We study the effect of resonant absorption of surface sausage and surface kink modes under photospheric conditions where the slow surface sausage modes undergo resonant damping in the slow continuum and the surface kink modes in the slow and Alfvén continua at the transitional layers. We use recently derived analytical formulas to obtain the damping rate (time). By considering linear density and linear pressure profiles for the transitional layers, we show that resonant absorption in the slow continuum could be an efficient mechanism for the wave damping of the slow surface sausage and slow surface kink modes whilst the damping rate of the slow surface kink mode in the Alfvén continuum is weak. It is also found that the resonant damping of the fast surface kink mode is much stronger than that of the slow surface kink mode, showing a similar efficiency as under coronal conditions. It is worth to notice that the slow body sausage and kink modes can also resonantly damp in the slow continuum for those linear profiles.
Aims. General analytical formulas for the damping rate by resonant absorption of slow sausage modes in the slow (cusp) continuum are derived and the resonant damping of the slow surface mode under photospheric conditions is investigated. Methods. The connection formula across the resonant layer is used to derive the damping rate for the slow sausage mode in the slow continuum by assuming a thin boundary. Results. It is shown that the effect of the resonant damping on the slow surface sausage mode in the slow continuum, which has been underestimated in previous interpretations, could be efficient under magnetic pore conditions. A simplified analytical formula for the damping rate of slow surface mode in the long wavelength limit is derived. This formula can be useful for a rough estimation of the damping rate due to resonant absorption for observational wave damping.
We study theoretically the issue of externally driven excitations of standing kink waves and their resonant absorption into torsionally polarized m = 1 waves in the coronal loops in pressureless plasmas. We use the ideal MHD equations, for which we develop an invariant imbedding method available in cylindrical geometry. We assume a sinusoidal density profile at the loop boundary where the density inside the loop is lower than the outside and vice versa. We present field distributions for these two cases and find that they have similar behaviors. We compare the results for the overdense loops, which describe the usual coronal loops, with the analytical solutions of Soler et al. obtained using the Frobenius method. Our results show some similarity for thin nonuniform layers but deviate a lot for thick nonuniform layers. For the first case, which describes the wave train propagation in funnels, we find that resonant absorption depends crucially on the thickness of the nonuniform boundary, loop length, and density contrast. The resonant absorption of the kink mode is dominant when the loop length is sufficiently larger compared with its radius (thin loop). The behavior of the far-field pattern of the scattered wave by the coronal loop is closely related to that of the resonant absorption. For the mode conversion phenomena in inhomogeneous plasmas, a certain universal behavior of the resonant absorption is found for the first time. We expect that the main feature may also apply to the overdense loops and discuss its relation to the damping rate.
Negative energy wave (NEW) phenomena may appear in shear flows in the presence of a wave decay mechanism and external energy supply. We study the appearance of negative energy surface waves in a plasma cylinder in the incompressible limit. The cylinder is surrounded by an axial magnetic field and by a plasma of different density. Considering flow inside and viscosity outside the flux tube, we derive dispersion relations and obtain analytical solutions for the phase speed and growth rate (increment) of the waves. It is found that the critical speed shear for the occurrence of the dissipative instability associated with NEWs and the threshold of Kelvin–Helmholtz instability (KHI) depend on the axial wavelength. The critical shear for the appearance of sausage NEW is lowest for the longest axial wavelengths, while for kink waves the minimum value of the critical shear is reached for the axial wavelength comparable to the diameter of the cylinder. The range between the critical speed of the dissipative instability and the KHI threshold is shown to depend on the difference of the Alfvén speeds inside and outside of the cylinder. For all axial wavenumbers, NEW appears for the shear flow speeds lower than the KHI threshold. It is easier to excite NEW in an underdense cylinder than in an overdense one. The negative energy surface waves can be effectively generated for an azimuthal number m = 0 with a large axial wavenumber and for higher modes (m > 0) with a small axial wavenumber.
Mode conversion of p-polarized electromagnetic waves into longitudinal plasma oscillations at resonance points in cold, unmagnetized, and stratified plasmas, where a small periodic density modulation is superimposed on a linear electron density profile, is theoretically studied. The mode conversion coefficient and the magnetic field distribution are calculated in a numerically exact manner using the invariant imbedding theory of mode conversion. It is found that resonant enhancement of mode conversion, which is sometimes as high as 100%, can be achieved by tuning the incident angle, the modulation period, or the wave frequency. This phenomenon is explained as due to the formation of a standing wave near the resonance point.
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