The effect of thermal misbalance on magnetohydrodynamic modes in coronal magnetic cylinders

Aims. It is well demonstrated that thermal misbalance, arising from the discrepancy between optically thin radiative energy loss and heating energy gain, disrupts the adiabatic nature of solar corona plasmas, directly affecting the propagation of slow magnetoacoustic waves. However, the extent to which this thermal misbalance, acting as a dispersion factor of an arbitrary intensity, influences the use of slow modes as seismological tools and affects sausage and kink harmonic modes within a magnetic plasma flux tube, remains unresolved. Methods. This study investigates the dispersion of magnetohydrodynamic waves influenced by thermal misbalance in a cylindrical configuration with a finite axial magnetic field within solar coronal plasmas. Specifically, it examines how thermal misbalance, characterized by two distinct timescales directly linked to the cooling and heating functions, influences the dispersion relation. This investigation is a key approach for understanding non-adiabatic effects on the behaviour of these waves. Results. The analysis explores the impact of non-adiabatic effects due to classical thermal misbalance, where the heating and cooling timescales vary across a range of values corresponding to each magnetohydrodynamic mode. The dispersion relation for magnetohydrodynamic waves propagating through a magnetic plasma tube, aligned with a finite magnetic field, is calculated under coronal conditions in the linear regime. Conclusions. Our findings reveal that the effect of thermal misbalance on fast sausage and kink modes, consistent with previous studies on slabs, is small but slightly more pronounced than previously thought. The impact is smaller at long-wavelength limits but increases at shorter wavelengths, leading to higher damping rates. This minor effect on fast modes occurs despite the complex interaction of thermal misbalance terms within the dispersion relation, even at low-frequency limits defined by the characteristic timescales. Additionally, a very small amplification is observed, indicating a suppressed damping state for the long-wavelength fundamental fast kink mode. In contrast, slow magnetoacoustic modes are significantly affected by thermal misbalance, with the cusp frequency shifting slightly to lower values, which is significant for smaller longitudinal wavenumbers. This thermal misbalance likely accounts for the substantial attenuation observed in the propagation of slow magnetoacoustic waves within the solar atmosphere. The long-wavelength limit leads to an analytical expression that accurately describes the frequency shifts in slow modes due to misbalance, closely aligning with both numerical and observational results.