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Given the recent interest in magnetohydrodynamic (MHD) waves in pores andsunspot umbrae, we examine the damping of slow surface kink modes (SSKMs) bymodeling solar photospheric waveguides with a cylindrical inhomogeneitycomprising a uniform interior, a uniform exterior, and a continuous transitionlayer (TL) in between. Performing an eigen-mode analysis in linear, resistive,gravity-free MHD, our approach is idealized in that, among other things, ourequilibrium is structured only in the radial direction. We can nonethelessaddress two damping mechanisms simultaneously, one being the Ohmic resistivity,and the other being the resonant absorption of SSKMs in the cusp andAlfv$\acute{\rm e}$n continua. We find that the relative importance of the twomechanisms depends sensitively on the magnetic Reynolds number ($R_{\rm m}$).Resonant absorption is the sole damping mechanism for realistically largevalues of $R_{\rm m}$, and the cusp resonance in general dominates theAlfv$\acute{\rm e}$n one unless the axial wavenumbers are at the lower end ofthe observationally relevant range. We also find that the thin-boundaryapproximation holds only when the TL-width-to-radius ratios are much smallerthan nominally expected. The Ohmic resistivity is far more important forrealistically small $R_{\rm m}$. Even in this case, SSKMs are only marginallydamped, with damping-time-to-period-ratios reaching $\sim 10$ in the parameterrange we examine.

Damping of slow surface kink modes in solar photospheric waveguides modeled by one-dimensional inhomogeneities