Slow Mode Oscillations Research Articles

Decayless low-amplitude transverse oscillations in short coronal loops as manifestations of driven slow modes

ABSTRACT A recent theoretical study of slow magnetoacoustic oscillations in a curved magnetic slab shows that the principal slow mode causes both dominant longitudinal motions and radial (transverse) kink-like motions of a slab. This modification of wave properties occurs due to the violation of the symmetry of wave motions with respect to the waveguide axis and the slow to fast wave interaction in curved magnetic configurations. In this work, we carry out a comprehensive investigation of the principal slow mode depending on the model parameters. It is shown that the dominance of longitudinal motions in the principal slow mode decreases as both the internal plasma-β and slab aspect ratio increase. The results are used to explain the observed small amplitude decayless transverse oscillations in short coronal loops. In particular, these phenomena are interpreted as direct manifestation of slow mode oscillations in curved coronal loops excited at the footpoints by compressible oscillations of the underlying atmospheric layers. Numerical calculations have shown that the observed velocity range of V = 0.6–5 km s−1 corresponds to radial velocity amplitudes in the principal slow mode, provided that the plasma-β inside the short loops is in the range of βi= 0.3–0.5 and the loop aspect ratio 0.15 ≤ a/R ≤ 0.25. These parameters appear to be typical for low-lying small coronal loops extending from the transition region to the lower corona.

Slow mode oscillations in curved arcade loops

ABSTRACT In this work we theoretically investigate the effect of curvature on the slow-mode oscillations in coronal loop arcade. A simple model of an arc circle magnetic slab is used to simulate curved coronal magnetic structures. Solving the set of magnetohydrodynamic (MHD) equations for a compressible plasma, we obtain the dispersion relation that governs the compressible MHD modes in the model. A band of slow body modes with phase speeds close to the internal tube speed and a single hybrid slow mode with phase speed close to the external tube speed are found to exist under typical coronal circumstances. The principal slow body and hybrid modes both produce radial kink-like displacements of the slab axis and distort its cross-section. These motions are accompanied with the dominating longitudinal oscillations. Such mode properties may result in Doppler shift and intensity oscillations as well as oscillating spatial displacements, observed in coronal loops. A number of observations of long-period oscillations in arcade loops are interpreted on the basis of the developed theory.

Excitation of ion-acoustic waves by non-linear finite-amplitude standing Alfvén waves

We investigate, using a multi-fluid approach, the main properties of standing ion-acoustic modes driven by non-linear standing Alfvén waves. The standing character of the Alfvénic pump is due to the superposition of two identical circularly polarised counter-propagating waves. We consider parallel propagation along the constant magnetic field and we find that left- and right-handed modes generate via ponderomotive forces the second harmonic of standing ion-acoustic waves. We demonstrate that parametric instabilities are not relevant in the present problem and the secondary ion-acoustic waves attenuate by Landau damping in the absence of any other dissipative process. Kinetic effects are included in our model where ions are considered as particles and electrons as a massless fluid, and hybrid simulations are used to complement the theoretical results. Analytical expressions are obtained for the time evolution of the different physical variables in the absence of Landau damping. From the hybrid simulations we find that the attenuation of the generated ion-acoustic waves follows the theoretical predictions even under the presence of an Alfvénic pump. Due to the non-linear induced ion-acoustic waves the system develops density cavities and an electric field parallel to the magnetic field. Theoretical expressions for this density and electric field fluctuations are derived. The implications of these results in the context of standing slow mode oscillations in coronal loops is discussed.

Role of Compressive Viscosity and Thermal Conductivity on the Damping of Slow Waves in Coronal Loops with and Without Heating–Cooling Imbalance

In the present paper, we derive a new dispersion relation for slow magnetoacoustic waves invoking the effect of thermal conductivity, compressive viscosity, radiation and unknown heating term along with the consideration of heating cooling imbalance from linearized MHD equations. We solve the general dispersion relation to understand role of compressive viscosity and thermal conductivity in damping of the slow waves in coronal loops with and without heating cooling imbalance. We have analyzed wave damping for the range of loop length $L$=50-500 Mm, temperature $T$=5-30 MK, and density $\rho$=10$^{-11}$-10$^{-9}$ kg m$^{-3}$. It was found that inclusion of compressive viscosity along with thermal conductivity significantly enhances the damping of fundamental mode oscillations in shorter (e.g., $L$=50 Mm) and super-hot ($T>$10 MK) loops. However, role of the viscosity in damping is insignificant in longer (e.g., $L$=500 Mm) and hot loops (T$\leq$10 MK) where, instead, thermal conductivity along with the presence of heating cooling imbalance plays a dominant role. For the shorter loops at the super-hot regime of the temperature, increment in loop density substantially enhances damping of the fundamental modes due to thermal conductivity when the viscosity is absent, however, when the compressive viscosity is added the increase in density substantially weakens damping. Thermal conductivity alone is found to play a dominant role in longer loops at lower temperatures (T$\leq$10 MK), while compressive viscosity dominates in damping at super-hot temperatures ($T>$10 MK) in shorter loops. The predicted scaling law between damping time ($\tau$) and wave period ($P$) is found to better match to observed SUMER oscillations when heating cooling imbalance is taken into account in addition to thermal conductivity and compressive viscosity for the damping of the fundamental slow mode oscillations.

