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Double Alfvén waves

Published online by Cambridge University Press:  17 October 2011

G. M. WEBB ,
Q. HU ,
B. DASGUPTA  and
G. P. ZANK
G. M. WEBB
Affiliation:
CSPAR, The University of Alabama in Huntsville, Huntsville AL 35805, USA (gmw0002@uah.edu)
Q. HU
Affiliation:
CSPAR, The University of Alabama in Huntsville, Huntsville AL 35805, USA (gmw0002@uah.edu)
B. DASGUPTA
Affiliation:
CSPAR, The University of Alabama in Huntsville, Huntsville AL 35805, USA (gmw0002@uah.edu)
G. P. ZANK
Affiliation:
CSPAR, The University of Alabama in Huntsville, Huntsville AL 35805, USA (gmw0002@uah.edu) Department of Physics, The University of Alabama in Huntsville, Huntsville AL 35899, USA
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Abstract

Double Alfvén wave solutions of the magnetohydrodynamic equations in which the physical variables (the gas density ρ, fluid velocity u, gas pressure p, and magnetic field induction B) depend only on two independent wave phases ϕ1(x,t) and ϕ2(x,t) are obtained. The integrals for the double Alfvén wave are the same as for simple waves, namely, the gas pressure, magnetic pressure, and group velocity of the wave are constant. Compatibility conditions on the evolution of the magnetic field B due to changes in ϕ1 and ϕ2, as well as constraints due to Gauss's law ∇ · B = 0 are discussed. The magnetic field lines and hodographs of B in which the tip of the magnetic field B moves on the sphere |B| = B = const. are used to delineate the physical characteristics of the wave. Hamilton's equations for the simple Alfvén wave with wave normal n(ϕ), and with magnetic induction B(ϕ) in which ϕ is the wave phase, are obtained by using the Frenet–Serret equations for curves x=X(ϕ) in differential geometry. The use of differential geometry of 2D surfaces in a 3D Euclidean space to describe double Alfvén waves is briefly discussed.

Type
Papers
Information
Journal of Plasma Physics , Volume 78 , Issue 1 , February 2012 , pp. 71 - 85
Copyright
Copyright © Cambridge University Press 2011

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