Building Block Of Plasma Turbulence Research Articles

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

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.

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

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.

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

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.

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

Turbulence in space and astrophysical plasmas is governed by the nonlinear interactions between counterpropagating Alfvén waves. Here, we present the theoretical considerations behind the design of the first laboratory measurement of an Alfvén wave collision, the fundamental interaction underlying Alfvénic turbulence. By interacting a relatively large-amplitude, low-frequency Alfvén wave with a counterpropagating, smaller-amplitude, higher-frequency Alfvén wave, the experiment accomplishes the secular nonlinear transfer of energy to a propagating daughter Alfvén wave. The predicted properties of the nonlinearly generated daughter Alfvén wave are outlined, providing a suite of tests that can be used to confirm the successful measurement of the nonlinear interaction between counterpropagating Alfvén waves in the laboratory.

Numerical modeling of Large Plasma Device Alfvén wave experiments using AstroGK

Collisions between counterpropagating Alfvén waves represent the fundamental building block of plasma turbulence, a phenomenon of great importance to a wide variety of fields, from space physics and astrophysics to controlled magnetic fusion. Proposed experiments to study Alfvén wave collisions on the Large Plasma Device (LAPD) [W. Gekelman, H. Pfister, Z. Lucky, J. Bamber, D. Leneman, and J. Maggs, Rev. Sci. Instrum. 62, 2875 (1991)] at the University of California, Los Angeles, will benefit significantly from numerical modeling capable of reproducing not only the linear dispersive effects of kinetic and inertial Alfvén waves, but also the nonlinear evolution of the Alfvénic turbulence. This paper presents a comparison of linear simulation results using the astrophysical gyrokinetics code, AstroGK, to the measured linear properties of kinetic and inertial Alfvén waves in the LAPD plasma. Results demonstrate that: (1) finite frequency effects due to the ion cyclotron resonance do not prevent satisfactory modeling of the LAPD plasma using gyrokinetic theory; and (2) an advanced collision operator, recently implemented in AstroGK, enables the code to successfully reproduce the collisionally enhanced damping rates of linear waves measured in recent LAPD experiments. These tests justify the use of AstroGK in the modeling of LAPD Alfvén wave experiments and suggest that AstroGK will be a valuable tool in modeling the nonlinear evolution of proposed Alfvén wave collision experiments.