Exact solution for slow magneto-acoustic and entropy waves in coronal loops with thermal misbalance and thermal conduction

Abstract Slow magneto-acoustic and entropy waves can serve as diagnostic tools not only for probing plasma parameters but also for investigating non-adiabatic processes. Under coronal conditions, these waves are strongly affected by both thermal conduction and thermal misbalance. In this work, we obtain an exact solution to the linear evolutionary equation describing wave dynamics in plasma under the assumption of an infinitely strong magnetic field. We show that two dispersion sources significantly expand the set of parametric regions with qualitatively similar behaviour of dispersion curves and increase the number of ways an arbitrary initial disturbance can develop. The resulting solution allows for monitoring the behaviour of individual harmonics of the eigenmodes for the plasma parameter of interest, thus expanding the possibilities for fitting observations and studying the behaviour of model signals. Using the obtained solution, we show that several thermal misbalance regimes enable quasi-periodic pulsation formation. We also demonstrate that additional information about non-adiabatic processes can be gained by considering the amplitude ratios of various plasma parameters and their phase shifts for arbitrary harmonic numbers. In particular, this may be of interest for plasma diagnostics using sloshing oscillations, which involve the simultaneous development of multiple oscillations. This article is part of the theme issue ‘Transferable mechanisms in the oscillatory processes of solar and stellar flares'.