scholarly journals Resonant absorption of kink oscillations in coronal flux tubes with continuous magnetic twist

2019 ◽  
Vol 490 (2) ◽  
pp. 1644-1651 ◽  
Author(s):  
Zanyar Ebrahimi ◽  
Karam Bahari
Keyword(s):  
Magnetic Field ◽  
Resonant Absorption ◽  
Realistic Model ◽  
Mhd Equations ◽  
Flux Tubes ◽  
Kink Mode ◽  
Background Magnetic Field ◽  
Inhomogeneous Density ◽  
Kink Wave ◽  
Kink Waves

ABSTRACT There are observational evidences for the existence of twisted magnetic field in the solar corona. Here, we have investigated resonant damping of the magnetohydrodynamic (MHD) kink waves in magnetic flux tubes. A realistic model of the tube with continuous magnetic twist and radially inhomogeneous density profile has been considered. We have obtained the dispersion relation of the kink wave using the solution to the linear MHD equations outside the density inhomogeneity and the appropriate connection formula to the solutions across the thin transitional boundary layer. The dependence of the oscillation frequency and damping rate of the waves on the twist parameter and longitudinal wavenumber has been investigated. For the flux tube parameters considered in this paper, we obtain rapid damping of the kink waves comparable to the observations. In order to justify this rapid damping, depending on the sign of the azimuthal kink mode number, $m=+1$ or $-1$, the background magnetic field must have left- or right-handed twisted profile, respectively. For the model considered here, the resonant absorption occurs only when the twist parameter is in a range specified by the density contrast.

The energy and helicity of knotted magnetic flux tubes

1995 ◽  
Vol 451 (1943) ◽  
pp. 609-629 ◽  
Keyword(s):  
Magnetic Field ◽  
Magnetic Energy ◽  
Minimum Energy ◽  
Circular Cross Section ◽  
Parametric Representation ◽  
Energy Functional ◽  
Helical Axis ◽  
Torus Knots ◽  
Flux Tubes ◽  
Kink Mode

Magnetic relaxation of a magnetic field embedded in a perfectly conducting incompressible fluid to minimum energy magnetostatic equilibrium states is considered. It is supposed that the magnetic field is confined to a single flux tube which may be knotted. A local non-orthogonal coordinate system, zero-framed with respect to the knot, is introduced, and the field is decomposed into toroidal and poloidal ingredients with respect to this system. The helicity of the field is then determined; this vanishes for a field that is either purely toroidal or purely poloidal. The magnetic energy functional is calculated under the simplifying assumptions that the tube is axially uniform and of circular cross-section. The case of a tube with helical axis is first considered, and new results concerning kink mode instability and associated bifurcations are obtained. The case of flux tubes in the form of torus knots is then considered and the ‘ground-state’ energy function ͞m ( h ) (where h is an internal twist parameter) is obtained; as expected, ͞m ( h ), which is a topological invariant of the knot, increases with increasing knot complexity. The function ͞m ( h ) provides an upper bound on the corresponding function m ( h ) that applies when the above constraints on tube structure are removed. The technique is applicable to any knot admitting a parametric representation, on condition that points of vanishing curvature are excluded.

scholarly journals Global stability solution of the 2D MHD equations with mixed partial dissipation

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yana Guo ◽  
Yan Jia ◽  
Bo-Qing Dong
Keyword(s):  
Magnetic Field ◽  
Global Stability ◽  
Mhd Equations ◽  
Bootstrap Argument ◽  
Partial Dissipation ◽  
Background Magnetic Field ◽  
Mhd System

<p style='text-indent:20px;'>This paper is devoted to understanding the global stability of perturbations near a background magnetic field of the 2D magnetohydrodynamic (MHD) equations with partial dissipation. We establish the global stability for the solutions of the nonlinear MHD system by the bootstrap argument.</p>

scholarly journals 3D YSO accretion shock simulations: a study of the magnetic, chromospheric and stochastic flow effects

