Nonlinear dynamics of fast magnetosonic 
waves ducted by a smooth plasma inhomogeneity

Nakariakov, V. M.; Roberts, B.; Petrukhin, N. S.

doi:10.1017/s0022377897005710

Cited by 16 publications

(11 citation statements)

References 16 publications

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“…If the density profile is smoother than that critical value, the group speed decreases gradually with the wave number. The group speed dependence on the wave number also has important implications for nonlinear phenomena, in particular, the modulational instability (Nakariakov et al 1997). These days the actual steepness of Send offprint requests to: V. Nakariakov, e-mail: valery@astro.warwick.ac.uk density profiles in the loops is a subject of an intensive discussion in connection with interpretation of the quick decay of coronal loop kink oscillations Ofman & Aschwanden 2002;Goossens et al 2002).…”

Section: Introductionmentioning

confidence: 99%

Short period fast waves in solar coronal loops

Cooper¹,

Nakariakov²,

Williams³

2003

A&A

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Abstract. Short period fast magnetoacoustic waves propagating along solar coronal loops, perturbing the loop boundary along the line of sight (LOS), may be observed by imaging telescopes. The relationship between the difference in emission intensity, the angle between the LOS and the direction of propagation and the wave amplitude and wavelength, is explored for kink and sausage fast waves. It is shown that the compressibility of the plasma in the loop significantly affects the observability of the waves. For both wave types there is an optimal observation angle which is determined by the ratio of the wave length and the loop radius. The change of the observational conditions because of the loop curvature predicts a significant, up to an order of magnitude, change in the observed wave amplitude. This prediction is confirmed by the analysis of the evolution of the fast wave train amplitude, observed with the SECIS instrument. The wave train amplitude experiences a sharp increase and then a decrease along the loop. The observational results are in a good agreement with the theory.

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Section: Introductionmentioning

confidence: 99%

Short period fast waves in solar coronal loops

Cooper¹,

Nakariakov²,

Williams³

2003

A&A

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“…The last mechanism has two stages: nonlinear generation of second harmonics and interaction of the second harmonics with a backward wave. In the case of magnetoacoustic waves, both mechanisms are acting together (Nakariakov et al, 1997b) leading to the appearance of a cubically nonlinear term in the evolutionary equation. Obviously, the cubically nonlinear effects should be taken into account only when quadratically nonlinear processes are suppressed due to, e.g., linear high frequency dispersion.…”

Section: Discussionmentioning

confidence: 99%

Magnetoacoustic Waves of Small Amplitude in Optically Thin Quasi‐isentropic Plasmas

Nakariakov

Mendoza-Briceño

Ibáñez

2000

ApJ

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The evolution of quasi-isentropic magnetohydrodynamic waves of small but finite amplitude in an optically thin plasma is analyzed. The plasma is assumed to be initially homogeneous, in thermal equilibrium and with a straight and homogeneous magnetic field frozen in. Depending on the particular form of the heating/cooling function, the plasma may act as a dissipative or active medium for magnetoacoustic waves, while Alfvén waves are not directly affected. An evolutionary equation for fast and slow magnetoacoustic waves in the single wave limit, has been derived and solved, allowing us to analyse the wave modification by competition of weakly nonlinear and quasiisentropic effects. It was shown that the sign of the quasi-isentropic term determines the scenario of the evolution, either dissipative or active. In the dissipative case, when the plasma is first order isentropically stable the magnetoacoustic waves are damped and the time for shock wave formation is delayed. However, in the active case when the plasma is isentropically overstable, the wave amplitude grows, the strength of the shock increases and the breaking time decreases. The magnitude of the above effects depends upon the angle between the wave vector and the magnetic field. For hot (T > 10 4 K) atomic plasmas with solar abundances either in the interstellar medium or in the solar atmosphere, as well as for the cold (T < 10 3 K) ISM molecular gas, the range of temperature where the plasma is isentropically unstable and the corresponding time and length-scale for wave breaking have been found.

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“…In particular, it means that for this choice of geometry if Alfvén waves are initially absent, they cannot be produced by nonlinearities (Nakariakov et al, 1997). The exponentially oscillating term in (35) plays a fundamental role in the closure procedure: its exponent should not vanish when k = κ + L. We shall look now for the resonant manifold's solution of the system…”

Section: Mhd Wavesmentioning

confidence: 99%

On wave turbulence in MHD

Galtier

Nazarenko

Newell

2001

Nonlin. Processes Geophys.

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Abstract. We describe the fundamental differences between weak (wave) turbulence in incompressible and weakly compressible MHD at the level of three-wave interactions. The main difference is in the structure of the resonant manifolds and the mechanisms of redistribution of spectral densities along the applied magnetic field B 0 . Similar to pure acoustic waves, a three-wave resonance between collinear wavevectors is observed but, in addition, we also have a resonance through tilted planes and spheres. The properties of resonances and their consequences for the asymptotics are also discussed.

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Nonlinear dynamics of fast magnetosonic waves ducted by a smooth plasma inhomogeneity

Cited by 16 publications

References 16 publications

Short period fast waves in solar coronal loops

Short period fast waves in solar coronal loops

Magnetoacoustic Waves of Small Amplitude in Optically Thin Quasi‐isentropic Plasmas

On wave turbulence in MHD

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