In the quest to solve the long-standing coronal heating problem, it has been suggested half a century ago that coronal loops could be heated by waves. Despite the accumulating observational evidence of the possible importance of coronal waves, still no 3D MHD simulations exist that show significant heating by MHD waves. Here we report on the first 3D coronal loop model heating the plasma against radiative cooling. The coronal loop is driven at the footpoint by transverse oscillations and subsequently the induced Kelvin-Helmholtz instability deforms the loop cross-section and generates small-scale structures. Wave energy is transfered to smaller scales where it is dissipated, overcoming the internal energy losses by radiation. These results open up a new avenue to address the coronal heating problem.

There has been considerable interest in sausage modes in photospheric waveguides like pores and sunspots, and slow surface sausage modes (SSSMs) have been suggested to damp sufficiently rapidly to account for chromospheric heating. Working in the framework of linear resistive magnetohydrodynamics, we examine how efficient electric resistivity and resonant absorption in the cusp continuum can be for damping SSSMs in a photospheric waveguide with equilibrium parameters compatible with recent measurements of a photospheric pore. For SSSMs with the measured wavelength, we find that the damping rate due to the cusp resonance is substantially less strong than theoretically expected with the thin-boundary approximation. The damping-time-to-period ratio (τ /P ) we derive for standing modes, equivalent to the damping-length-to-wavelength ratio for propagating modes given the extremely weak dispersion, can reach only ∼ 180. However, the accepted values for electric resistivity (η) correspond to a regime where both the cusp resonance and resistivity play a role. The values for τ /P attained at the largest allowed η may reach ∼ 30. We conclude that electric resistivity can be considerably more efficient than the cusp resonance for damping SSSMs in the pore in question, and it needs to be incorporated into future studies on the damping of SSSMs in photospheric waveguides in general.

We perform three dimensional (3D) ideal magnetohydrodynamic (MHD) simulations to study the parametric decay instability of Alfvén waves in turbulent plasmas and explore its possible applications in the solar wind. We find that, over a broad range of parameters in background turbulence amplitudes, the parametric decay instability of an Alfvén wave with various amplitudes can still occur, though its growth rate in turbulent plasmas tends to be lower than both the theoretical linear theory prediction and that in the non-turbulent situations. Spatial -temporal FFT analyses of density fluctuations produced by the parametric decay instability match well with the dispersion relation of the slow MHD waves. This result may provide an explanation of the generation mechanism of slow waves in the solar wind observed at 1 AU. It further highlights the need to explore the effects of density variations in modifying the turbulence properties as well as in heating the solar wind plasmas.

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