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Title: Dispersive Evolution of Nonlinear Fast Magnetoacoustic Wave Trains

Abstract

Quasi-periodic rapidly propagating wave trains are frequently observed in extreme ultraviolet observations of the solar corona, or are inferred by the quasi-periodic modulation of radio emission. The dispersive nature of fast magnetohydrodynamic waves in coronal structures provides a robust mechanism to explain the detected quasi-periodic patterns. We perform 2D numerical simulations of impulsively generated wave trains in coronal plasma slabs and investigate how the behavior of the trapped and leaky components depend on the properties of the initial perturbation. For large amplitude compressive perturbations, the geometrical dispersion associated with the waveguide suppresses the nonlinear steepening for the trapped wave train. The wave train formed by the leaky components does not experience dispersion once it leaves the waveguide and so can steepen and form shocks. The mechanism we consider can lead to the formation of multiple shock fronts by a single, large amplitude, impulsive event and so can account for quasi-periodic features observed in radio spectra.

Authors:
; ;  [1]
  1. Centre for Fusion, Space and Astrophysics, Department of Physics, University of Warwick, Coventry CV4 7AL (United Kingdom)
Publication Date:
OSTI Identifier:
22654378
Resource Type:
Journal Article
Resource Relation:
Journal Name: Astrophysical Journal Letters; Journal Volume: 847; Journal Issue: 2; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; COMPUTERIZED SIMULATION; DISPERSIONS; DISTURBANCES; EMISSION; EVOLUTION; EXTREME ULTRAVIOLET RADIATION; FAST MAGNETOACOUSTIC WAVES; MAGNETOACOUSTICS; MAGNETOHYDRODYNAMICS; NONLINEAR PROBLEMS; PERIODICITY; PERTURBATION THEORY; PLASMA; SHOCK WAVES; SOLAR CORONA; SPECTRA; SUN; TWO-DIMENSIONAL CALCULATIONS; WAVEGUIDES

