Dynamics of fast and slow magnetoacoustic waves in plasma slabs with thermal misbalance

Non-uniformity of the solar atmosphere along with the presence of non-adiabatic processes such as radiation cooling and unspecified heating can significantly affect the dynamics and properties of magnetoacoustic (MA) waves. To address the co-influence of these factors on the dispersion properties of MA waves, we considered a single magnetic slab composed of the thermally active plasma. Using the perturbation theory, we obtained a differential equation that determines the dynamics of the two-dimensional perturbations. Applying the assumption of strong magnetic structuring, we derived the dispersion relations for the sausage and kink MA modes. The numerical solution of the dispersion relations for the coronal conditions was performed to investigate the interplay between the non-uniformity and the thermal misbalance. For the heating scenario considered, it was obtained that the phase speed of both the sausage and kink slow MA waves is highly affected by the thermal misbalance in the long wavelength limit. The obtained characteristic timescales of the slow waves dissipation coincide with the periods of waves observed in the corona. Simultaneously, the phase speed of the fast waves is not affected by the thermal misbalance. The geometry of the magnetic structure still remains the main dispersion mechanism for the fast waves. Our estimation reveals that dissipation of the fast waves is weaker than dissipation of the slow waves in the coronal conditions. The obtained results are of importance for using the magnetoacoustic waves not only as a tool for estimating plasma parameters, but also as a tool for estimating the non-adiabatic processes

The solar corona as an active medium for magnetoacoustic waves

The presence and interplay of continuous cooling and heating processes maintaining the corona of the Sun at the observed one million K temperature were recently understood to have crucial effects on the dynamics and stability of magnetoacoustic (MA) waves. These essentially compressive waves perturb the coronal thermal equilibrium, leading to the phenomenon of a wave-induced thermal misbalance (TM). Representing an additional natural mechanism for the exchange of energy between the plasma and the wave, TM makes the corona an active medium for MA waves, so that the wave can not only lose but also gain energy from the coronal heating source (similarly to burning gases, lasers and masers). We review recent achievements in this newly emerging research field, focussing on the effects that slow-mode MA waves experience as a back-reaction of this perturbed coronal thermal equilibrium. The new effects include enhanced frequency-dependent damping or amplification of slow waves, and effective, not associated with the coronal plasma non-uniformity, dispersion. We also discuss the possibility to probe the unknown coronal heating function by observations of slow waves and linear theory of thermal instabilities. The manifold of the new properties that slow waves acquire from a thermodynamically active nature of the solar corona indicate a clear need for accounting for the effects of combined coronal heating/cooling processes not only for traditional problems of the formation and evolution of prominences and coronal rain, but also for an adequate modelling and interpretation of magnetohydrodynamic waves

Damping of slow magnetoacoustic oscillations by the misbalance between heating and cooling processes in the solar corona

Context. Rapidly decaying slow magnetoacoustic waves are regularly observed in the solar coronal structures, offering a promising tool for a seismological diagnostics of the coronal plasma, including its thermodynamical properties. Aims. The effect of damping of standing slow magnetoacoustic oscillations in the solar coronal loops is investigated accounting for field-aligned thermal conductivity and a wave-induced misbalance between radiative cooling and some unspecified heating rates. Methods. The non-adiabatic terms were allowed to be arbitrarily large, corresponding to the observed values. The thermal conductivity was taken in its classical form, and a power-law dependence of the heating function on the density and temperature was assumed. The analysis was conducted in the linear regime and in the infinite magnetic field approximation. Results. The wave dynamics is found to be highly sensitive to the characteristic timescales of the thermal misbalance. Depending on certain values of the misbalance, timescales three regimes of the wave evolution were identified, namely the regime of a suppressed damping, enhanced damping in which the damping rate drops down to observational values, and acoustic over-stability. The specific regime is determined by the dependences of the radiative cooling and heating functions on thermodynamical parameters of the plasma in the vicinity of the perturbed thermal equilibrium. Conclusions. The comparison of the observed and theoretically derived decay times and oscillation periods allows us to constrain the coronal heating function. For typical coronal parameters, the observed properties of standing slow magnetoacoustic oscillations could be readily reproduced with a reasonable choice of the heating function

Formation of quasi-periodic slow magnetoacoustic wave trains by the heating/cooling misbalance

Slow magnetoacoustic waves are omnipresent in both natural and laboratory plasma systems. The wave-induced misbalance between plasma cooling and heating processes causes the amplification or attenuation, and also dispersion, of slow magnetoacoustic waves. The wave dispersion could be attributed to the presence of characteristic time scales in the system, connected with the plasma heating or cooling due to the competition of the heating and cooling processes in the vicinity of the thermal equilibrium. We analysed linear slow magnetoacoustic waves in a plasma in a thermal equilibrium formed by a balance of optically thin radiative losses, field-align thermal conduction, and an unspecified heating. The dispersion is manifested by the dependence of the effective adiabatic index of the wave on the wave frequency, making the phase and group speeds frequency-dependent. The mutual effect of the wave amplification and dispersion is shown to result into the occurrence of an oscillatory pattern in an initially broadband slow wave, with the characteristic period determined by the thermal misbalance time scales, i.e. by the derivatives of the combined radiation loss and heating function with respect to the density and temperature, evaluated at the equilibrium. This effect is illustrated by estimating the characteristic period of the oscillatory pattern, appearing because of thermal misbalance in the plasma of the solar corona. It is found that by an order of magnitude the period is about the typical periods of slow magnetoacoustic oscillations detected in the corona