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Abstract
We analyse the behaviour of linear magnetohydrodynamic perturbations of a coronal arcade modelled by a half-cylinder with an azimuthal magnetic field and non-uniform radial profiles of the plasma pressure, temperature, and the field. Attention is paid to the perturbations with short longitudinal (in the direction along the arcade) wavelengths. The radial structure of the perturbations, either oscillatory or evanescent, is prescribed by the radial profiles of the equilibrium quantities. Conditions for the corrugation instability of the arcade are determined. It is established that the instability growth rate increases with decreases in the longitudinal wavelength and the radial wave number. In the unstable mode, the radial perturbations of the magnetic field are stronger than the longitudinal perturbations, creating an almost circularly corrugated rippling of the arcade in the longitudinal direction. For coronal conditions, the growth time of the instability is shorter than one minute, decreasing with an increase in the temperature. Implications of the developed theory for the dynamics of coronal active regions are discussed.
Highlights
Arcades of plasma loops are a typical feature of solar coronal active regions
Waves guided by various plasma non-uniformities are often considered as a superposition of eigenmodes of certain spatially localised resonators where the perturbations have an oscillatory structure between some reflecting or refractive walls and are evanescent outside (e.g. Nakariakov et al, 2016; Cheremnykh, Klimushkin, and Mager, 2016). This approach was applied to the study of unstable small-scale corrugation perturbations of a plasma arcade filled in with a radially non-uniform plasma of finite temperature. This allowed us to understand the influence of the radial wave structure on the instability of an arcade
We focused on perturbations with wavelengths along the arcade much smaller than the radius of the arcade
Summary
Arcades of plasma loops are a typical feature of solar coronal active regions. Examples of coronal arcades are sets of postflare loops in two-ribbon flares and closed magnetic configurations overlying eruptive magnetic ropes. Oliver, Hood, and Priest (1996) considered a general two-dimensional arcade equilibrium structure with no longitudinal magnetic field component, and derived governing equations for the coupled slow and fast modes, while the Alfvén mode was decoupled from the magnetoacoustic modes. The source of the filamentation of an arcade, i.e. the appearance of corrugated fine structure that is often detected in post-flare plasma arcades, is of interest These processes require consideration of MHD perturbations that have a characteristic scale along the arcade axis (i.e., across the field) much shorter than the lengths of the loops that form the arcade. Burdo, Cheremnykh, and Verkhoglyadova (2000) showed that the coupling of the Alfvén and slow magnetoacoustic modes gives rise to a ballooning instability in the dipole field These authors formulated for the first time the instability criterion outside the local approximation.
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