regime for gyrokinetics, is not recovered and an accentuated nonlocal behavior of the IR interactions is found instead, in spite of the local energy cascade observed.
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Affiliation(s)
- Bogdan Teaca
- Ecole Polytechnique Fédérale de Lausanne (EPFL), Centre de Recherches en Physique des Plasmas, Association Euratom-Confédération Suisse, CH-1015 Lausanne, Switzerland.
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15
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Servidio S, Valentini F, Califano F, Veltri P. Local kinetic effects in two-dimensional plasma turbulence. PHYSICAL REVIEW LETTERS 2012; 108:045001. [PMID: 22400851 DOI: 10.1103/physrevlett.108.045001] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/28/2011] [Indexed: 05/31/2023]
Abstract
Using direct numerical simulations of a hybrid Vlasov-Maxwell model, kinetic processes are investigated in a two-dimensional turbulent plasma. In the turbulent regime, kinetic effects manifest through a deformation of the ion distribution function. These patterns of non-Maxwellian features are concentrated in space nearby regions of strong magnetic activity: the distribution function is modulated by the magnetic topology, and can elongate along or across the local magnetic field. These results open a new path on the study of kinetic processes such as heating, particle acceleration, and temperature anisotropy, commonly observed in astrophysical and laboratory plasmas.
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Affiliation(s)
- S Servidio
- Dipartimento di Fisica, Università della Calabria, I-87036 Cosenza, Italy
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16
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Barnes M, Parra FI, Schekochihin AA. Critically balanced ion temperature gradient turbulence in fusion plasmas. PHYSICAL REVIEW LETTERS 2011; 107:115003. [PMID: 22026680 DOI: 10.1103/physrevlett.107.115003] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/22/2011] [Indexed: 05/31/2023]
Abstract
Scaling laws for ion temperature gradient driven turbulence in magnetized toroidal plasmas are derived and compared with direct numerical simulations. Predicted dependences of turbulence fluctuation amplitudes, spatial scales, and resulting heat fluxes on temperature gradient and magnetic field line pitch are found to agree with numerical results in both the driving and inertial ranges. Evidence is provided to support the critical balance conjecture that parallel streaming and nonlinear perpendicular decorrelation times are comparable at all spatial scales, leading to a scaling relationship between parallel and perpendicular spatial scales. This indicates that even strongly magnetized plasma turbulence is intrinsically three dimensional.
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Affiliation(s)
- M Barnes
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3NP, United Kingdom.
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17
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Turner AJ, Gogoberidze G, Chapman SC, Hnat B, Müller WC. Nonaxisymmetric anisotropy of solar wind turbulence. PHYSICAL REVIEW LETTERS 2011; 107:095002. [PMID: 21929247 DOI: 10.1103/physrevlett.107.095002] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/10/2011] [Indexed: 05/31/2023]
Abstract
A key prediction of turbulence theories is frame-invariance, and in magnetohydrodynamic (MHD) turbulence, axisymmetry of fluctuations with respect to the background magnetic field. Paradoxically the power in fluctuations in the turbulent solar wind are observed to be ordered with respect to the bulk macroscopic flow as well as the background magnetic field. Here, nonaxisymmetry across the inertial and dissipation ranges is quantified using in situ observations from Cluster. The observed inertial range nonaxisymmetry is reproduced by a "fly through" sampling of a direct numerical simulation of MHD turbulence. Furthermore, fly through sampling of a linear superposition of transverse waves with axisymmetric fluctuations generates the trend in nonaxisymmetry with power spectral exponent. The observed nonaxisymmetric anisotropy may thus simply arise as a sampling effect related to Taylor's hypothesis and is not related to the plasma dynamics itself.
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Affiliation(s)
- A J Turner
- Centre for Fusion, Space and Astrophysics, University of Warwick, Coventry, CV4 7AL, United Kingdom.
