Measurement of the rugged invariants of magnetohydrodynamic turbulence in the solar wind

TLDR

These quantities are the three rugged invariants of three‑dimensional ideal incompressible MHD turbulence theory. The theoretical technique for measuring the magnetic helicity from the matrix of two‑point correlations is shown. Measurements of the solar wind’s total energy, cross helicity, and magnetic helicity at 1, 2.8, and 5 AU reveal that magnetic helicity occurs at scales equal to or larger than magnetic energy, typically at larger scales consistent with inverse cascade and selective decay, oscillates in sign at smaller scales, and that cross helicity oscillates in sign—especially at 5 AU—indicating both outward and inward propagating fluctuations, contrary to the usual outward‑Alfvénic interpretation.

Abstract

Measurements of the total energy, cross helicity, and magnetic helicity of the solar wind at 1, 2.8, and 5 AU are presented. These quantities are the three rugged invariants of three‐dimensional ideal incompressible MHD turbulence theory. The theoretical technique for measuring the magnetic helicity from the matrix of two‐point correlations is shown. The length scales characterizing the magnetic helicity are found to be equal to or greater than those which characterize the magnetic energy. The magnetic helicity typically lies at scales larger than the magnetic correlation length, consistent with the expectations of the inverse cascade and selective decay hypotheses of three‐dimensional MHD turbulence. At smaller scales, the magnetic helicity oscillates in sign. Our measurements of the cross helicity are not fully consistent with the usual interpretation in terms of outward propagating Alfvénic functuations. Especially during the interval at 5 AU the cross helicity is found to oscillate in sign indicating fluctuations propagating both outward and inward.