Magnetohydrodynamic Perturbations Research Articles

The role of Rayleigh-Taylor instabilities in filament threads

Many solar filaments and prominences show short-lived horizontal threads lying parallel to the photosphere. In this work the possible link between Rayleigh-Taylor instabilities and thread lifetimes is investigated. This is done by calculating the eigenmodes of a thread modelled as a Cartesian slab under the presence of gravity. An analytical dispersion relation is derived using the incompressible assumption for the magnetohydrodynamic (MHD) perturbations. The system allows a mode that is always stable, independently of the value of the Alfv\'en speed in the thread. The character of this mode varies from being localised at the upper interface of the slab when the magnetic field is weak, to having a global nature and resembling the transverse kink mode when the magnetic field is strong. On the contrary, the slab model permits another mode that is unstable and localised at the lower interface when the magnetic field is weak. The growth rates of this mode can be very short, of the order of minutes for typical thread conditions. This Rayleigh-Taylor unstable mode becomes stable when the magnetic field is increased, and in the limit of strong magnetic field it is essentially a sausage magnetic mode. The gravity force might have a strong effect on the modes of oscillation of threads, depending on the value of the Alfv\'en speed. In the case of threads in quiescent filaments, where the Alfv\'en speed is presumably low, very short lifetimes are expected according to the slab model. In active region prominences, the stabilising effect of the magnetic tension might be enough to suppress the Rayleigh-Taylor instability for a wide range of wavelengths.

Toward detailed prominence seismology

Context. Prominence seismology exploits our knowledge of the linear eigenoscillations for representative magnetohydro- dynamic models of filaments. To date, highly idealized models for prominences have been used, especially with respect to the overall magnetic configurations. Aims. We initiate a more systematic survey of filament wave modes, where we consider full multi-dimensional models with twisted magnetic fields representative of the surrounding magnetic flux rope. This requires the ability to compute accurate 2.5 dimensional magnetohydrodynamic equilibria that balance Lorentz forces, gravity, and pressure gradients, while containing density enhancements (static or in motion). Methods. The governing extended Grad-Shafranov equation is discussed, along with an analytic prediction for circular flux ropes for the Shafranov shift of the central magnetic axis due to gravity. Numerical equilibria are computed with a finite element-based code, demonstrating fourth order accuracy on an explicitly known, non-trivial test case. Results. The code is then used to construct more realistic prominence equilibria, for all three possible choices of a free flux-function. We quantify the influence of gravity, and generate cool condensations in hot cavities, as well as multi- layered prominences. Conclusions. The internal flux rope equilibria computed here have the prerequisite numerical accuracy to allow a yet more advanced analysis of the complete spectrum of linear magnetohydrodynamic perturbations, as will be demonstrated in the companion paper.

Understanding complex magnetohydrodynamic activities associated with a relaxation in the HT-7 tokamak

A new relaxation instability with complex magnetohydrodynamics (MHD) activities is found in the HT-7 tokamak operational region, which manifests itself in bursts of hydrogen alpha-ray radiations, electron cyclotron emission and soft x-ray (SX) radiations on outer channels, as well as complex MHD perturbations, but without hard disruptions. The MHD modes are identified as m/n = 2/1, m/n = 3/2 and m/n = 5/3 just before the relaxation (m and n are poloidal and toroidal mode numbers, respectively). The Poincaré mapping, according to the measured perturbations of the MHD modes at the edge, is used to show the topology of magnetic field lines. It is found that a stochastic annular belt resulted just before the relaxation due to the m/n = 5/3 island overlapping with m/n = 2/1 and m/n = 3/2 islands. This qualitatively coincides with the results of SX tomography.

The eigenfrequency spectrum of linear magnetohydrodynamic perturbations in stationary equilibria: A variational principle

The frequencies of the normal modes of oscillation of linear magnetohydrodynamic perturbations of a stationary equilibrium are related to the stationary points of a quadratic functional over the Hilbert space of Lagrangian displacement vectors, which is subject to a constraint. In the absence of a background flow (or of a uniform flow), the relation reduces to the well-known Rayleigh–Ritz variational principle. In contrast to the existing variational principles for perturbations of stationary equilibria, the present treatment does neither impose additional symmetry restrictions on the equilibrium, nor does it involve the generalization to bilinear functionals instead of quadratic forms. This allows a more natural interpretation of the quadratic forms as energy functionals.

