  A magnetohydrodynamic model that includes a complete electrical conductivity
tensor is used to estimate conditions for photospherically driven, linear,
non-plane Alfvenic oscillations extending from the photosphere to the lower
corona to drive a chromospheric heating rate due to Pedersen current
dissipation that is comparable to the net chromospheric net radiative loss of
$\sim 10^7$ ergs-cm$^{-2}$-sec$^{-1}$. The heating rates due to electron
current dissipation in the photosphere and corona are also computed. The wave
amplitudes are computed self-consistently as functions of an inhomogeneous
background (BG) atmosphere. The effects of the conductivity tensor are resolved
numerically using a resolution of 3.33 m. The oscillations drive a
chromospheric heating flux $F_{Ch} \sim 10^7 - 10^8$ ergs-cm$^{-2}$-sec$^{-1}$
at frequencies $\nu \sim 10^2 - 10^3$ mHz for BG magnetic field strengths $B
\gtrsim 700$ G and magnetic field perturbation amplitudes $\sim 0.01 - 0.1$
$B$. The total resistive heating flux increases with $\nu$. Most heating occurs
in the photosphere. Thermalization of Poynting flux in the photosphere due to
electron current dissipation regulates the Poynting flux into the chromosphere,
limiting $F_{Ch}$. $F_{Ch}$ initially increases with $\nu$, reaches a maximum,
and then decreases with increasing $\nu$ due to increasing electron current
dissipation in the photosphere. The resolution needed to resolve the
oscillations increases from $\sim 10$ m in the photosphere to $\sim 10$ km in
the upper chromosphere, and is proportional to $\nu^{-1/2}$. Estimates suggest
that these oscillations are normal modes of photospheric flux tubes with
diameters $\sim 10-20$ km, excited by magnetic reconnection in current sheets
with thicknesses $\sim 0.1$ km.
