Dispersion and wave coupling in inhomogeneous MHD waveguides

Abstract

The propagation of the fast mode is considered in nonuniform waveguides. We show how the natural dispersion inherent in a waveguide will select waveguide modes with a small wavenumber (ky) along the guide to remain near a localized source region of fast mode energy. It is these modes that are shown to have a coherent periodic time dependence over many cycles that are suitable for driving observable Alfvén resonances (magnetic pulsations). We expect the frequencies of Alfvén resonances to be very close to the eigenfrequencies of waveguide modes with ky = 0.

Time‐limited excitation of damped field‐line resonances: Implications for satellite observations

“…(24)] was used to obtain the waveguide cutoff frequencies for each of (j,k), which together define a waveguide mode, where k is the radial harmonic and j is the field-line harmonic. These cutoff frequencies closely approximate the optimum frequency of excitation of shear mode oscillations by the waveguide mode [Wright, 1994].…”

“…The question of whether such excitation is physically reasonable is, at this point, a separate issue. If the magnetopause is perturbed over this frequency band consistent with the above description, what would the consequence be in terms of the magnetospheric waveguide model [Wright, 1994]? Wright [1994] showed that those waveguide mode signals which are effective in coupling to FLRs must have frequencies close to but just above the cutoff frequency of one of the waveguide modes.…”

“…If the magnetopause is perturbed over this frequency band consistent with the above description, what would the consequence be in terms of the magnetospheric waveguide model [Wright, 1994]? Wright [1994] showed that those waveguide mode signals which are effective in coupling to FLRs must have frequencies close to but just above the cutoff frequency of one of the waveguide modes. Signal energy at higher frequencies in one of these modes will propagate along the waveguide initially at increasingly larger velocity as the frequency increases and later at relatively high velocity [Wright, 1994].…”

“…Wright [1994] showed that those waveguide mode signals which are effective in coupling to FLRs must have frequencies close to but just above the cutoff frequency of one of the waveguide modes. Signal energy at higher frequencies in one of these modes will propagate along the waveguide initially at increasingly larger velocity as the frequency increases and later at relatively high velocity [Wright, 1994]. This diminishes the contact interval that such an excitation signal will have with any given resonant flux tube.…”

Compressional MHD waves in the magnetosphere: A new approach

“…When the timescale of such wave coupling and ohmic dissipation is not so relatively small, it becomes an important issue how these compressional waves behave inside the magnetosphere, especially in comparison with observations. One of the efforts made in the last decade was the introduction of cavity modes Southwood, 1985, 1986; Allan el al., 1985; Lee and Lysak, 1989] and waveguide modes [Samson el al., 1992;Wright, 1994]. Both scenarios are based on the assumption that the magnetospheric domain is well defined by relatively sharp boundaries such as the magnetopause and the bow shock where the physical quantities undergo strong gradients.…”