  We present theoretical models of chromospheric heating for 55 Cancri, an
orange dwarf of relatively low activity. Self-consistent, nonlinear and
time-dependent ab-initio numerical computations are pursued encompassing the
generation, propagation, and dissipation of waves. We consider longitudinal
waves operating among arrays of flux tubes as well as acoustic waves pertaining
to nonmagnetic stellar regions. Additionally, flux enhancements for the
longitudinal waves are also taken into account as supplied by transverse tube
waves. The Ca II K fluxes are computed (multi-ray treatment) assuming partial
redistribution as well as time-dependent ionization. The self-consistent
treatment of time-dependent ionization (especially for hydrogen) greatly
impacts the atmospheric temperatures and electron densities (especially behind
the shocks); it also affects the emergent Ca II fluxes. Particularly, we focus
on the influence of magnetic heating on the stellar atmospheric structure and
the emergent Ca II emission, as well as the impact of nonlinearities. Our study
shows that a higher photospheric magnetic filling factor entails a larger Ca II
emission; however, an increased initial wave energy flux (e.g., associated with
mode coupling) is of little difference. Comparisons of our theoretical results
with observations will be conveyed in forthcoming Paper II.