Citation Formats

Pascoe, D. J., Goddard, C. R., and Nakariakov, V. M., E-mail: D.J.Pascoe@warwick.ac.uk. Dispersive Evolution of Nonlinear Fast Magnetoacoustic Wave Trains. United States: N. p., 2017. Web. doi:10.3847/2041-8213/AA8DB8.
Pascoe, D. J., Goddard, C. R., & Nakariakov, V. M., E-mail: D.J.Pascoe@warwick.ac.uk. Dispersive Evolution of Nonlinear Fast Magnetoacoustic Wave Trains. United States. doi:10.3847/2041-8213/AA8DB8.
Pascoe, D. J., Goddard, C. R., and Nakariakov, V. M., E-mail: D.J.Pascoe@warwick.ac.uk. 2017. "Dispersive Evolution of Nonlinear Fast Magnetoacoustic Wave Trains". United States. doi:10.3847/2041-8213/AA8DB8.
@article{osti_22654378,
title = {Dispersive Evolution of Nonlinear Fast Magnetoacoustic Wave Trains},
author = {Pascoe, D. J. and Goddard, C. R. and Nakariakov, V. M., E-mail: D.J.Pascoe@warwick.ac.uk},
abstractNote = {Quasi-periodic rapidly propagating wave trains are frequently observed in extreme ultraviolet observations of the solar corona, or are inferred by the quasi-periodic modulation of radio emission. The dispersive nature of fast magnetohydrodynamic waves in coronal structures provides a robust mechanism to explain the detected quasi-periodic patterns. We perform 2D numerical simulations of impulsively generated wave trains in coronal plasma slabs and investigate how the behavior of the trapped and leaky components depend on the properties of the initial perturbation. For large amplitude compressive perturbations, the geometrical dispersion associated with the waveguide suppresses the nonlinear steepening for the trapped wave train. The wave train formed by the leaky components does not experience dispersion once it leaves the waveguide and so can steepen and form shocks. The mechanism we consider can lead to the formation of multiple shock fronts by a single, large amplitude, impulsive event and so can account for quasi-periodic features observed in radio spectra.},
doi = {10.3847/2041-8213/AA8DB8},
journal = {Astrophysical Journal Letters},
number = 2,
volume = 847,
place = {United States},
year = 2017,
month =
}
  • Fast magnetoacoustic waves guided along the magnetic field by plasma non-uniformities, in particular coronal loops, fibrils, and plumes, are known to be highly dispersive, which lead to the formation of quasi-periodic wave trains excited by a broadband impulsive driver, e.g., a solar flare. We investigated the effects of cylindrical geometry on the fast sausage wave train formation. We performed magnetohydrodynamic numerical simulations of fast magnetoacoustic perturbations of a sausage symmetry, propagating from a localized impulsive source along a field-aligned plasma cylinder with a smooth radial profile of the fast speed. The wave trains are found to have pronounced period modulation,more » with the longer instant period seen in the beginning of the wave train. The wave trains also have a pronounced amplitude modulation. Wavelet spectra of the wave trains have characteristic tadpole features, with the broadband large-amplitude heads preceding low-amplitude quasi-monochromatic tails. The mean period of the wave train is about the transverse fast magnetoacoustic transit time across the cylinder. The mean parallel wavelength is about the diameter of the wave-guiding plasma cylinder. Instant periods are longer than the sausage wave cutoff period. The wave train characteristics depend on the fast magnetoacoustic speed in both the internal and external media, the smoothness of the transverse profile of the equilibrium quantities, and also the spatial size of the initial perturbation. If the initial perturbation is localized at the axis of the cylinder, the wave trains contain higher radial harmonics that have shorter periods.« less
  • The nonlinear theory of driven magnetohydrodynamics (MHD) waves in strongly anisotropic and dispersive plasmas, developed for slow resonance by Clack and Ballai [Phys. Plasmas 15, 2310 (2008)] and Alfven resonance by Clack et al. [Astron. Astrophys. 494, 317 (2009)], is used to study the weakly nonlinear interaction of fast magnetoacoustic (FMA) waves in a one-dimensional planar plasma. The magnetic configuration consists of an inhomogeneous magnetic slab sandwiched between two regions of semi-infinite homogeneous magnetic plasmas. Laterally driven FMA waves penetrate the inhomogeneous slab interacting with the localized slow or Alfven dissipative layer and are partly reflected, dissipated, and transmitted bymore » this region. The nonlinearity parameter defined by Clack and Ballai (2008) is assumed to be small and a regular perturbation method is used to obtain analytical solutions in the slow dissipative layer. The effect of dispersion in the slow dissipative layer is to further decrease the coefficient of energy absorption, compared to its standard weakly nonlinear counterpart, and the generation of higher harmonics in the outgoing wave in addition to the fundamental one. The absorption of external drivers at the Alfven resonance is described within the linear MHD with great accuracy.« less
  • The evolution of strongly nonlinear, strongly modulated wave packets is investigated in a dispersive plasma using a hybrid numerical code. These wave packets have amplitudes exceeding the strength of the external magnetic field, along which they propagate. Alfven (left helicity) wave packets show strong steepening for [beta][lt]1, while fast (right helicity) wave packets hardly steepen for any [beta]. Substantial regions of opposite helicity form on the leading side of steepened Alfven wave packets. This behavior differs qualitatively from that exhibited by the solutions to the derivative nonlinear Schroedinger (DNLS) equation.
  • An investigation of the evolution of strongly nonlinear, low frequency (ion gyrofrequency), parallel propagating wave packets in a dispersive, collisionless, and low beta(= 8piP/B-squared = 0.3) plasma is undertaken using a hybrid numerical code. These strongly nonlinear wave packets have a transverse magnetic field strength, or wave amplitude, which is of order or greater the field strength along the direction of propagation, and their evolution can differ qualitatively from that of weakly nonlinear packets. The development of spreading fast wave (right helicity) and rarefraction regions competes strongly with steepening, and leads to a long time waveform which differs greatly frommore » that for weak nonlinearity. Results are used to suggest that strongly nonlinear wave evolution occurs frequently in the earth's foreshock. 18 refs.« less
  • An asymptotic procedure is proposed to describe the slow modulations of dispersive wave trains when the dispersive effects and the nonlinear distorsion are of the same order of magnitude. For a model equation, the system of modulation equations is derived up to the second order. At this order of approximation, it is seen that the dispersion relation includes partial derivatives not only of the amplitude but also of the wave vector components. Under some assumptions, a partial differential equation is obtained for the complex amplitude. This equation reveals common features with the modified Korteweg-de Vries equation and with a nonlinearmore » Schroedinger equation. At the first order, it reduces to the cubic Schroedinger equation which had been directly obtained by several authors. Finally, the theory is applied to a plasma wave example.« less