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18
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Howes GG, TenBarge JM, Dorland W, Quataert E, Schekochihin AA, Numata R, Tatsuno T. Gyrokinetic simulations of solar wind turbulence from ion to electron scales. PHYSICAL REVIEW LETTERS 2011; 107:035004. [PMID: 21838370 DOI: 10.1103/physrevlett.107.035004] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/21/2011] [Indexed: 05/31/2023]
Abstract
A three-dimensional, nonlinear gyrokinetic simulation of plasma turbulence resolving scales from the ion to electron gyroradius with a realistic mass ratio is presented, where all damping is provided by resolved physical mechanisms. The resulting energy spectra are quantitatively consistent with a magnetic power spectrum scaling of k(-2.8) as observed in in situ spacecraft measurements of the "dissipation range" of solar wind turbulence. Despite the strongly nonlinear nature of the turbulence, the linear kinetic Alfvén wave mode quantitatively describes the polarization of the turbulent fluctuations. The collisional ion heating is measured at subion-Larmor radius scales, which provides evidence of the ion entropy cascade in an electromagnetic turbulence simulation.
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Affiliation(s)
- G G Howes
- Department of Physics and Astronomy, University of Iowa, Iowa City, Iowa 52242, USA.
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19
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Plunk GG, Tatsuno T. Energy transfer and dual cascade in kinetic magnetized plasma turbulence. PHYSICAL REVIEW LETTERS 2011; 106:165003. [PMID: 21599375 DOI: 10.1103/physrevlett.106.165003] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/15/2010] [Indexed: 05/30/2023]
Abstract
The question of how nonlinear interactions redistribute the energy of fluctuations across available degrees of freedom is of fundamental importance in the study of turbulence and transport in magnetized weakly collisional plasmas, ranging from space settings to fusion devices. In this Letter, we present a theory for the dual cascade found in such plasmas, which predicts a range of new behavior that distinguishes this cascade from that of neutral fluid turbulence. These phenomena are explained in terms of the constrained nature of spectral transfer in nonlinear gyrokinetics. Accompanying this theory are the first observations of these phenomena, obtained via direct numerical simulations using the gyrokinetic code AstroGK. The basic mechanisms that are found provide a framework for understanding the turbulent energy transfer that couples scales both locally and nonlocally.
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Affiliation(s)
- G G Plunk
- Department of Physics and IREAP, University of Maryland, College Park, Maryland 20742, USA.
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20
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Hatch DR, Terry PW, Jenko F, Merz F, Nevins WM. Saturation of gyrokinetic turbulence through damped eigenmodes. PHYSICAL REVIEW LETTERS 2011; 106:115003. [PMID: 21469869 DOI: 10.1103/physrevlett.106.115003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/23/2010] [Revised: 01/25/2011] [Indexed: 05/30/2023]
Abstract
In the context of toroidal gyrokinetic simulations, it is shown that a hierarchy of damped modes is excited in the nonlinear turbulent state. These modes exist at the same spatial scales as the unstable eigenmodes that drive the turbulence. The larger amplitude subdominant modes are weakly damped and exhibit smooth, large-scale structure in velocity space and in the direction parallel to the magnetic field. Modes with increasingly fine-scale structure are excited to decreasing amplitudes. In aggregate, damped modes define a potent energy sink. This leads to an overlap of the spatial scales of energy injection and peak dissipation, a feature that is in contrast with more traditional turbulent systems.
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Affiliation(s)
- D R Hatch
- University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
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Bañón Navarro A, Morel P, Albrecht-Marc M, Carati D, Merz F, Görler T, Jenko F. Free energy cascade in gyrokinetic turbulence. PHYSICAL REVIEW LETTERS 2011; 106:055001. [PMID: 21405402 DOI: 10.1103/physrevlett.106.055001] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/24/2010] [Indexed: 05/30/2023]
Abstract
In gyrokinetic theory, the quadratic nonlinearity is known to play an important role in the dynamics by redistributing (in a conservative fashion) the free energy between the various active scales. In the present study, the free energy transfer is analyzed for the case of ion temperature gradient driven turbulence. It is shown that it shares many properties with the energy transfer in fluid turbulence. In particular, one finds a (strongly) local, forward (from large to small scales) cascade of free energy in the plane perpendicular to the background magnetic field. These findings shed light on some fundamental properties of plasma turbulence, and encourage the development of large-eddy-simulation techniques for gyrokinetics.
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Affiliation(s)
- A Bañón Navarro
- Université Libre de Bruxelles, Faculté des Sciences, Physique Statistique et Plasmas CP 231, EURATOM Association, Campus Plaine, 1050 Brussels, Belgium
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