We present a linear stability analysis of the perturbation modes in anisotropic MHD flows with velocity shear and strong magnetic field. Collisionless or weakly collisional plasma is described within the 16-momentum MHD fluid closure model, that take
s into account not only the effect of pressure anisotropy, but also the effect of anisotropic heat fluxes. In this model the low frequency acoustic wave is revealed into a standard acoustic mode and higher frequency fast thermo-acoustic and lower frequency slow thermo-acoustic waves. It is shown that thermo-acoustic waves become unstable and grow exponentially when the heat flux parameter exceeds some critical value. It seems that velocity shear makes thermo-acoustic waves overstable even at subcritical heat flux parameters. Thus, when the effect of heat fluxes is not profound acoustic waves will grow due to the velocity shear, while at supercritical heat fluxes the flow reveals compressible thermal instability. Anisotropic thermal instability should be also important in astrophysical environments, where it will limit the maximal value of magnetic field that a low density ionized anisotropic flow can sustain.
The main goal is to study the dynamics of the gravitationally stratified, field-free cavities in the solar atmosphere, located under small-scale, cylindrical magnetic canopies, in response to explosive events in the lower-lying regions (due to granul
ation, small-scale magnetic reconnection, etc.). We derive the two-dimensional Klein-Gordon equation for isothermal density perturbations in cylindrical coordinates. The equation is first solved by a standard normal mode analysis in order to obtain the free oscillation spectrum of the cavity. Then, the equation is solved in the case of impulsive forcing associated to a pressure pulse specified in the lower-lying regions. The normal mode analysis shows that the entire cylindrical cavity of granular dimensions tends to oscillate with frequencies of 5-8 mHz and also with the atmospheric cut-off frequency. Furthermore, the passage of a pressure pulse, excited in the convection zone, sets up a wake in the cavity oscillating with the same cut-off frequency. The wake oscillations can resonate with the free oscillation modes, which leads to an enhanced observed oscillation power. The resonant oscillations of these cavities explain the observed power halos near magnetic network cores and active regions.
A model of the Lu-Hamilton kind is applied to the study of critical behavior of the magnetized solar atmosphere. The main novelty is that its driving is done via sources undergoing a diffusion. This mimics the effect of a virtual turbulent substrate
forcing the system. The system exhibits power-law statistics not only in the size of the flares, but also in the distribution of the waiting times.
The propagation of compressional MHD waves is studied for an externally driven system. It is assumed that the combined action of the external sources and sinks of the entropy results in the harmonic oscillation of the entropy (and temperature) in the
system. It is found that with the appropriate resonant conditions fast and slow waves get amplified due to the phenomenon of parametric resonance. Besides, it is shown that the considered waves are mutually coupled as a consequence of the nonequilibrium state of the background medium. The coupling is strongest when the plasma $beta approx 1$. The proposed formalism is sufficiently general and can be applied for many dynamical systems, both under terrestrial and astrophysical conditions.