Identification and Predictive Analysis of a Multi-Area WECC Power System Model Using Synchrophasors

This paper describes the construction of a reduced-order five-machine dynamic equivalent electro-mechanical model of the Western Electricity Coordinating Council (WECC) 500 kV power system network using slow mode oscillations of power flows derived from phasor measurement unit data. We first extract the slow oscillations using modal decomposition, and use them to estimate four key parameters of the reduced-order system, namely, the inter-area transmission line impedances, intra-area Thevenin reactances, rotational inertia, and damping of the aggregated synchronous generators. The resulting five-machine equivalent model is validated using different ranges of contingencies such as generation loss and line loss, and thereafter used for accurate prediction of oscillation mode frequencies and their damping factors. Finally, we present an algorithm by which this reduced-order model can be used to determine the criticality of line loss events within any area based on the divergence of load flow. The conclusions are drawn with the possible applications of the model for transient stability assessment, and prediction of stability limits needed to sustain increasing wind power penetration in the WECC.

Slow-Mode Oscillations and Damping of Hot Solar Coronal Loops

The effect of temperature inhomogeneity on the periods, their ratios (fundamental vs. first overtone), and the damping times of the standing slow modes in gravitationally stratified solar coronal loops are studied. The effects of optically thin radiation, compressive viscosity, and thermal conduction are considered. The linearized one-dimensional magnetohydrodynamic (MHD) equations (under low-$\beta$ condition) were reduced to a fourth--order ordinary differential equation for the perturbed velocity. The numerical results indicate that the periods of non-isothermal loops (i.e. temperature increases from the loop base to apex) are smaller compared to those of isothermal loops. In the presence of radiation, viscosity, and thermal conduction, an increase in the temperature gradient is followed by a monotonic decrease in the periods (compared with the isothermal case), while the period ratio turns out to be a sensitive function of the gradient of the temperature and the loop lengths. We verify that radiative dissipation is not a main cooling mechanism of both isothermal and non-isothermal hot coronal loops and has a small effect on the periods. Thermal conduction and compressive viscosity are primary mechanisms in the damping of slow modes of the hot coronal loops. The periods and damping times in the presence of compressive viscosity and/or thermal conduction dissipation are consistent with the observed data in specific cases. By tuning the dissipation parameters, the periods and the damping times could be made consistent with the observations in more general cases.

The effect of non-uniform magnetic field on the slow mode oscillations

In this paper, the slow MHD mode oscillations of the coronal plasma are studied. The aim is to identify the effect of structuring (such as magnetic field, temperature, density, and pressure) on the frequencies of oscillations. We modelled the coronal medium as a low- β plasma with longitudinally density and pressure stratifications and a weakly inhomogeneous magnetic field varied slowly with height and radial directions. The linearized ideal MHD equations reduced to a single Klein–Gordon differential equation for square of oscillatory frequencies. The eigenfunctions and analytical dispersion relations are derived. The dispersion relations were solved numerically. In the case of uniform magnetic field, the previous studies verified. Our numerical results show that, the frequencies and their ratios are very sensitive functions of pressure scale height, and slightly varying functions of inhomogeneity parameter of magnetic field. By changing the magnetic field strength between the apex and footpoints of the loop about 50%, the frequencies ratio are changed about 5%. We concluded that, the pressure scale height and temperature gradient are first order effects and inhomogeneity of magnetic field is a second order effect on the slow mode oscillations.

Damping of Slow MHD Coronal Loop Oscillations by Shocks

The damping of slow magnetoacoustic coronal loop oscillations by shock dissipation is investigated. Observations of large-amplitude slow-mode observations made by SUMER show a clear dependency of the damping rate on the oscillation amplitude. Fully nonlinear MHD simulations of slow-mode oscillations in the presence of thermal conduction are performed that show that shock dissipation is an important damping mechanism at large amplitudes, enhancing the damping rate by up to 50% above the rate given by thermal conduction alone. A comparison between the numerical simulations and the SUMER observations shows that although the shock dissipation model can indeed produce an enhanced damping rate that is a function of the oscillation amplitude, the dependency that we found is not as strong as that for the observations, even after observational corrections and the inclusion of enhanced linear dissipation were considered.

Coronal loop slow mode oscillations driven by the kink instability

Aims. To establish the dominant wave modes generated by an internal, m = 1 kink instability in a short coronal flux tube. Methods. The 3D MHD numerical simulations are performed using Lare3d to model the kink instability and the subsequent wave generation. The initial conditions are a straight, zero net current flux tube containing a twist higher than the kink instability threshold. Results. It is shown that the kink instability initially sets up a 1st harmonic (1st overtone) that is converted through the rearrangement of the magnetic field into two out-of-phase fundamental slow modes. These slow modes are in the two entwined flux tubes created during the kink instability. Conclusions. The long-lived oscillations established after a kink instability provide a possible way to identify whether sudden, short coronal loop brightenings may have resulted from a confined kink instability. The mode oscillation structure changes from the 1st harmonic to fundamental due to field line relaxation. The subsequent decay in the fundamental mode is comparable to observations and is caused by shock dissipation. This result has important consequences for the damping of the slow mode oscillations observed by SUMER.

Damping of standing slow waves in hot coronal loops

AbstractThe damping of standing slow mode oscillations in hot (T > 6 MK) coronal loops is described in the linear limit. The effects of energy dissipation by thermal conduction, viscosity, and radiative losses and gains are examined for both stratified and nonstratified loops. We find that thermal conduction acts on the way of increasing the period of the oscillations over the sound crossing time, whereas the decay times are mostly determined by viscous dissipation. Thermal conduction alone results in slower damping of the density and velocity waves compared to the observations. Only when viscosity is added do these waves damp out at the same rate of the observed SUMER loop oscillations. In the linear limit, the periods and decay times are barely affected by gravity.