Note: Tangential x-ray diagnosis for investigating fast MHD events in EAST tokamak

A tangential x-ray diagnosis has been installed in the experimental advanced superconducting tokamakvacuum vessel for the study of fast magnetohydrodynamics (MHD) events. This system is based on absolute x-ray ultraviolet detectors with a collimator which is processed by laser machine. The first experimental results have proved its ability to measure the small-scale and transient MHD perturbations.

Perturbation Theory Approach to Stellarator Coil Optimization

Two new methods for designing modular stellarator coils are presented. Stellarator coils provide necessary magnetic field to produce the plasma shape for a desired magnetohydrodynamic (MHD) equilibrium. The methods optimize a continuous current on a surface - i.e., coil current is represented by a continuous-current sheet on a toroidal winding surface - and the process of coil cutting is not addressed. In contrast to previously published continuous-current methods that optimize coil current by minimizing the flux at the plasma boundary, the new methods presented in this paper search for optimal solutions by minimizing the displacement of the plasma boundary, i.e., the last closed magnetic surface. The physical displacement of the plasma boundary is computed from the magnetic field normal using linear MHD perturbation theory. A comparison with two similar continuous-current codes is given in terms of both methodology and results. The new codes show modest improvement over previously published continuous-current codes.

Fast-Ion Losses due to High-Frequency MHD Perturbations in the ASDEX Upgrade Tokamak

Time-resolved energy and pitch angle measurements of fast-ion losses correlated in frequency and phase with high-frequency magnetohydrodynamic perturbations have been obtained for the first time in a magnetic fusion device and are presented here. A detailed analysis of fast-ion losses due to toroidal Alfvén eigenmodes has revealed the existence of a new core-localized magnetohydrodynamic perturbation, the sierpes mode. The sierpes mode is a non-Alfvénic instability which dominates the losses of fast ions in ion cyclotron resonance heated discharges, and it is named for its footprint in the spectrograms ("sierpes" means "snake" in Spanish). The sierpes mode has been reconstructed by means of highly resolved multichord soft-x-ray measurements.

Peculiarities of entropy and magnetosonic waves in optically thin cosmic plasma

The stability problem for small magnetohydrodynamic (MHD) perturbations in an optically thin, perfectly conducting uniform plasma with a cosmic abundance of elements is solved in the linear approximation. The electron heat conduction along the magnetic field and the proton heat conduction across the field are taken into account. We have shown for the first time that the entropy waves can grow exponentially, while the magnetosonic waves are damped in a wide range of physical conditions closest to the conditions in stellar coronae with the proper allowance for radiative losses. Slow magnetosonic waves are damped particularly rapidly. For the solar corona, the calculated damping decrement of slow magnetosonic waves agrees well with the averaged one in 11 quasi-periodic events observed from the TRACE satellite in extreme ultraviolet radiation. Other possible astrophysical applications of the results obtained are briefly discussed.

Coulomb Bubbles: Overstable Driving of Magnetoacoustic Waves Due to the Rapid and Anisotropic Diffusion of Energy

We perform a linear magnetohydrodynamic perturbation analysis for a stratified magnetized envelope where the diffusion of heat is mediated by charged particles that are confined to flow along magnetic field lines. We identify an instability, the "Coulomb bubble instability," which may be thought of as standard magnetosonic fast and slow waves, driven by the rapid diffusion of heat along the direction of the magnetic field. We calculate the growth rate and stability criteria for the Coulomb bubble instability for various choices of equilibrium conditions. The Coulomb bubble instability is intimately related to the photon bubble instability. The bulk thermodynamic properties of both instability mechanisms are quite similar in that they require the timescale for heat to diffuse across a wavelength to be shorter than the corresponding wave crossing time. Furthermore, overstability occurs only as long as the driving resulting from the presence of the background heat flux can overcome diffusive Silk damping. However, the geometric and therefore mechanical properties of the Coulomb bubble instability are the complete mirror opposite of the photon bubble instability. The Coulomb bubble instability is most strongly driven for weakly magnetized atmospheres that are strongly convectively stable. We briefly discuss a possible application of astrophysical interest: diffusion of interstellar cosmic rays in the hot T ∼ 106 K Galactic corona. We show that for commonly accepted values of the cosmic-ray and gas pressure as well as its overall characteristic dimensions, the Galactic corona is in a marginal state of stability with respect to a cosmic-ray Coulomb bubble instability. The implication being that a cosmic-ray Coulomb bubble instability plays a role in regulating both the pressure and transport properties of interstellar cosmic rays, while serving as a source of acoustic power above the Galactic disk.

