Non-WKB Alfven waves in the solar wind
We treat, both analytically and numerically, small-amplitude, undamped, toroidal Alfven waves in a model of axisymmetric solar wind flow in which solar rotation is neglected. There is no restriction to WKB waves; the waves may have any frequency. By transforming in simple ways the equations governing the waves we are able to obtain exact formal solutions to the general time-dependent problem as well as to the Fourier-analyzed problem. We discuss the equations and their solutions in terms of coupled inward and outward propagating waves. One integral of the equations for the Fourier amplitudes is obtained: it relates the amplitudes of the ingoing and outgoing waves. The integral is a special case of a general law of conservation of wave action, which we show to hold for finite wavelengths. The statement of the conservation of wave action is shown to be analogous to the conservation of particle-antiparticle pairs in relativistic quantum theory. We obtain the condition required for WKB waves and show that it depends on the coupling of waves in a flowing medium. The solar wind problem is discussed in terms of the Fourier amplitudes. It is shown that there is a singularity in the equations, at the Alfven point, which determines physically acceptable solar wind solutions. A qualitative account of the amplitudes far from the sun is given based on an exact solution for a model with constant solar wind flow speed. A conservation equation for the wave energy is obtained, and the relations among the wave energy density, energy flux density, force, and acceleration are stated. Numerical solutions, based on realistic solar wind profile, are given. We show that non-WKB waves with wave periods of about a day or two have some-same amplitude at 1 A.U. On th other hand, non-WKB waves of any wave period are no more effective in accelerating the plasma than are WKB waves; they are much less effective for wave periods of a day or more.
- Research Organization:
- Department of Physics, Boston College, Chestnul Hill, Massachusetts 02167
- OSTI ID:
- 5286211
- Journal Information:
- J. Geophys. Res.; (United States), Journal Name: J. Geophys. Res.; (United States) Vol. 85:A3; ISSN JGREA
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ACCELERATION
ALFVEN WAVES
ANALYTICAL SOLUTION
ENERGY DENSITY
FOURIER ANALYSIS
HYDROMAGNETIC WAVES
NUMERICAL SOLUTION
PLASMA ACCELERATION
PLASMA WAVES
SOLAR ACTIVITY
SOLAR WIND
WAVE PROPAGATION
WKB APPROXIMATION