1
|
Helander P, Plunk GG. Upper Bounds on Gyrokinetic Instabilities in Magnetized Plasmas. PHYSICAL REVIEW LETTERS 2021; 127:155001. [PMID: 34678019 DOI: 10.1103/physrevlett.127.155001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/10/2021] [Revised: 07/28/2021] [Accepted: 08/27/2021] [Indexed: 06/13/2023]
Abstract
A family of rigorous upper bounds on the growth rate of local gyrokinetic instabilities in magnetized plasmas is derived from the evolution equation for the Helmholtz free energy. These bounds hold for both electrostatic and electromagnetic instabilities, regardless of the number of particle species, their collision frequency, and the geometry of the magnetic field. A large number of results that have earlier been derived in special cases and observed in numerical simulations are thus brought into a unifying framework. These bounds apply not only to linear instabilities but also imply an upper limit to the nonlinear growth of the free energy.
Collapse
Affiliation(s)
- P Helander
- Max-Planck-Institut für Plasmaphysik, 17491 Greifswald, Germany
| | - G G Plunk
- Max-Planck-Institut für Plasmaphysik, 17491 Greifswald, Germany
| |
Collapse
|
2
|
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.
Collapse
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
| |
Collapse
|
4
|
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.
Collapse
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
| |
Collapse
|
5
|
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.
Collapse
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
| | | | | | | |
Collapse
|
6
|
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.
Collapse
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.
| | | | | | | | | |
Collapse
|
7
|
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.
Collapse
Affiliation(s)
- M Barnes
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3NP, United Kingdom.
| | | | | |
Collapse
|
8
|
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.
Collapse
Affiliation(s)
- D R Hatch
- University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
| | | | | | | | | |
Collapse
|