Field patterns of Alfven wave resonance cones

One of the fascinating observations from recent rocket and satellite experiments is on the solitary Alfven waves (SAW). SAWs are electromagnetic structures with a spatial width ∼1 km across the Earth's magnetic field B0. The measurements from Freja have revealed that the SAWs are not simply the product of an obliquely propagating plane Alfven wave; instead, they are the radiation (field) patterns of distant Alfven wave sources (AWS) oscillating at frequencies ω < Ωi, the ion cyclotron frequency. The field pattern of an AWS is highly directional in the form of a cone aligned with B0, and with half‐cone angle θc, less than a milliradian or so when ω ≪ Ωi Such radiation patterns are known as resonance cones (RC) or more specifically Alfven wave RC (AWRC), and they are intimately determined by the allowable directions of the group‐velocity vector in the anisotropic plasma. We have studied here the group‐velocity pattern of shear Alfven waves including both warm plasma and inertial effects. It is found that both the kinetic and the inertial Alfven waves show group‐velocity resonance‐cone patterns. Along any direction within the cone there are two group‐velocity vectors having wave vectors with different directions and magnitudes, giving rise to a slow and a fast wave contributing to the propagation. The RC field pattern of a filamentary field‐aligned current source oscillating at frequencies ω < Ωi, is studied. The far‐field pattern shows that within the cone there are two waves propagating at any angle θ < θc as determined by the group‐velocity directions; these waves produce an interference pattern. Near RC surface the interference pattern is given by the Airy function. The scaling laws for the interference pattern and nonlinear effects arising from the pondermotive force are analyzed. Possible applications of the AWRC field pattern, its scaling laws, and the associated nonlinear effects to SAWs are discussed.