Turbulence is a ubiquitous phenomenon in space and astrophysical plasmas, driving a cascade of energy from large to small scales and strongly influencing the plasma heating resulting from the dissipation of the turbulence. Modern theories of plasma turbulence are based on the fundamental concept that the turbulent cascade of energy is caused by the nonlinear interaction between counterpropagating Alfvén waves, yet this interaction has never been observationally or experimentally verified. We present here the first experimental measurement in a laboratory plasma of the nonlinear interaction between counterpropagating Alfvén waves, the fundamental building block of astrophysical plasma turbulence. This measurement establishes a firm basis for the application of theoretical ideas developed in idealized models to turbulence in realistic space and astrophysical plasma systems.Introduction.-Turbulence profoundly affects many space and astrophysical plasma environments, playing a crucial role in the heating of the solar corona and acceleration of the solar wind [1], the dynamics of the interstellar medium [2][3][4], the regulation of star formation [5], the transport of heat in galaxy clusters [6], and the transport of mass and energy into the Earth's magnetosphere [7]. At the large length scales and low frequencies characteristic of the turbulence in these systems, the turbulent motions are governed by the physics of Alfvén waves [8], traveling disturbances of the plasma and magnetic field. Theories of Alfvénic turbulence based on idealized models, such as incompressible magnetohydrodynamics (MHD), suggest that the turbulent cascade of energy from large to small scales is driven by the nonlinear interaction between counterpropagating Alfvén waves [9][10][11][12]. However, the applicability of this key concept in the moderately to weakly collisional conditions relevant to astrophysical plasmas has not previously been observationally or experimentally demonstrated. Verification is important because the distinction between the two leading theories for strong MHD turbulence [11,12] arises from the detailed nature of this nonlinear interaction. Furthermore, verification is required to establish the applicability of turbulence theories, utilizing simplified fluid models such as incompressible MHD, to the weakly collisional conditions of diffuse astrophysical plasmas.

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.

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.

We have designed an electric and magnetic field probe which simultaneously measure both quantities in the directions perpendicular to the background magnetic field for application to Alfvén wave experiments in the Large Plasma Device at UCLA. This new probe allows for the projection of measured wave fields onto generalized Elsässer variables. Experiments were conducted in a singly ionized He plasma at 1850 G in which propagation of Alfvén waves was observed using this new probe. We demonstrate that a clear separation of transmitted and reflected signals and determination of Poynting flux and Elsässer variables can be achieved.