Global structures in a composite system of two scale-free discs with a coplanar magnetic field

We investigate a theoretical magnetohydrodynamic (MHD) disc problem involving a composite disc system of gravitationally coupled stellar and gaseous discs with a coplanar magnetic field in the presence of an axisymmetric dark matter halo. The two discs are expediently approximated as razor-thin, with a barotropic equation of state, a power-law surface mass density, a ring-like magnetic field, and a power-law rotation curve of radius r. By imposing the scale-free condition, we construct analytically stationary global MHD perturbation configurations for both aligned and logarithmic spiral patterns, using our composite MHD disc model. MHD perturbation configurations in a composite system of partial discs in the presence of an axisymmetric dark matter halo are also considered. Our study generalizes the previous analyses of Lou & Shen and Shen & Lou on the unmagnetized composite system of two gravitationally coupled isothermal and scale-free discs, of Lou and Shen et al. on the cases of a single coplanarly magnetized isothermal and scale-free disc, and of Lou & Zou on magnetized two coupled singular isothermal discs. We derive analytically the stationary MHD dispersion relations for both aligned and unaligned perturbation structures and analyse the corresponding phase relationships between surface mass densities and the magnetic field. Compared with earlier results, we obtain three solution branches corresponding to superfast MHD density waves (sFMDWs), fast MHD density waves (FMDWs) and slow MHD density waves (SMDWs), respectively. We examine the m = 0 cases for both aligned and unaligned MHD perturbations. By evaluating the unaligned m = 0 case, we determine the marginal stability curves where the two unstable regimes corresponding to Jeans collapse instability and ring fragmentation instability are identified. We find that the aligned m = 0 case is simply the limit of the unaligned m = 0 case with the radial wavenumber ξ → 0 (i.e. the breathing mode) which does not merely represent a rescaling of the equilibrium state. We further show that a composite system of partial discs behaves much differently from a composite system of full discs in certain aspects. We provide numerical examples by varying dimensionless parameters β (rotation velocity index), η (ratio of effective sound speeds of the two discs), δ (ratio of surface mass densities of the two discs), q (a measure of coplanar magnetic field strength), F (gravitational potential ratio), ξ (radial wavenumber). Our formalism provides a useful theoretical framework in the study of stationary global perturbation configurations for MHD disc galaxies with bars, spirals and barred spirals.

Generation of compressible modes in MHD turbulence

Astrophysical turbulence is magnetohydrodynamic (MHD) in nature. We discuss fundamental properties of MHD turbulence and in particular the generation of compressible MHD waves by Alfvénic turbulence and show that this process is inefficient. This allows us to study the evolution of different types of MHD perturbations separately. We describe how to separate MHD fluctuations into three distinct families: Alfvén, slow, and fast modes. We find that the degree of suppression of slow and fast modes production by Alfvénic turbulence depends on the strength of the mean field. We review the scaling relations of the modes in strong MHD turbulence. We show that Alfvén modes in compressible regime exhibit scalings and anisotropy similar to those in incompressible regime. Slow modes passively mimic Alfvén modes. However, fast modes exhibit isotropy and a scaling similar to that of acoustic turbulence both in high and low β plasmas. We show that our findings entail important consequences for star formation theories, cosmic ray propagation, dust dynamics, and gamma ray bursts. We anticipate many more applications of the new insight to MHD turbulence and expect more revisions of the existing paradigms of astrophysical processes as the field matures.

