On the validity of nonlinear Alfvén resonance in space plasmas

Aims. In the approximation of linear dissipative magnetohydrodynamics (MHD), it can be shown that driven MHD waves in magnetic plasmas with high Reynolds number exhibit a near resonant behaviour if the frequency of the wave becomes equal to the local Alfvén (or slow) frequency of a magnetic surface. This behaviour is confined to a thin region, known as the dissipative layer, which embraces the resonant magnetic surface. Although driven MHD waves have small dimensionless amplitude far away from the resonant surface, this near-resonant behaviour in the dissipative layer may cause a breakdown of linear theory. Our aim is to study the nonlinear effects in Alfvén dissipative layer Methods. In the present paper, the method of simplified matched asymptotic expansions developed for nonlinear slow resonant waves is used to describe nonlinear effects inside the Alfvén dissipative layer. Results. The nonlinear corrections to resonant waves in the Alfvén dissipative layer are derived, and it is proved that at the Alfvén resonance (with isotropic/anisotropic dissipation) wave dynamics can be described by the linear theory with great accuracy

Waves and Instabilities in Accretion Disks: MHD Spectroscopic Analysis

A complete analytical and numerical treatment of all magnetohydrodynamic waves and instabilities for radially stratified, magnetized accretion disks is presented. The instabilities are a possible source of anomalous transport. While recovering results on known hydrodynamicand both weak- and strong-field magnetohydrodynamic perturbations, the full magnetohydrodynamic spectra for a realistic accretion disk model demonstrates a much richer variety of instabilities accessible to the plasma than previously realized. We show that both weakly and strongly magnetized accretion disks are prone to strong non-axisymmetric instabilities.The ability to characterize all waves arising in accretion disks holds great promise for magnetohydrodynamic spectroscopic analysis.Comment: FOM-Institute for plasma physics "Rijnhuizen", Nieuwegein, the Netherlands 12 pages, 3 figures, Accepted for publication in ApJ

Transverse oscillations of systems of coronal loops

We study the collective kinklike normal modes of a system of several cylindrical loops using the T-matrix theory. Loops that have similar kink frequencies oscillate collectively with a frequency which is slightly different from that of the individual kink mode. On the other hand, if the kink frequency of a loop is different from that of the others, it oscillates individually with its own frequency. Since the individual kink frequency depends on the loop density but not on its radius for typical 1 MK coronal loops, a coupling between kink oscillations of neighboring loops take place when they have similar densities. The relevance of these results in the interpretation of the oscillations studied by \citet{schrijver2000} and \citet{verwichte2004}, in which transverse collective loop oscillations seem to be detected, is discussed. In the first case, two loops oscillating in antiphase are observed; interpreting this motion as a collective kink mode suggests that their densities are roughly equal. In the second case, there are almost three groups of tubes that oscillate with similar periods and therefore their dynamics can be collective, which again seems to indicate that the loops of each group share a similar density. All the other loops seem to oscillate individually and their densities can be different from the rest

Double-resonant fast particle-wave interaction

In future fusion devices fast particles must be well confined in order to transfer their energy to the background plasma. Magnetohydrodynamic instabilities like Toroidal Alfv\'en Eigenmodes or core-localized modes such as Beta Induced Alfv\'en Eigenmodes and Reversed Shear Alfv\'en Eigenmodes, both driven by fast particles, can lead to significant losses. This is observed in many ASDEX Upgrade discharges. The present study applies the drift-kinetic HAGIS code with the aim of understanding the underlying resonance mechanisms, especially in the presence of multiple modes with different frequencies. Of particular interest is the resonant interaction of particles simultaneously with two different modes, referred to as 'double-resonance'. Various mode overlapping scenarios with different q profiles are considered. It is found that, depending on the radial mode distance, double-resonance is able to enhance growth rates as well as mode amplitudes significantly. Surprisingly, no radial mode overlap is necessary for this effect. Quite the contrary is found: small radial mode distances can lead to strong nonlinear mode stabilization of a linearly dominant mode.Comment: 12 pages, 11 figures; Nuclear Fusion 52 (2012

Application of the Jacobi-Davidson method to spectral calculations in magnetohydrodynamics

For the solution of the generalized complex non-Hermitian eigenvalue problems $Ax=\lambda Bx$ occurring in the spectral study of linearized resistive magnetohydrodynamics (MHD) a new parallel solver based on the recently developed Jacobi-Davidson~\cite{Sleijpen96a} method has been developed. A brief presentation of the implementation of the solver is given here. The new solver is very well suited for the computation of some selected interior eigenvalues related to the resistive Alfv\'{e}n wave spectrum and is well parallelizable. All features of the spectrum are easily and accurately computed with only a few target shifts