2013 ◽  
Vol 9 (S302) ◽  
pp. 66-69 ◽  
Author(s):  
T. Matsakos ◽  
J.-P. Chièze ◽  
C. Stehlé ◽  
M. González ◽  
L. Ibgui ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Dynamical Evolution ◽  
Acoustic Energy ◽  
Local Magnetic Field ◽  
Flux Tubes ◽  
Background Magnetic Field ◽  
Post Shock ◽  
Uniform Background ◽  
Flow Effects ◽  
Accretion Shock

AbstractThe structure and dynamics of young stellar object (YSO) accretion shocks depend strongly on the local magnetic field strength and configuration, as well as on the radiative transfer effects responsible for the energy losses. We present the first 3D YSO shock simulations of the interior of the stream, assuming a uniform background magnetic field, a clumpy infalling gas, and an acoustic energy flux flowing at the base of the chromosphere. We study the dynamical evolution and the post-shock structure as a function of the plasma-beta (thermal pressure over magnetic pressure). We find that a strong magnetic field (~hundreds of Gauss) leads to the formation of fibrils in the shocked gas due to the plasma confinement within flux tubes. The corresponding emission is smooth and fully distinguishable from the case of a weak magnetic field (~tenths of Gauss) where the hot slab demonstrates chaotic motion and oscillates periodically.

Magnetosonic solitons in space plasmas: dark or bright solitons?

2007 ◽  
Vol 73 (6) ◽  
pp. 981-992 ◽  
Author(s):  
O. A. POKHOTELOV ◽  
O.G. ONISHCHENKO ◽  
M. A. BALIKHIN ◽  
L. STENFLO ◽  
P. K. SHUKLA
Keyword(s):  
Magnetic Field ◽  
Distribution Function ◽  
Velocity Distribution Function ◽  
Mhd Equations ◽  
Space Plasmas ◽  
Ion Distribution ◽  
Loss Cone ◽  
Solitary Solution ◽  
Background Magnetic Field ◽  
The Magnetic Field

AbstractThe nonlinear theory of large-amplitude magnetosonic (MS) waves in highβ space plasmas is revisited. It is shown that solitary waves can exist in the form of ‘bright’ or ‘dark’ solitons in which the magnetic field is increased or decreased relative to the background magnetic field. This depends on the shape of the equilibrium ion distribution function. The basic parameter that controls the nonlinear structure is the wave dispersion, which can be either positive or negative. A general dispersion relation for MS waves propagating perpendicularly to the external magnetic field in a plasma with an arbitrary velocity distribution function is derived.It takes into account general plasma equilibria, such as the Dory–Guest–Harris (DGH) or Kennel–Ashour-Abdalla (KA) loss-cone equilibria, as well as distributions with a power-law velocity dependence that can be modelled by κdistributions. It is shown that in a bi-Maxwellian plasma the dispersion is negative, i.e. the phase velocity decreases with an increase of the wavenumber. This means that the solitary solution in this case has the form of a ‘bright’ soliton with the magnetic field increased. On the contrary, in some non-Maxwellian plasmas, such as those with ring-type ion distributions or DGH plasmas, the solitary solution may have the form of a magnetic hole. The results of similar investigations based on nonlinear Hall–MHD equations are reviewed. The relevance of our theoretical results to existing satellite wave observations is outlined.

scholarly journals Non-Linear Damping of Surface Alfvén Waves Due to Uniturbulence

2022 ◽  
Vol 8 ◽  
Author(s):  
Rajab Ismayilli ◽  
Tom Van Doorsselaere ◽  
Marcel Goossens ◽  
Norbert Magyar
Keyword(s):  
Magnetic Field ◽  
Alfven Waves ◽  
Equilibrium Density ◽  
Alfvén Waves ◽  
Constant Density ◽  
Analytical Prediction ◽  
Background Magnetic Field ◽  
Kink Waves ◽  
Linear Damping ◽  
Analytical Expressions

