A Physical Explanation of Difficulties Appearing in the Theory of Toroidal Magnetohydrodynamic Oscillations

Burghes, David; Kendall, P.C.; Sweet, P. A.

doi:10.1093/mnras/143.1.9

Cited by 14 publications

(5 citation statements)

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“…Initially, the width is governed by the phase mixing length (as mentioned above), which determines the smallest scales appearing in the domain. Phase mixing is the process by which neighboring field lines drift out of phase over time, due to the inhomogeneous background Alfvén frequency [ Burghes et al , ; Heyvaerts and Priest , ], which creates steep gradients in space. Dissipation limits the phase mixing length, such that the scales do not decrease indefinitely.…”

Section: Resultsmentioning

confidence: 99%

The theoretical foundation of 3‐D Alfvén resonances: Time‐dependent solutions

Elsden

Wright

2017

JGR Space Physics

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We present results from a 3‐D numerical simulation which investigates the coupling of fast and Alfvén magnetohydrodynamic (MHD) waves in a nonuniform dipole equilibrium. This represents the time‐dependent extension of the normal mode ( ∝exp(−iωt)) analysis of Wright and Elsden (2016) and provides a theoretical basis for understanding 3‐D Alfvén resonances. Wright and Elsden (2016) show that these are fundamentally different to resonances in 1‐D and 2‐D. We demonstrate the temporal behavior of the Alfvén resonance, which is formed within the “Resonant Zone”; a channel of the domain where a family of solutions exists such that the natural Alfvén frequency matches the fast‐mode frequency. At early times, phase mixing leads to the production of prominent ridges in the energy density, whose shape is determined by the Alfvén speed profile and the chosen background magnetic field geometry. These off resonant ridges decay in time, leaving only a main 3‐D resonant sheet in the steady state. We show that the width of the 3‐D resonance in time and in space can be accurately estimated by adapting previous analytical estimates from 1‐D theory. We further provide an analytical estimate for the resonance amplitude in 3‐D, based upon extending 2‐D theory.

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Section: Resultsmentioning

confidence: 99%

The theoretical foundation of 3‐D Alfvén resonances: Time‐dependent solutions

Elsden

Wright

2017

JGR Space Physics

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“…The other process at work is phase mixing (Pridmore-Brown 1966; Burghes et al 1969;Tataronis & Grossmann 1973;Hasegawa & Chen 1974;Heyvaerts & Priest 1983). Returning to Fig.…”

Section: Alfvén Wavesmentioning

confidence: 99%

Solar flares and focused energy transport by MHD waves

Russell

Stackhouse

2013

A&A

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Context. Transport of flare energy from the corona to the chromosphere has traditionally been assigned to electron beams; however, interest has recently been renewed in magnetohydrodynamic (MHD) waves as a complementary or alternative mechanism. Aims. We determine whether, and under what conditions, MHD waves deliver spatially localised energy to the chromosphere, as required if MHD waves are to contribute to emission from flare ribbons and kernels. This paper also highlights several properties of MHD waves that are relevant to solar flares and demonstrates their application to the flare problem. Methods. Transport is investigated using a magnetic arcade model and 2.5D MHD simulations. Different wave polarisations are considered and the effect of fine structuring transverse to the magnetic field is also examined. Ray tracing provides additional insight into the evolution of waveguided fast waves. Results. Alfvén waves are very effective at delivering energy fluxes to small areas of chromosphere, localisation being enhanced by magnetic field convergence and phase mixing. Fast waves, in the absence of fine coronal structure, are more suited to powering emission from diffuse rather than compact sources; however, fast waves can be strongly localised by coronal waveguides, in which case focused energy is best transported to the chromosphere when waveguides are directly excited by the energy release. Conclusions. MHD waves pass an important test for inclusion in future flare models.

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“…In ideal MHD there is no mechanism for dissipation of the energy in the field line continuum. Burghes et al [ 1969] showed how the small dissipative quantities (magnetic viscosity r/and kinematic viscosity v) neglected in ideal MHD must become significant after some finite time, and lead to rapid decay of the energy in the continuum oscillations. This process was termed "phase mixing" by Heyvaerts and Priest [1983].…”

Section: Phase Mixing In the Magnetospherementioning

confidence: 99%

Damping of magnetospheric cavity modes: A discussion

Allan¹,

Poulter²

1989

J. Geophys. Res.

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Impulsive changes in the solar wind can deposit energy into magnetospheric cavity modes. We discuss the coupling of cavity modes to the field line continuum, and show that the time scales for dissipative phase mixing and mode conversion to kinetic Alfvén waves in the magnetosphere are long compared with lifetimes of MHD wave events with periods that vary continuously with radial distance. Therefore the ultimate dissipative sink for cavity mode energy should be the ionosphere. For model magnetospheres in which all wave components have a complex field aligned wave number kz = kz0 (1+iκ) to simulate a Poynting flux into the ionosphere, we use simple arguments to show that the coupled cavity mode damping decrement is given approximately by γ/ω0 = (γ/ω0)c + (kz0/k)² κ. Here (γ/ω0)c is the damping via coupling to the field line continuum alone, and k is the total wave number magnitude. Detailed numerical calculations in a cylindrical magnetospheric model support this, although significant departures from the approximate expression can occur for small κ. Following earlier work by other authors, we emphasize that complex kz may not simulate the appropriate boundary condition for the coupled cavity mode outside resonance regions.

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A Physical Explanation of Difficulties Appearing in the Theory of Toroidal Magnetohydrodynamic Oscillations

Cited by 14 publications

References 0 publications

The theoretical foundation of 3‐D Alfvén resonances: Time‐dependent solutions

The theoretical foundation of 3‐D Alfvén resonances: Time‐dependent solutions

Solar flares and focused energy transport by MHD waves

Damping of magnetospheric cavity modes: A discussion

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