Magnetohydrostatic solar prominences in near-potential coronal magnetic fields

We present numerical magnetohydrostatic solutions describing the gravitationally stratified, bulk equilibrium of cool, dense prominence plasma embedded in a near-potential coronal field. These solutions are calculated using the FINESSE magnetohydrodynamics equilibrium solver and describe the morphologies of magnetic field distributions in and around prominences and the cool prominence plasma that these fields support. The equilibrium condition for this class of problem is usually different in distinct subdomains, separated by free boundaries, across which solutions are matched by suitable continuity or jump conditions describing force balance. We employ our precise finite element elliptic solver to calculate solutions not accessible by previous analytical techniques with temperature or entropy prescribed as free functions of the magnetic flux function, including a range of values of the polytropic index, temperature variations mainly across magnetic field lines and photospheric field profiles sheared close to the polarity inversion line. Out of the many examples computed here, perhaps the most noteworthy is one which reproduces precisely the three-part structure often encountered in observations: a cool dense prominence within a cavity/flux rope embedded in a hot corona. The stability properties of these new equilibria, which may be relevant to solar eruptions, can be determined in the form of a full resistive MHD spectrum using a companion hyperbolic stability solver.Comment: To appear in ApJ August 200

Impulsive phase flare energy transport by large-scale Alfven waves and the electron acceleration problem

The impulsive phase of a solar flare marks the epoch of rapid conversion of energy stored in the pre-flare coronal magnetic field. Hard X-ray observations imply that a substantial fraction of flare energy released during the impulsive phase is converted to the kinetic energy of mildly relativistic electrons (10-100 keV). The liberation of the magnetic free energy can occur as the coronal magnetic field reconfigures and relaxes following reconnection. We investigate a scenario in which products of the reconfiguration - large-scale Alfven wave pulses - transport the energy and magnetic-field changes rapidly through the corona to the lower atmosphere. This offers two possibilities for electron acceleration. Firstly, in a coronal plasma with beta < m_e/m_p, the waves propagate as inertial Alfven waves. In the presence of strong spatial gradients, these generate field-aligned electric fields that can accelerate electrons to energies on the order of 10 keV and above, including by repeated interactions between electrons and wavefronts. Secondly, when they reflect and mode-convert in the chromosphere, a cascade to high wavenumbers may develop. This will also accelerate electrons by turbulence, in a medium with a locally high electron number density. This concept, which bridges MHD-based and particle-based views of a flare, provides an interpretation of the recently-observed rapid variations of the line-of-sight component of the photospheric magnetic field across the flare impulsive phase, and offers solutions to some perplexing flare problems, such as the flare "number problem" of finding and resupplying sufficient electrons to explain the impulsive-phase hard X-ray emission.Comment: 31 pages, 6 figure

Fast magnetoacoustic waves in curved coronal loops. I, Trapped and leaky modes

A study of vertically polarised fast magnetoacoustic waves in a curved coronal loop is presented. The loop is modeled as a semi-circular magnetic slab in the zero plasma-β limit. The governing equations for linear waves are derived. We show that the wave mode behaviour depends on the slope of the equilibrium density profile, which is modeled as a piece-wise continuous power law curve of index α. For all profiles, except for α = −4, wave modes are not trapped in the loop and leak out into the external medium through wave tunneling. The particular case of α = −4, which corresponds to a linearly increasing Alfvén speed profile, is examined in more detail as this is the only model that can support trapped wave modes. We compare the results with a straight slab model and find similar behaviour. Coupling between sausage and kink wave modes has not been found in the model

Rayleigh-Taylor Instabilities with Sheared Magnetic Fields

Magnetic Rayleigh-Taylor (MRT) instabilities may play a relevant role in many astrophysical problems. In this work the effect of magnetic shear on the growth rate of the MRT instability is investigated. The eigenmodes of an interface and a slab model under the presence of gravity are analytically calculated assuming that the orientation of the magnetic field changes in the equilibrium, i.e., there is magnetic shear. We solve the linearized magnetohydrodynamic equations in the incompressible regime. We find that the growth rate is bounded under the presence of magnetic shear. We have derived simple analytical expressions for the maximum growth rate, corresponding to the most unstable mode of the system. These expressions provide the explicit dependence of the growth rate on the various equilibrium parameters. For small angles the growth time is linearly proportional to the shear angle, and in this regime the single interface problem and the slab problem tend to the same result. On the contrary, in the limit of large angles and for the interface problem the growth time is essentially independent of the shear angle. In this regime we have also been able to calculate an approximate expression for the growth time for the slab configuration. Magnetic shear can have a strong effect on the growth rates of the instability. As an application of the results found in this paper we have indirectly determined the shear angle in solar prominence threads using their lifetimes and the estimation of the Alfvén speed of the structure