This investigation is concerned with uniturbulence associated with surface Alfvén waves that exist in a Cartesian equilibrium model with a constant magnetic field and a piece-wise constant density. The surface where the equilibrium density changes in a discontinuous manner are the source of surface Alfvén waves. These surface Alfvén waves create uniturbulence because of the variation of the density across the background magnetic field. The damping of the surface Alfvén waves due to uniturbulence is determined using the Elsässer formulation. Analytical expressions for the wave energy density, the energy cascade, and the damping time are derived. The study of uniturbulence due to surface Alfvén waves is inspired by the observation that (the fundamental radial mode of) kink waves behave similarly to surface Alfvén waves. The results for this relatively simple case of surface Alfvén waves can help us understand the more complicated case of kink waves in cylinders. We perform a series of 3D ideal MHD simulations for a numerical demonstration of the non-linearly self-cascading model of unidirectional surface Alfvén waves using the code MPI-AMRVAC. We show that surface Alfvén waves damping time in the numerical simulations follows well our analytical prediction for that quantity. Analytical theory and the simulations show that the damping time is inversely proportional to the amplitude of the surface Alfvén waves and the density contrast. This unidirectional cascade may play a role in heating the coronal plasma.

scholarly journals Simulation study on parametric dependence of whistler-mode hiss generation in the plasmasphere

2021 ◽  
Vol 73 (1) ◽  
Author(s):  
Yin Liu ◽  
Yoshiharu Omura ◽  
Mitsuru Hikishima
Keyword(s):  
Magnetic Field ◽  
Electron Density ◽  
Nonlinear Process ◽  
Background Field ◽  
Realistic Model ◽  
Equatorial Region ◽  
Generation Process ◽  
Hot Electron ◽  
Wave Growth ◽  
Background Magnetic Field

AbstractWe conduct electromagnetic particle simulations to examine the applicability of nonlinear wave growth theory to the generation process of plasmaspheric hiss. We firstly vary the gradient of the background magnetic field from a realistic model to a rather steep gradient model. Under such variation, the threshold amplitude in the nonlinear theory increases quickly and the overlap between threshold and optimum amplitude disappears correspondingly, the nonlinear process is suppressed. In the simulations, as we enlarge the gradient coefficient of the background magnetic field, waves generated near the equator do not grow through propagation. By examining the range of suitable values of inhomogeneity factor S (i.e., $$|S|<2$$ | S | < 2 ), we find the generation of wave packets is limited to the equatorial region when the background field is steep, showing a good agreement with what is indicated by critical distance in the theory. We then check the dependence of generation of hiss emissions on different hot electron densities. Since the overlap between threshold and optimum amplitude vanishes, the nonlinear process is weakened when hot electron density becomes smaller. In the simulation results, we find similar wave structures in all density cases, yet with different magnitudes. The existence of suitable S values implies that the nonlinear process occurs even at a low level of hot electron density. However, by examining $$J_E$$ J E that closely relates to the wave growth, we find energy conveyed from particles to waves is much limited in small density cases. Therefore, the nonlinear process is suppressed when hot electron density is small, which agrees with the theoretical analysis. Graphical Abstract

scholarly journals Resonant absorption in expanding coronal magnetic flux tubes with uniform density

2019 ◽  
Vol 631 ◽  
pp. A105 ◽  
Author(s):  
T. A. Howson ◽  
I. De Moortel ◽  
P. Antolin ◽  
T. Van Doorsselaere ◽  
A. N. Wright
Keyword(s):  
Magnetic Flux ◽  
Flux Tube ◽  
Density Profile ◽  
Resonant Absorption ◽  
Magnetic Flux Tube ◽  
Length Scales ◽  
Flux Tubes ◽  
Kink Mode ◽  
Wave Heating ◽  
Field Lines

