Slow magnetohydrodynamic waves in the solar atmosphere

There is increasingly strong observational evidence that slow magnetoacoustic modes arise in the solar atmosphere, either as propagating or standing waves. Sunspots, coronal plumes and coronal loops all appear to support slow modes. Here we examine theoretically how the slow mode may be extracted from the magnetohydrodynamic equations, considering the special case of a vertical magnetic field in a stratified medium: the slow mode is described by the Klein–Gordon equation. We consider its application to recent observations of slow waves in coronal loops.

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Mode Coupling in the Solar Corona. IV. Magnetohydrodynamic Waves

Australian Journal of Physics ◽

10.1071/ph770647 ◽

1977 ◽

Vol 30 (6) ◽

pp. 647 ◽

Cited By ~ 4

Author(s):

DB Melrose ◽

MA Simpson

Keyword(s):

General Theory ◽

Solar Corona ◽

Mode Coupling ◽

Stratified Medium ◽

Mhd Waves ◽

Fast Mode ◽

Slow Mode ◽

Magnetohydrodynamic Waves ◽

Quartic Equation ◽

Obliquely Incident

A general theory for coupling between MHD waves obliquely incident on a stratified medium is developed. Coupling between the Alfvtln mode and the magnetoacoustic mode (the fast mode for VA > cs and the slow mode for VA < cs) is affected little by the finiteness of Cs/VA for VA >> Cs and the coupling becomes weaker as Cs/VA is increased towards unity. Coupling between the fast and slow modes for VA ≈ C. is discussed qualitatively using solutions of the MHD counterpart of the Booker quartic equation.

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Magneto-seismology of solar atmospheric loops by means of longitudinal oscillations

Proceedings of the International Astronomical Union ◽

10.1017/s1743921312005224 ◽

2011 ◽

Vol 7 (S286) ◽

pp. 437-440

Author(s):

M. Luna-Cardozo ◽

G. Verth ◽

R. Erdélyi

Keyword(s):

Solar Atmosphere ◽

Wave Theory ◽

Observational Evidence ◽

Coronal Loops ◽

Density Structure ◽

Magnetoacoustic Waves

AbstractThere is increasingly strong observational evidence that slow magnetoacoustic modes arise in the solar atmosphere. Solar magneto-seismology is a novel tool to derive otherwise directly un-measurable properties of the solar atmosphere when magnetohydrodynamic (MHD) wave theory is compared to wave observations. Here, MHD wave theory is further developed illustrating how information about the magnetic and density structure along coronal loops can be determined by measuring the frequencies of the slow MHD oscillations. The application to observations of slow magnetoacoustic waves in coronal loops is discussed.

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APPROXIMATE ℓ-STATE SOLUTIONS OF A SPIN-0 PARTICLE FOR WOODS–SAXON POTENTIAL

International Journal of Modern Physics C ◽

10.1142/s0129183109013881 ◽

2009 ◽

Vol 20 (04) ◽

pp. 651-665 ◽

Cited By ~ 11

Author(s):

ALTUĞ ARDA ◽

RAMAZAN SEVER

Keyword(s):

Schrodinger Equation ◽

Bound States ◽

Gordon Equation ◽

Saxon Potential ◽

Radial Part ◽

Centrifugal Barrier ◽

Klein Gordon ◽

Uvarov Method ◽

Special Case ◽

Klein Gordon Equation

The radial part of Klein–Gordon equation is solved for the Woods–Saxon potential within the framework of an approximation to the centrifugal barrier. The bound states and the corresponding normalized eigenfunctions of the Woods–Saxon potential are computed by using the Nikiforov–Uvarov method. The results are consistent with the ones obtained in the case of generalized Woods–Saxon potential. The solutions of the Schrödinger equation by using the same approximation are also studied as a special case, and obtained the consistent results with the ones obtained before.

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A COMPLEX FINSLER APPROACH OF GRAVITY

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887812500582 ◽

2012 ◽

Vol 09 (07) ◽

pp. 1250058 ◽

Cited By ~ 2

Author(s):

GHEORGHE MUNTEANU ◽

NICOLETA ALDEA

Keyword(s):

Gordon Equation ◽

Finsler Metric ◽

Energy Relation ◽

Two Dimensional ◽

Curvature Invariant ◽

Plane Wave Solution ◽

Curvature Invariants ◽

Complex Finsler Metric ◽

Klein Gordon ◽

Special Case

In this paper our aim is mainly to obtain a two-dimensional complex Finsler model of the real gravitation space-time. We prove that, at least in the special case of the weakly gravitational field, this is possible and it leads to some interesting geometrical and physical aspects, such as the study of curvature invariants with respect to complex Berwald frame, intensively studied recently by us for a two-dimensional complex Finsler space. A generalization of the Klein–Gordon equation is proposed and we find solutions which are in concordance to the classical plane wave solution of momentum-energy relation. The last part of the paper is devoted to some applications in which the complex gravitational potential leads to the Bergman metric and to a more general case which leads to a non-purely Hermitian complex Finsler metric, with negative curvature invariant.

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Magnetohydrodynamic waves and coronal seismology: an overview of recent results

Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rsta.2011.0640 ◽

2012 ◽

Vol 370 (1970) ◽

pp. 3193-3216 ◽

Cited By ~ 230

Author(s):

Ineke De Moortel ◽

Valery M. Nakariakov

Keyword(s):

Solar Atmosphere ◽

Solar Flares ◽

Mhd Waves ◽

Alfvén Waves ◽

Coronal Loops ◽

Magnetohydrodynamic Waves ◽

Coronal Seismology ◽

Wide Range ◽

Current Controversy ◽

Intense Debate

Recent observations have revealed that magnetohydrodynamic (MHD) waves and oscillations are ubiquitous in the solar atmosphere, with a wide range of periods. We give a brief review of some aspects of MHD waves and coronal seismology that have recently been the focus of intense debate or are newly emerging. In particular, we focus on four topics: (i) the current controversy surrounding propagating intensity perturbations along coronal loops, (ii) the interpretation of propagating transverse loop oscillations, (iii) the ongoing search for coronal (torsional) Alfvén waves, and (iv) the rapidly developing topic of quasi-periodic pulsations in solar flares.

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Die Unschärferelation in den Dirac-Gleichungen und in der relativistischen Schrödinger-Gleichung

Zeitschrift für Naturforschung A ◽

10.1515/zna-1956-0201 ◽

1956 ◽

Vol 11 (2) ◽

pp. 101-118

Author(s):

Henning Harmuth

Keyword(s):

Difference Equation ◽

Uncertainty Relation ◽

Gordon Equation ◽

Schroedinger Equation ◽

Precise Position ◽

Relativistic Mass ◽

Klein Gordon ◽

Mass Increase ◽

Special Case ◽

Klein Gordon Equation

HEISENBERG’S uncertainty relation results as condition for convergence of the solution of a difference equation which is an analogue to the SCHROEDINGER equation. From DIRAC’S equations and the relativistic SCHROEDINGER equation (KLEIN-GORDON equation) — written as difference equations — one obtains in the same manner a generalized uncertainty relation, from which HEISENBERG’S is derived as a special case for negligible relativistic mass increase and not too precise position and time measurements.

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