A Parametric Study On The Damping Of Slow Surface Sausage Modes In Solar Photospheric Waveguides

Identifying magnetohydrodynamic(MHD)waves in the structured solar at-mosphere is vital from the perspectives of both solar magneto-seismology and atmospheric heating.While coronal waves and oscillations remain a focus,vari-ous MHD modes have also been observed in a considerable number of structures in the lower solar atmosphere.In particular,photospheric pores and sunspots were shown to host a variety of waves.Thanks to modern ground-based,high-cadence and high spatial resolution instruments like the Rapid Oscillations in the Solar Atmosphere,these waves were ascertained,on the bases of parity and axial phase speed,to be either fast or slow sausage waves.More recently,measurements of the spatial distribution of wave power enabled these waves to be further grouped into surface and body modes.If these low-frequency waves are able to carry sig-nificant energy flux,they may dissipate and release a large amount of energy into the solar atmosphere and contribute to maintaining the high-temperature of the chromosphere and solar corona.On the other hand,based on the measurements of the waves and oscillations in the solar lower atmosphere as well as the theo-ry on the collective MHD waves,it is possible for us to infer the physical and sub-resolution geometrical parameters that are difficult to measure directly.Among the above-mentioned studies on waves in photospheric structures,of particular interest are the recent multi-wavelength measurements of slow surface sausage modes(SSSMs)in a magnetic pore by Grant et al.(Grant15 for short),where propagating SSSMs were shown to damp over a length scale as short as a quarter of the wavelength,so as to be important in heating the chromosphere.Working under the thin-boundary(TB)approximation,Yu et.al.showed that the resonant absorption of SSSMs in the cusp continuum may play a substantial role in their damping,with the damping-time-to-period ratio ?/P reaching down to?10.Note that while this damping was obtained for standing modes,the damping-length-to-wavelength ratio LD/? is nearly identical to ?/P because of the extremely weak dispersion of SSSMs.In 2018,working in the framework of linear resistive MHD,Chen et al.(Chen18 for short)relaxed the TB approxi-mation and examined how efficient both cusp resonant absorption and electric resistivity can be for damping SSSMs in a photospheric waveguide with equilibri-um parameters compatible with recent measurements of the photospheric pore in Grant15.For SSSMs with the measured wavelength,Chen et al.found that the damping rate due to the cusp resonance is substantially less strong than theoret-ically expected with the TB approximation.The damping-time-to-period ratio?/P derived for standing modes,equivalent to the damping-length-to-wavelength ratio for propagating modes given the extremely weak dispersion,can reach only?100.However,the accepted values for electric resistivity ? correspond to a regime where both the cusp resonance and electric resistivity play a role.The values for ?/P attained at the largest allowed ? may reach?30.In conclusion,electric resistivity can be considerably more efficient than the cusp resonance for damping SSSMs in the pore in Grant15,and needs to be incorporated into future studies on the damping of SSSMs in photospheric waveguides in general.However,the conclusions in Chen18 are obtained for a special kind of trans-versely continuous distribution of equilibrium parameters.In order to achieve more general results,in Chapter 3,we further investigate the damping of SSSMs due to both the cusp resonant absorption and the direct resistivity for photo-spheric magnetic flux tubes with the sandwich-like transverse structuring.The main results can be summarized as follows.1)We present the first systematic study of the cusp resonant absorption of SSSMs in photospheric waveguides with the sandwich-like transverse parameter distribution.We find that the qualitative behavior of SSSMs in magnetic flux tubes with different distribution is the same while the quantitative results are much dependent on the details of the profile.2)We present the first systematic study of the damping of SSSMs owing to the direct resistivity in photospheric waveguides with the sandwich-like transverse parame-ter profile and also estimate the relative significance of cusp resonant absorption and electric resistive dissipation.We find that the electric resistivity can be much more efficient than the cusp resonance for damping SSSMs in the photospheric pores.3)We investigate the severe damping of propagating SSSMs in Grant15 and try to interpret their damping in the framework of resistive MHD theory.Through extensive numerical computations,we find that neither direct electric resistivity nor cusp resonant absorption can lead to the observed severe damping,provided that the values and transverse distribution of equilibrium parameters are adopted in the regime of our work.