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Entanglement of helicity and energy in kinetic Alfvén wave/whistler turbulence

Part of: Present Achievements in SpacePlasmas

Published online by Cambridge University Press:  25 September 2014

Sébastien Galtier  and
Romain Meyrand
Sébastien Galtier*
Affiliation:
Laboratoire de Physique des Plasmas, Ecole Polytechnique, F-91128 Palaiseau Cedex, France
Romain Meyrand
Affiliation:
Laboratoire de Physique des Plasmas, Ecole Polytechnique, F-91128 Palaiseau Cedex, France
*
†Email address for correspondence: [email protected]
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Abstract

The role of magnetic helicity is investigated in kinetic Alfvén wave and oblique whistler turbulence in presence of a relatively intense external magnetic field b0e∥. In this situation, turbulence is strongly anisotropic and the fluid equations describing both regimes are the reduced electron magnetohydrodynamics (REMHD) whose derivation, originally made from the gyrokinetic theory, is also obtained here from compressible Hall magnetohydrodynamics (MHD). We use the asymptotic equations derived by Galtier and Bhattacharjee (2003 Phys. Plasmas10, 3065–3076) to study the REMHD dynamics in the weak turbulence regime. The analysis is focused on the magnetic helicity equation for which we obtain the exact solutions: they correspond to the entanglement relation, n + ñ = −6, where n and ñ are the power law indices of the perpendicular (to b0) wave number magnetic energy and helicity spectra, respectively. Therefore, the spectra derived in the past from the energy equation only, namely n = −2.5 and ñ = −3.5, are not the unique solutions to this problem but rather characterize the direct energy cascade. The solution ñ = −3 is a limit imposed by the locality condition; it is also the constant helicity flux solution obtained heuristically. The results obtained offer a new paradigm to understand solar wind turbulence at sub-ion scales where it is often observed that −3 < n < −2.5.

Type
Research Article
Information
Journal of Plasma Physics , Volume 81 , Issue 1 , January 2015 , 325810106
Copyright
Copyright © Cambridge University Press 2014 

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