Excitation of Low-Frequency Plasma Waves by a Conducting, Tethered Satellite

Because Alfven waves play an important role in natural space phenomena, there has developed in recent years an interest in exciting these low frequency waves in situ in the magnetosphere. Previous investigators have treated the excitation of Alfven waves from a magnetohydrodynamic viewpoint which reduces the problem to solving a one-dimensional wave equation. This approach is applicable only for very low frequencies. Two questions that previous research has left unanswered are at what point the magnetohydrodynamic theory breaks down and how the amplitude of the waves changes as the frequency is increased above the magnetohydrodynamic threshold. This paper seeks to answer these questions by solving the nonhomogenous wave equation in a cold uniform plasma-nonhomogenous in the sense that a known current source is included in the formulation. The current source is assumed to be moving with respect to the background plasma. The method of solution employs a phase integral method to solve the inverse-Fourier transform of the wave equation which leads to a solution asymptotically valid in the far field of the source. Careful examination of the phase integral shows that the minimum distance to the far field depends upon the curvature of the wavenumber surface for the medium. The amplitude and spatial size of shear size of shear-Alfven-wave packets excited by the motion of the source has been found. These wave packets are guided by magnetic field lines at very low frequencies but tend to disperse into individual Fourier components at frequencies near the ion-cyclotron frequency. As the wave packet proceeds away from the source, this filtering action acts to increase the physical size of the packet, with a corresponding decrease in amplitude. Excitation of the shear wave is dominated by the motion of the source and is little affected by a modulation in the source current. The compressional-Alfven wave below the ion-cyclotron frequency and the whistler wave above are not excited to any appreciable extent by the motion of the source. However, pulsation in the tether current can excite these wave modes. The amplitude of the waves has been calculated in the far-field zone for various frequencies of interest. It is found that the distance to the far field is highly dependent upon the wave frequency. For a tether length of 20 kilometers and at frequencies just above the ion cyclotron, the distance to the far field is on the order of hundreds of kilometers. However near the lower hybrid frequency this distance increases to approximately one million kilometers. The method used to find the amplitude of the waves in the far field is not valid in regions of changing plasma densities. Therefore, the subsequent evolution of these waves after excitation has been found by a full wave analysis for frequencies much below the ion-cyclotron frequency and by ray tracing at relatively higher frequencies. The results of this analysis show some waves reaching the ground, some waves guided by the F region density peak in the ionosphere, and some waves propagating into more distant regions of the ionosphere.