Fast magnetoacoustic wave trains with time-dependent drivers

Abstract

Context. Frequent observations of quasi-periodic rapidly-propagating wave trains in coronal structures have been made in the last decade. The dispersive evolution of fast magnetohydrodynamic waves propagating in coronal waveguides can provide a physical interpretation for many of these observations. Aims. Previous studies have considered the generation of fast wave trains by impulsive drivers which deposit energy instantaneously. The signatures of dispersively formed wave trains must depend on the temporal nature of the driver. We investigate the effect of varying the temporal width of the driving perturbation. Methods. 2D magnetohydrodynamic numerical simulations of impulsively generated wave trains in a guiding field-aligned density enhancement were performed with the novel addition of a time-dependant driver. Results. The final spatial and spectral signatures of the guided wave trains are found to depend strongly on the temporal duration of the initial perturbation. In particular, the wavelength (or frequency) of highest spectral amplitude is found to increase (decrease) with increasing temporal duration, whereas the spectral width decreases. Additionally, the efficiency of generation of fast wave trains is found to decrease strongly with increasing temporal width of the driver, with a cut-off at twice the internal Alfvén crossing time.

Observational signatures of the third harmonic in a decaying kink oscillation of a coronal loop

“…It is also possible that the temporal profile of the driver could influence the generation of higher harmonics, since an impulsive driver localised in space and time is broadband in k − ω space and allows a wide range of frequencies to be excited. This was recently demonstrated for the case of propagating sausage modes (Goddard et al 2019). Either way we might expect the fifth harmonic to also be present with an amplitude about an order of magnitude weaker than the third harmonic, though that would be undetectable because of its very small period of oscillation, damping rate, and amplitude.…”

Fast magnetoacoustic wave trains: from tadpoles to boomerangs

“…A similar conclusion was drawn in a more recent work by Yu et al (2017), who found that a spatial extent of the initial impulsive driver has to be comparable to the waveguide width for the effective formation of quasi-periodic fast wave trains. Likewise, Goddard et al (2019) demonstrated that the efficiency of generation of fast wave trains strongly decreases with increasing temporal duration of the impulsive driver. Hence, we expect that the drivers less localised in space and time would lead to a less efficient formation of essentially broadband boomerang-shaped fast wave trains.…”

Magnetohydrodynamic Fast Sausage Waves in the Solar Corona

“…It is just that there are certain requirements for the sketch to apply, with the need to sample a wavetrain at a distance sufficiently far from the exciter already implied in Equation ( 7). On top of that, some further time-dependent simulations have suggested that the duration of the exciter needs to be R/v Ai (Goddard et al 2019), and the spatial extent of the exciter needs to be comparable to the waveguide radius (Yu et al 2017). We take these requirements as encouraging rather than discouraging for one to further examine impulsive wavetrains, because the deviations of the signatures of observed wavetrains from the sketch actually encode a rich set of seismic information on, say, the exciters.…”

“…Implied by R08 is that the temporal signatures of WTs are determined essentially by the dispersive properties of FSMs, which in turn depend only on the equilibrium. However, time-dependent simulations indicated that these signatures depend on the details of the initial perturbations as well, the temporal (Goddard et al 2019) and spatial extent (e.g., Shestov et al 2015) in particular. This latter point was evident already in Equation ( 6).…”