Influence of ionospheric conductivity on the ballooning modes in the inner magnetosphere of the Earth

The generation of ballooning perturbations in the inner magnetosphere of the Earth was investigated in the dipole model of the geomagnetic field taking into account the ionospheric boundary conditions. The ionosphere is considered as a thin layer with finite conductivity. A special attention was paid to the study of the influence of ionospheric conductivity on the stability of ballooning perturbations. It was demonstrated that in the case of insulating ionosphere, flute perturbations are generated and they determine the stability of magnetospheric magnetohydrodynamic modes. An analytical stability criterion was obtained for these perturbations. Conforming to the results of the paper (Hameiri, E., Ballooning modes on open magnetic field lines. Phys. Plasmas 6(3), 674–685, 1999), it also determines the stability boundary of magnetospheric magnetohydrodynamic perturbations in the resistive boundary case. In the case of resistive ionosphere, stable toroidal Alfvén waves are slowly decaying. The spectrum of coupled poloidal Alfvén and slow magnetosonic eigenmodes was also investigated for perfectly conductive ionosphere.

Structures in a class of magnetized scale-free discs

We construct analytically stationary global configurations for both aligned and logarithmic spiral coplanar magnetohydrodynamics (MHD) perturbations in an axisymmetric background MHD disc with a power-law surface mass density Σ 0 r -α , a coplanar azimuthal magnetic field B 0 oc r -γ , a consistent self-gravity and a power-law rotation curve v 0 oc r -β , where v 0 is the linear azimuthal gas rotation speed. The barotropic equation of state n Σ n is adopted for both MHD background equilibrium and coplanar MHD perturbations where n is the vertically integrated pressure and n is the barotropic index. For a scale-free background MHD equilibrium, a relation exists among a, β, y and n such that only one parameter (e.g. β) is independent. For a linear axisymmetric stability analysis, we provide global criteria in various parameter regimes. For non-axisymmetric aligned and logarithmic spiral cases, two branches of perturbation modes (i.e. fast and slow MHD density waves) can be derived once β is specified. To complement the magnetized singular isothermal disc analysis of Lou, we extend the analysis to a wider range of -1/4 < β < 1/2. As an illustrative example, we discuss specifically the β = 1/4 case when the background magnetic field is force-free. Angular momentum conservation for coplanar MHD perturbations and other relevant aspects of our approach are discussed.

Minimizing the magnetohydrodynamic potential energy for the current hole region in tokamaks

The current hole region in the tokamak has been observed to arise naturally during the development of internal transport barriers. The magnetohydrodynamic (MHD) potential energy in the current hole region is shown to be determined completely in terms of the displacements at the edge of the current hole. For modes with finite toroidal mode number n≠0, the minimized potential energy is the same as if the current hole region were a vacuum region. For modes with toroidal mode number n=0, the displacement is a superposition of three types of independent displacements: a vertical displacement or displacements that compress only the plasma, or the toroidal field uniformly. Thus for ideal MHD perturbations of plasma with a current hole, the plasma behaves as if it were bordered by an extra “internal vacuum region.” The relevance of the present work to computer simulations of plasma with a current hole region is also discussed.

Effects of nonresonant hot ions with large orbits on Alfvén cascades and on magnetohydrodynamic instabilities in tokamaks

The effects of nonresonating hot ions on the spectrum of magnetohydrodynamic (MHD) waves and instabilities in tokamaks are studied in the limit when the width of the hot ion drift orbits is much larger than the radial scale length of the MHD perturbations. Due to the large magnetic drift velocities the hot ions cannot contribute to the MHD perturbations directly, but two main effects of the hot ions, the hot-ion density-dependent effect and the hot-ion pressure-dependent effect, influence the MHD perturbations indirectly. The physics of both effects is elucidated and it is shown that both these effects can be described in MHD approach. A new code, MISHKA-H (MISHKA including the hot-ion indirect effects), is developed as an extension of the ideal MHD code MISHKA-D [Huysmans et al., Phys. Plasmas 8, 4292 (2002)]. Analytical benchmarks for this code are given. Results of the MISHKA-H code on Alfvén spectrum in a shear-reversed discharges with ion-cyclotron resonance frequency (ICRF) heating are presented. Modeling of Alfvén cascades and their transition into toroidal Alfvén eigenmodes in shear-reversed tokamak equilibrium is considered. The hot-ion effect on the unstable branch of the MHD spectrum is studied for the test case of an n=1 ideal MHD internal kink mode, which is relevant to short-period sawteeth in low-density plasmas observed in Joint European Torus (JET) [Rebut et al., Proceedings of the 10th International Conference, Plasma Physics and Controlled Nuclear Fusion, London (International Atomic Energy Agency, Vienna, 1985), Vol. I, p. 11] experiments with high-power ICRF heating.

