Corrugation Instability of a Coronal Arcade

Abstract

We analyse the behaviour of linear magnetohydrodynamic perturbations of a coronal arcade modelled by a half-cylinder with an azimuthal magnetic field and nonuniform 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.

Ballooning Instability in the Magnetospheric Plasma: Two‐Dimensional Eigenmode Analysis

“…As was demonstrated in Zhu et al (2004), Parnowski (2007, Agapitov et al (2008), Mazur et al (2012), and Leonovich and Kozlov (2013), the increase of the k r value deteriorates conditions for the development of the ballooning instability. As was shown in Mazur et al (2013) and Klimushkin et al (2017), in this case the unstable mode is captured in a resonator across the magnetic shells where only the modes with some discrete k r values can exist. It should not be considered as a free parameter, because the transverse structure of the perturbation must be sensitive to a radial profile of the plasma density and pressure.…”

“…This instability (coined as the ballooning instability) can develop at steep decrease of the plasma pressure with distance from the Earth (Coppi, 1977). The ballooning instability can be responsible for the magnetospheric substorm initiation (Chen et al, 2003;Kalmoni et al, 2015;Roux et al, 1991), generation of the different kinds of the oscillations in the Earth's magnetosphere (Golovchanskaya et al, 2006;Safargaleev & Maltsev, 1986;Viñas & Madden, 1986), and development of the eruptive processes in the Solar corona (Cheremnykh et al, 2018;Hood, 1992;Klimushkin et al, 2017;Stepanov et al, 2008).…”

“…The eigenvalue of the former problem will be used as a parameter of the latter one. In doing so, various asymptotical methods earlier developed in Leonovich and Mazur (, ) and Klimushkin et al () are applied. As a result, the solution of this system completely determines two‐dimensional spatial structure of the ballooning instability in the two‐dimensionally inhomogeneous model of the magnetosphere.…”

Magnetic structure of solar flare regions producing hard X-ray pulsations

“…This hypotheses, however, requires further study, and is beyond the scope of the present work, which will be addressed elsewhere. In addition, the spatial quasi-periodicity could, in particular, result from some instabilities of a reconnecting macroscopic current sheet (e.g., Artemyev and Zimovets, 2012;Ledentsov and Somov, 2016) created during an MFR rise, or from the corrugation instability of a coronal arcade recently described by Klimushkin et al (2017).…”

Thermal Trigger for Solar Flares I: Fragmentation of the Preflare Current Layer

“…Often, a similar solution was sought in the interaction of the current layer with magnetohydrodynamic (MHD) waves (Vorpahl, 1976;Nakariakov et al, 2006;Artemyev and Zimovets, 2012). Also, a spatially inhomogeneous energy release was considered as a result of corrugation instability of a coronal arcade (Klimushkin et al, 2017). The magnetic field frozen into a plasma displaced by the instability could reconnect with the overlying magnetic field, leading to the heating of the unstable flux tube.…”