Coupling of magnetospheric cavity modes to field line resonances: A study of resonance widths

Abstract

By using a box model for the magnetosphere and by using a matrix eigenvalue method to solve the cold hnearized ideal MHD equations, we examine the temporal evolution of the irreversible coupling between fast magnetospheric cavity modes and field hne resonances (FLRs). By considering the fast mode frequency to be of the form wy = wy• -iwyi, and using a Fourier transform approach, we have determined the full time-dependent evolution of resonance energy widths. We find that at short times the resonances are broad, and narrower widths continue to develop in time. Ultimately, an asymptotic resonance Alfv6n frequency full width at half maximum (FWHM) of Aw• = 2coyi develops on a timescale of ryi -c0•/1. On timescales longer than ryi, we find that the resonance perturbations can continue to develop even finer scales by phase mixing. Thus, at any time, the finest scales within the resonance are governed by the phase mixing length Lph(t) -2•r (tdwA/dx) -1. The combination of these two effects naturally explains the localisation of pulsations in L shells observed in data, and the finer perturbation scales which may exist within them. During their evolution, FLRs may have their finest perturbation scales limited by either ionospheric dissipation or by kinetic effects (including the breakdown of single fluid MHD). For a continually driven resonance, we define an ionospheric limiting timescale wI in terms of the height-integrated Pealersen conductivity Ep, and hence derive a limiting ionospheric perturbation scale Li -2•r(ri&oA/dx) -1, in agreement with previous steady state analyses. For sufficiently high •p, FLR might be able to evolve so that their radial scales reach a kinetic scale length Lk. For this to occur, we require the pulsations to live for longer than r/• -27r (LkdcoA/dx) -1. For t < r/•, ri, kinetic effects and ionospheric dissipation are not dominant, and the ideal MHD results presented here may be expected to model realistically the growth phase of ULF pulsations. ground-based magnetometers, in the form of ultralow frequency (ULF) waves standing on dipolar field lines. The Doppler signatures of these pulsations are also of-Copyright 1995 by the American Geophysical Union. Paper number 95JA00820. 0148-0227/95/95JA-00820505.00 ten observed by HF radar at the ionospheric footpoints of oscillating field lines. Dungey [1954, 1967] first suggested that pulsations were standing Alfvdn waves on dipolar field lines (toroidal modes). He also identified fast poloidal compressional waves, which should propagate across the background magnetic field, and subsequently completed the first decoupled studies of these modes. Southwood [1974] and Chen and Hasegawa [1974] independently presented the first attempts at a full theoretical analysis of the coupled pulsation problem. They proposed that the solar wind, incident upon the magnetospheric cavity and driving magnetosheath flows, could excite a travelling Kelvin-Helmholtz surface wave on the magnetopause. Having an evanescent structure within the magnetosphere, this wave mode...

Development of parallel electric fields at the plasma sheet boundary layer

“…In such a situation, Alfvén phase fronts that cross the gradient will be sheared, decreasing the perpendicular wavelength of these waves, a phenomenon known as phase mixing and often invoked in studies of field line resonances [e.g., Wei et al, 1994;Mann et al, 1995]. Phase mixing at the plasma sheet boundary layer has been discussed by Allan and Wright [1998] and more recently by Lysak et al [2009].…”

“…Here S A = 1/m 0 V A , and is sometimes called the Alfvén wave conductance (more properly, an admittance). An estimate of the width of the field line resonance can be given by finding the decrease in scale length in one damping time, giving L damp ∼ n/w′ 0 ∼ (n/w 0 )L 0 [e.g., Mann et al, 1995], where L 0 is the gradient scale length. Thus for weak damping, phase mixing can produce structures much smaller than the original gradient scale length.…”

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

“…In the lossy case, the damping of the excitation must increase in step with the ionospheric loss to maintain the resonance condition. Again, as in the lossless case [Mann et al, 1995], the dynamic spectral width of the response approaches zero with time under the resonance condition. However, with ionospheric loss, the amplitude of the resonance response also approaches zero with time, and thus this limiting spectral width is not physically observable.…”

“…As the ionospheric loss increases and/or as the decay rate of the excitation signal increases, the interval between the onset of the excitation and the time of maximum response decreases. Since the dynamic spectral width of the response decreases with the duration of excitation [Mann et al, 1995] We have produced a possible explanation for the AMPTE/CCE observations in terms of waveguide modes. A propagating wave packet, which may be described as a combination of such modes, has now been observed [Mann et al, 1998].…”

“…First of all, the excitation is short-lived, i.e., decidedly not monochromatic. Second, for excitations of interest, FLR widths diminish with time [Mann et al, 1995], and the ionospheric damping of these resonances in concert with their short-lived excitation ensures that they are time-limited. The widths most likely to be observed are those corresponding to a time near that of the maximum amplitude of the pulsation.…”