Alfvén Simple Waves: Euler Potentials and Magnetic Helicity

Details Alfvén Simple Waves: Euler Potentials and Magnetic Helicity Alfvén Simple Waves: Euler Potentials and Magnetic Helicity

Dec 2010

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2010apj...725.2128w&link_type=abstract

The Astrophysical Journal, Volume 725, Issue 2, pp. 2128-2151 (2010).

Astronomy and Astrophysics

Astronomy

3

Magnetohydrodynamics: Mhd, Solar Wind, Sun: Magnetic Topology, Waves

Scientific paper

The magnetic helicity characteristics of fully nonlinear, multi-dimensional Alfvén simple waves are investigated, by using relative helicity formulae and also by using an approach involving poloidal and toroidal decomposition of the magnetic field and magnetic vector potential. Different methods to calculate the magnetic vector potential are used, including the homotopy and Biot-Savart formulae. Two basic Alfvén modes are identified: (1) the plane one-dimensional Alfvén simple wave given in standard texts, in which the Alfvén wave propagates along the z-axis with wave phase phiv = k 0(z - λt), where k 0 is the wave number and λ is the group velocity of the wave and (2) the generalized Barnes simple Alfvén wave in which the wave normal n moves in a circle in the xy-plane perpendicular to the mean field, which is directed along the z-axis. The plane Alfvén wave (1) is analogous to the slab Alfvén mode and the generalized Barnes solution (2) is analogous to the two-dimensional mode in Alfvénic, incompressible turbulence. The helicity characteristics of these two basic Alfvén modes are distinct. The helicity characteristics of more general multi-dimensional simple Alfvén waves are also investigated. Applications to nonlinear Alfvénic fluctuations and structures observed in the solar wind are discussed.

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