Field Line Resonance Frequencies Research Articles

Analytic formulation and quantitative solutions of the coupled ULf wave problem

In the terrestrial magnetosphere, the inhomogeneous magnetic field and plasma density give rise to a continuous spectrum of field line resonant frequencies. Compressional disturbances with characteristic frequencies lying within the range of the spectrum may couple to transverse oscillations of resonant field lines. The coupling is of particular interest for global compressional modes trapped in the magnetic cavity. These modes decay in time through the coupling, even in the absence of dissipation. The importance of the process is that, through the damping of the global modes, large‐scale motion can drive localized field line resonances. In this study, we investigate the mode coupling and examine the parameter dependence of the damping rate of the global mode. The problem is discussed as an initial value problem in the box model which retains most of the significant physics yet remains mathematically tractable. To treat the coupling, we use the analogy of Landau damping in a homogeneous plasma. From the Laplace transform approach, we obtain the complex frequencies of the compressional wave by finding the singularities of the associated Green's function. Once the complex frequency has been found numerically, we obtain the corresponding waveforms in the box. Many observed wave properties can then be obtained. The calculations agree well with other simulation work and correspond to results obtained for the reflection of radio waves from the ionosphere and for plasma heating by absorption of radiation.

The Alfvén wave equation for magnetospheric plasmas

It is shown that besides the continuous spectrum which damps away as inverse power of time, the coupled Alfvén wave equation, which gives coupling between a shear Alfvén wave and a surface wave, can also admit a well behaved harmonic solution in the closed form for a set of initial conditions. This solution, though valid for finite time intervals, points out that the Alfvén surface waves can have a band of frequency (instead of a monochromatic frequency for a nonsheared magnetic field) within which the local field line resonance frequency can lie, and thus can excite magnetic pulsations with latitude‐dependent frequency. By considering magnetic fields not only varying in magnitude but also in direction, it is shown that the time interval for the validity of the harmonic solution depend upon the angle between the magnetic field directions on either side of the magnetopause. For small values of the angle the time interval can become appreciably large.

Coupling of global magnetospheric MHD eigenmodes to field line resonances

Many features of the magnetospheric hydromagnetic wave spectrum are fully understood, but a remaining puzzle is why selected field line resonances appear to be excited by a broadband source. In this paper, we propose that the preferential resonances correspond to global eigenmodes of the magnetospheric cavity. In order to understand the behavior of ultralow frequency waves in the terrestrial magnetosphere (geomagnetic pulsations), we describe the structure of global eigenmodes in the hydromagnetic box model of an inhomogeneous plasma. Global modes are large‐scale modes whose frequencies match field line resonance frequencies somewhere in the system. The coupling between localized field line resonance effects and the large‐scale mode leads to damping of the latter. In the box model the eigenmode equation yields a spectrum of discrete eigenfrequencies. For each eigenfrequency, the equation contains singular points where the field line resonance occurs. We base much of our discussion on earlier works which have used the same equation in other contexts. We describe solutions and then use the results to outline features of the modes that may be observable.