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Alfvén wave collisions, the fundamental building block of plasma turbulence. III. Theory for experimental design
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Image of FIG. 1.

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FIG. 1.

Schematic diagram of the waveforms of two Alfvén wavepackets. (a) A waveform that is symmetric about , and that therefore has no component. (b) An asymmetric waveform that includes a significant component.

Image of FIG. 2.

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FIG. 2.

Schematic of the Alfvén wave turbulence experiment on the LAPD. The Loop antenna generates a large-amplitude distorting Alfvén wave, with the wave magnetic field dominantly polarized in the -direction, traveling up the equilibrium axial magnetic field, . The ASW antenna generates a small-amplitude probe Alfvén wave polarized in the -direction traveling down the axial magnetic field.

Image of FIG. 3.

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FIG. 3.

Each panel depicts the component of the rightward propagating distorting Loop Alfvén wave (upper) and the component of the leftward propagating probe ASW Alfvén wave (lower). The length of the distorting Alfvén wave that has interacted with one point on the probe Alfvén wave (open circle) is depicted by the thick solid line in the upper plot of each panel.

Image of FIG. 4.

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FIG. 4.

Fourier decomposition of the distorting Alfvén wave signal over a length , showing that the waveform contains a significant component.

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2013-07-15
2014-04-19

Abstract

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.

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Scitation: Alfvén wave collisions, the fundamental building block of plasma turbulence. III. Theory for experimental design
http://aip.metastore.ingenta.com/content/aip/journal/pop/20/7/10.1063/1.4812808
10.1063/1.4812808
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