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

doi:https://doi.org/10.1063/1.4812805

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

Full Record
Other Related Research

Abstract

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 are 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 blockmore » of astrophysical plasma turbulence.« less

Authors:

Howes, G. G.; Nielson, K. D. ^[1]

Department of Physics and Astronomy, University of Iowa, Iowa City, Iowa 52242 (United States)

Publication Date:: 2013-07-15

OSTI Identifier:: 22227939

Resource Type:: Journal Article

Journal Name:: Physics of Plasmas

Additional Journal Information:: Journal Volume: 20; Journal Issue: 7; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1070-664X

Country of Publication:: United States

Language:: English

Subject:: 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ALFVEN WAVES; ANALYTICAL SOLUTION; ASTROPHYSICS; ASYMPTOTIC SOLUTIONS; ENERGY TRANSFER; FLUCTUATIONS; MAGNETOHYDRODYNAMICS; NONLINEAR PROBLEMS; PLASMA; PLASMA WAVES; TURBULENCE; WAVE PROPAGATION

Citation Formats


                    Howes, G. G., and Nielson, K. D. Alfvén wave collisions, the fundamental building block of plasma turbulence. I. Asymptotic solution.  United States: N. p., 2013. 
        Web.  doi:10.1063/1.4812805.

Copy to clipboard


                    Howes, G. G., & Nielson, K. D. Alfvén wave collisions, the fundamental building block of plasma turbulence. I. Asymptotic solution.  United States.  https://doi.org/10.1063/1.4812805

Copy to clipboard


                    Howes, G. G., and Nielson, K. D. Mon .  
        "Alfvén wave collisions, the fundamental building block of plasma turbulence. I. Asymptotic solution".  United States.  https://doi.org/10.1063/1.4812805.

Copy to clipboard


                    
@article{osti_22227939,

  title        = {Alfvén wave collisions, the fundamental building block of plasma turbulence. I. Asymptotic solution},

  author       = {Howes, G. G. and Nielson, K. D.},

  abstractNote = {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 are 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.},

  doi          = {10.1063/1.4812805},

  url          = {https://www.osti.gov/biblio/22227939},
  journal      = {Physics of Plasmas},

  issn         = {1070-664X},

  number       = 7,

  volume       = 20,

  place        = {United States},

  year         = {2013},

  month        = {7}

}

Copy to clipboard

Journal Article:

https://doi.org/10.1063/1.4812805

Other availability

Find in Google Scholar

Search WorldCat to find libraries that may hold this journal

Save / Share:

Export Metadata

Save to My Library

Similar records in OSTI.GOV collections:

The Alfvénic nature of energy transfer mediation in localized, strongly nonlinear Alfvén wavepacket collisions

Journal Article Verniero, J. L. ; Howes, G. G. - Journal of Plasma Physics

In space and astrophysical plasmas, violent events or instabilities inject energy into turbulent motions at large scales. Nonlinear interactions among the turbulent fluctuations drive a cascade of energy to small perpendicular scales at which the energy is ultimately converted into plasma heat. Previous work with the incompressible magnetohydrodynamic (MHD) equations has shown that this turbulent energy cascade is driven by the nonlinear interaction between counterpropagating Alfvén waves – also known as Alfvén wave collisions. Direct numerical simulations of weakly collisional plasma turbulence enables deeper insight into the nature of the nonlinear interactions underlying the turbulent cascade of energy. In thismore »« less
https://doi.org/10.1017/s0022377818000090
Spatially localized particle energization by Landau damping in current sheets produced by strong Alfvén wave collisions

Journal Article Howes, Gregory G. ; McCubbin, Andrew J. ; Klein, Kristopher G. - Journal of Plasma Physics

Understanding the removal of energy from turbulent fluctuations in a magnetized plasma and the consequent energization of the constituent plasma particles is a major goal of heliophysics and astrophysics. Previous work has shown that nonlinear interactions among counterpropagating Alfvén waves – or Alfvén wave collisions – are the fundamental building block of astrophysical plasma turbulence and naturally generate current sheets in the strongly nonlinear limit. A nonlinear gyrokinetic simulation of a strong Alfvén wave collision is used to examine the damping of the electromagnetic fluctuations and the associated energization of particles that occurs in self-consistently generated current sheets. A simple model explains themore »« less
https://doi.org/10.1017/s0022377818000053
Nonlinear energy transfer and current sheet development in localized Alfvén wavepacket collisions in the strong turbulence limit

Journal Article Verniero, J. L. ; Howes, G. G. ; Klein, K. G. - Journal of Plasma Physics

In space and astrophysical plasmas, turbulence is responsible for transferring energy from large scales driven by violent events or instabilities, to smaller scales where turbulent energy is ultimately converted into plasma heat by dissipative mechanisms. The nonlinear interaction between counterpropagating Alfvén waves, denoted Alfvén wave collisions, drives this turbulent energy cascade, as recognized by early work with incompressible magnetohydrodynamic (MHD) equations. Recent work employing analytical calculations and nonlinear gyrokinetic simulations of Alfvén wave collisions in an idealized periodic initial state have demonstrated the key properties that strong Alfvén wave collisions mediate effectively the transfer of energy to smaller perpendicular scales and self-consistently generatemore »« less
https://doi.org/10.1017/s0022377817001003
Alfvén wave collisions, the fundamental building block of plasma turbulence. II. Numerical solution

Journal Article Nielson, K. D. ; Howes, G. G. ; Dorland, W. - Physics of Plasmas

Here, this paper presents the numerical verification of an asymptotic analytical solution for the nonlinear interaction between counterpropagating Alfvén waves, the fundamental building block of astrophysical plasma turbulence. The analytical solution, derived in the weak turbulence limit using the equations of incompressible MHD, is compared to a nonlinear gyrokinetic simulation of an Alfvén wave collision. Finally, the agreement between these methods signifies that the incompressible solution satisfactorily describes the essential dynamics of the nonlinear energy transfer, even under the weakly collisional plasma conditions relevant to many astrophysical environments.
Cited by 17
https://doi.org/10.1063/1.4812807

Full Text Available
Alfvén wave collisions, the fundamental building block of plasma turbulence. II. Numerical solution

Journal Article Nielson, K. D. ; Howes, G. G. ; Dorland, W. - Physics of Plasmas

This paper presents the numerical verification of an asymptotic analytical solution for the nonlinear interaction between counterpropagating Alfvén waves, the fundamental building block of astrophysical plasma turbulence. The analytical solution, derived in the weak turbulence limit using the equations of incompressible MHD, is compared to a nonlinear gyrokinetic simulation of an Alfvén wave collision. The agreement between these methods signifies that the incompressible solution satisfactorily describes the essential dynamics of the nonlinear energy transfer, even under the weakly collisional plasma conditions relevant to many astrophysical environments.
https://doi.org/10.1063/1.4812807

Similar Records