Trapped sausage modes in magnetic pores: existence criteria and viscous damping

Abstract The conditions governing the existence and evolution of trapped sausage waves in photospheric magnetic pores are investigated, with particular emphasis on the limitations of analytical cut-off criteria and the role of viscous dissipation. A pore is modelled as a cylindrical magnetic flux tube with smoothly varying radial profiles of magnetic field and density, subject to the constraint that its temperature is lower than that of the surrounding atmosphere. For finite plasma-β, the linearised equations governing sausage-mode perturbations are derived, and an initial-value problem is solved numerically to obtain the full spatio-temporal evolution of the waves. The applicability of the analytical cut-off relation derived for a flux tube with step-function equilibrium profiles is examined, revealing that its predictions depend on the equilibrium parameters. The simulations reveal distinct wave behaviours across different parameter regimes, including the simultaneous excitation of trapped fast and slow sausage waves for a representative photospheric parameter set. Viscous damping is further investigated through the temporal evolution of the wave energy. Energy dissipation increases with decreasing viscous Reynolds number, increasing longitudinal wavenumber, and increasing radial magnetic-field contrast. These trends are consistent with enhanced viscous damping associated with increasingly fine spatial gradients generated through phase mixing. The findings highlight the importance of radial equilibrium structure in assessing sausage-wave trapping and demonstrate the sensitivity of wave-energy dissipation to the physical parameters of photospheric magnetic pores.