Aims. We investigate the transfer of energy between a fundamental standing kink mode and azimuthal Alfvén waves within an expanding coronal magnetic flux tube. We consider the process of resonant absorption in a loop with a non-uniform Alfvén frequency profile but in the absence of a radial density gradient. Methods. Using the three dimensional magnetohydrodynamic (MHD) code, Lare3d, we modelled a transversely oscillating magnetic flux tube that expands radially with height. An initially straight loop structure with a magnetic field enhancement was allowed to relax numerically towards a force-free state before a standing kink mode was introduced. The subsequent dynamics, rate of wave damping and formation of small length scales are considered. Results. We demonstrate that the transverse gradient in Alfvén frequency required for the existence of resonant field lines can be associated with the expansion of a high field-strength flux tube from concentrated flux patches in the lower solar atmosphere. This allows for the conversion of energy between wave modes even in the absence of the transverse density profile typically assumed in wave heating models. As with standing modes in straight flux tubes, small scales are dominated by the vorticity at the loop apex and by currents close to the loop foot points. The azimuthal Alfvén wave exhibits the structure of the expanded flux tube and is therefore associated with smaller length scales close to the foot points of the flux tube than at the loop apex. Conclusions. Resonant absorption can proceed throughout the coronal volume, even in the absence of visible, dense, loop structures. The flux tube and MHD waves considered are difficult to observe and our model highlights how estimating hidden wave power within the Sun’s atmosphere can be problematic. We highlight that, for standing modes, the global properties of field lines are important for resonant absorption and coronal conditions at a single altitude will not fully determine the nature of MHD resonances. In addition, we provide a new model in partial response to the criticism that wave heating models cannot self-consistently generate or sustain the density profile upon which they typically rely.

scholarly journals Modelling 3D magnetic networks in a realistic solar atmosphere

2019 ◽  
Vol 489 (1) ◽  
pp. 28-35
Author(s):  
Frederick A Gent ◽  
Ben Snow ◽  
Viktor Fedun ◽  
Robertus Erdélyi
Keyword(s):  
Magnetic Field ◽  
Magnetic Flux ◽  
Solar Atmosphere ◽  
Energy Transport ◽  
Solar Dynamics Observatory ◽  
Lower Corona ◽  
Flux Tubes ◽  
Background Magnetic Field ◽  
Magnetic Flux Tubes ◽  
Open Magnetic Flux

ABSTRACT The magnetic network extending from the photosphere (solar radius ≃ R⊙) to the lower corona ($\mathrm{ R}_\odot +10\, {\rm Mm}$) plays an important role in the heating mechanisms of the solar atmosphere. Here we develop further the models of the authors with realistic open magnetic flux tubes, in order to model more complicated configurations. Closed magnetic loops and combinations of closed and open magnetic flux tubes are modelled. These are embedded within a stratified atmosphere, derived from observationally motivated semi-empirical and data-driven models subject to solar gravity and capable of spanning from the photosphere up into the chromosphere and lower corona. Constructing a magnetic field comprising self-similar magnetic flux tubes, an analytic solution for the kinetic pressure and plasma density is derived. Combining flux tubes of opposite polarity, it is possible to create a steady background magnetic field configuration, modelling a solar atmosphere exhibiting realistic stratification. The result can be applied to the Solar and Heliospheric Observatory Michelson Doppler Imager (SOHO/MDI), Solar Dynamics Observatory Helioseismic and Magnetic Imager (SDO/HMI) and other magnetograms from the solar surface, for which photospheric motions can be simulated to explore the mechanism of energy transport. We demonstrate this powerful and versatile method with an application to HMI data.

On the Calculation of the Phase Shift of a Superconducting Flux Line Lattice

2000 ◽  
Vol 6 (S2) ◽  
pp. 1032-1033
Author(s):  
M. Beleggia ◽  
G. Pozzi ◽  
A. Tonomura
Keyword(s):  
Magnetic Field ◽  
Electron Beam ◽  
Phase Shift ◽  
Flux Line ◽  
Realistic Model ◽  
Regular Lattice ◽  
Transmission Experiment ◽  
Line Lattice ◽  
Flux Tubes ◽  
London Model

Recently out-of-focus, low angle electron diffraction and Foucault experiments have been carried out on superconducting specimens in a range of applied magnetic fields where the fluxons form a more or less regular lattice. Let us recall that in order to describe the effect on the electron beam in a transmission experiment of a fluxon in a tilted specimen, the fluxon itself has been approximated by a suitable bundle of straight flux tubes, relying on the important result that the phase shift of the flux tube can be calculated analytically even in the tilted specimen geometry. In this way, it is only necessary to convolute this phase shift with the chosen projected magnetic field distribution (in our case a London model with a phenomenological penetration depth of 50 nm) in order to obtain a fairly realistic model. Therefore, in order to interpret the main features of the experimental results,

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