MHD solar fluctuations and solar neutrinos

We analyze how solar neutrino experiments could detect time fluctuations of the solar neutrino flux due to magnetohydrodynamic (MHD) perturbations of the solar plasma. We state that if such time fluctuations are detected, this would provide a unique signature of the Resonant Spin-Flavor Precession (RSFP) mechanism as a solution to the Solar Neutrino Problem.

Solar Mhd Waves And Solar Neutrinos

We analyze here how solar neutrino experiments could detect time fluctuations of the solar neutrino flux due to magnetohydrodynamics (MHD) perturbations of the solar plasma. We state that if such time fluctuations are detected, this would provide a unique signature of the Resonant Spin-Flavor Precession (RSFP) mechanism as a solution to the Solar Neutrino Problem.

On the propagation of magnetohydrodynamic perturbations in a Harris‐type current sheet 1. Propagation on discrete modes and signal reconstruction

We propose a study of the propagation of magnetohydrodynamic linear perturbations in a 1‐D model of the magnetotail current sheet. Starting from a mathematical analysis of the impulsive linear response of a Harris sheet to external excitations, we study the propagation of the different types of perturbations in the sheet. The structure of the discrete modes of propagation is analyzed, and their coupling to the initial perturbation is discussed. Using various types of initial perturbations (with different characteristic temporal and spatial scales, centered on the neutral sheet or shifted toward the lobe), we reconstruct the full spatial–temporal evolution of the magnetic, velocity, and pressure perturbations. We thus completely determined the perturbations that would be detected by a spacecraft in the tail if the propagation of the perturbations obeys to the ideal linear MHD equations. For example, it is shown that pulse‐like initial perturbations result in the propagation of long quasi‐monochromatic wave packets. The typical period is of the order of 1 min with a maximum amplitude for both the magnetic and thermal pressure perturbations that reach at maximum a few percent of the static value (for an initial pulse with maximum amplitude of the order of the total equilibrium pressure). The highest amplitudes are obtained with initial pulse with spatial scales of the order of the current sheet width.

On the propagation of magnetohydrodynamic perturbations in a Harris‐type current sheet: 2. Propagation on continuous modes and resonant absorption

We study the propagation of magnetohydrodynamic perturbations in a one‐dimensional (1‐D) model of the magnetotail current sheet. Starting from a general analysis of the MHD linear response of a Harris current sheet to external pressure pulse, we reconstruct the magnetic, velocity, and pressure perturbations for successive times and at different positions. The spatial‐temporal evolution of the signal propagating on the discrete modes has been studied by Fruit et al. [2002]. We here describe the propagation in the continuous spectrum domain that results from the existence of a spatial singularity in the differential equation defining the modes of propagation. At t = 0, the current sheet is supposed to be excited by an external pressure pulse. We estimate the energy that propagates in the continuum domain and will thus be absorbed by the resonant absorption process. Initial pulses of different shapes and characteristic spatial and temporal scales are used. Since we perform the complete inverse Laplace and Fourier transform of the continuous modes, we get the full description of the perturbations in real space, hence, the typical temporal and spatial scales of the absorption process. For example, starting with a pulse of total amplitude of 1 Pme (magnetic pressure in the lobe) with a spatial scale of 4 Earth radii and a temporal scale of 20 s, we show that 2% of the initial plasma thermal energy are transferred to the sheet over a distance of 20 Earth radii and in less than 10 min. Pulses of larger scales have no energetic consequences.

MHD fluctuations and low energy solar neutrinos

We analyze here how future solar neutrino experiments could detect neutrino flux fluctuations due to magnetohydrodynamics (MHD) perturbations on the solar plasma. We state that if such time fluctuations are detected, this would provide a unique signature of the resonant spin-flavor precession (RSFP) mechanism as a solution to the solar neutrino problem.