Propagation of transverse waves in a radially expanding plasma (original) (raw)

1974, Journal of Geophysical Research

We have investigated the properties of low-frequency transverse waves in an expanding plasma. The wave vector k, the background magnetic field B, and the streaming velocity of the plasma V are all assumed to lie along the radial direction. We present expressions for the radial dependence of the amplitude and phase of left and right circularly polarized waves, correct to first order in the wave frequency divided by the proton cyclotron frequency. Differences in the phase velocities of these two circular polarizations result in a Faraday rotation that can be substantial for typical interplanetary conditions near I AU. We also consider the implications of these results for a realistic solar wind model with the interplanetary magnetic field along the spiral direction. Since the formulation of solar wind theory [Parker, 1958] much effort has been directed toward understanding perturbations in the steady coronal expansion. Waves, tangential and rotational discontinuities, turbulence, and shocks are observed perturbations in the steady flow of the solar wind. In particular, Alfv6nic fluctuations with characteristic periods of a few hours and less are a well-known feature of the interplanetary magnetic field [Coleman, 1967, 1968; Unti and Neugebauer, 1968; Belcher et al., 1969; Belcher and Davis, 1971]. Since these waves are observed to propagate away from the sun in the rest frame of the solar wind, it is generally accepted that they are generated close to the sun in regions in which the plasma flow is sub-Alfv6nic. Theoretical work on ray tracing the Alfv6n wave mode into the spiral interplanetary magnetic field [Barnes, 1969; Vi•lk and Alpers, 1973] predicts that near I AU the wave vector k should be essentially radial, the polarization of the waves being perpendicular to the plane formed by the radial direction and the average magnetic field direction. Observationally, there appears to be a small preference for such a polarization [Belcher and Davis, 1971], although the magnitude of the observed effect is at best a factor of 10 less than that predicted. In addition, there is strong observational evidence that k tends to lie along the average field direction at I AU, rather than along the radial direction [Belcher and Davis, 1971; Daily, 1973]. The reason for these discrepancies between observations and theoretical predictions is not well understood. Vi•lk and Alpers [1973] and Daily [1973] speculate that the waves undergo substantial scattering in the interplanetary medium between the sun and the earth. However, as Daily [1973] points out, it is not clear why such scattering would cause the preferential refraction of the wave vector k into directions along magnetic field lines. Barnes and Hollweg [1973] and Vi•lk and Alpers [1973] suggest that nonlinear effects could be dominant in the solar wind, since the observed amplitudes of the Alfv6n waves are comparable to the background field strength. Thus the results of a linearized ray-tracing analysis may be inapplicable. The authors are presently involved in an extensive spectral and cross-spectral analysis of Alfv6nic fluctuations in the solar wind. In the context of this study we have undertaken a limited theoretical investigation of the importance of finite cyclotron effects on the properties of magnetic field fluctuations with spacecraft periods between 15 s and a few minutes.