Alfvén wave collisions, the fundamental building block of plasma turbulence. III. Theory for experimental design

Howes, G. G.; Nielson, Kevin; Drake, D. J.; Schroeder, James W.; Skiff, F.; Kletzing, C. A.; Carter, T. A.

doi:10.1063/1.4812808

Cited by 22 publications

(29 citation statements)

References 62 publications

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“…. simulations in the MHD regime [18] and verified experimentally in the laboratory [57][58][59], establishing Alfvén wave collisions as the fundamental building block of astrophysical plasma turbulence. This nonlinear mechanism is likely to be the physics leading to a non-zero thirdmoment of turbulent magnetic field measurements, a statistical measure often used to estimate the turbulent energy cascade rate [60].…”

Section: (A) How Is Energy Transferred To Small Scales?mentioning

confidence: 82%

A dynamical model of plasma turbulence in the solar wind

Howes

2015

Phil. Trans. R. Soc. A.

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One contribution of 11 to a theme issue 'Dissipation and heating in solar wind turbulence' . 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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Section: (A) How Is Energy Transferred To Small Scales?mentioning

confidence: 82%

A dynamical model of plasma turbulence in the solar wind

Howes

2015

Phil. Trans. R. Soc. A.

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“…96 As a complement to the analytical derivation presented here, quantitative verification of this analytical solution using gyrokinetic numerical simulations is presented in Paper II. 60 A detailed description of the theoretical considerations involved in the experimental design and supporting numerical simulations is contained in Paper III, 97 and the specifics of the experimental procedure and data analysis appear in Paper IV. 98 Future extensions of this work will explore the transition to the limit of strong turbulence and the nature of the nonlinear energy transfer in the small-scale, dispersive regime of kinetic and inertial Alfvén waves.…”

Section: Discussionmentioning

confidence: 99%

Alfvén wave collisions, the fundamental building block of plasma turbulence. I. Asymptotic solution

2013

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The nonlinear interaction between counterpropagating Alfvén waves is the physical mechanism underlying the cascade of energy to small scales in astrophysical plasma turbulence. Beginning with the equations for incompressible MHD, an asymptotic analytical solution for the nonlinear evolution of these Alfvén wave collisions is derived in the weakly nonlinear limit. The resulting qualitative picture of nonlinear energy transfer due to this mechanism involves two steps: first, the primary counterpropagating Alfvén waves interact to generate an inherently nonlinear, purely magnetic secondary fluctuation with no parallel variation; second, the two primary waves each interact with this secondary fluctuation to transfer energy secularly to two tertiary Alfvén waves. These tertiary modes are linear Alfvén waves with the same parallel wavenumber as the primary waves, indicating the lack of a parallel cascade. The amplitude of these tertiary modes increases linearly with time due to the coherent nature of the resonant four-wave interaction responsible for the nonlinear energy transfer. The implications of this analytical solution for turbulence in astrophysical plasmas is discussed. The solution presented here provides valuable intuition about the nonlinear interactions underlying magnetized plasma turbulence, in support of an experimental program to verify in the laboratory the nature of this fundamental building block of astrophysical plasma turbulence.a)

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“…II, we briefly discuss the underlying theory. A more detailed theory can be found in the three companion papers by Howes 24 , hereafter Paper III. In Sec.…”

Section: Introductionmentioning

confidence: 99%

Alfvén wave collisions, the fundamental building block of plasma turbulence. IV. Laboratory experiment

et al. 2013

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Turbulence is a phenomenon found throughout space and astrophysical plasmas. It plays an important role in solar coronal heating, acceleration of the solar wind, and heating of the interstellar medium. Turbulence in these regimes is dominated by Alfvén waves. Most turbulence theories have been established using ideal plasma models, such as incompressible MHD. However, there has been no experimental evidence to support the use of such models for weakly to moderately collisional plasmas which are relevant to various space and astrophysical plasma environments. We present the first experiment to measure the nonlinear interaction between two counterpropagating Alfvén waves, which is the building block for astrophysical turbulence theories. We present here four distinct tests that demonstrate conclusively that we have indeed measured the daughter Alfvén wave generated nonlinearly by a collision between counterpropagating Alfvén waves.

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Alfvén wave collisions, the fundamental building block of plasma turbulence. III. Theory for experimental design

Cited by 22 publications

References 62 publications

A dynamical model of plasma turbulence in the solar wind

A dynamical model of plasma turbulence in the solar wind

Alfvén wave collisions, the fundamental building block of plasma turbulence. I. Asymptotic solution

Alfvén wave collisions, the fundamental building block of plasma turbulence. IV. Laboratory experiment

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