  An extensive investigation is made of the interior structure of self-similar
accreting charged black holes. In this, the first of two papers, the black hole
is assumed to accrete a charged, electrically conducting, relativistic baryonic
fluid. The mass and charge of the black hole are generated self-consistently by
the accreted material. The accreted baryonic fluid undergoes one of two
possible fates: either it plunges directly to the spacelike singularity at zero
radius, or else it drops through the Cauchy horizon. The baryons fall directly
to the singularity if the conductivity either exceeds a certain continuum
threshold kappa_oo, or else equals one of an infinite spectrum kappa_n of
discrete values. Between the discrete values kappa_n, the solution is
characterized by the number of times that the baryonic fluid cycles between
ingoing and outgoing. If the conductivity is at the continuum threshold
kappa_oo, then the solution cycles repeatedly between ingoing and outgoing,
displaying a discrete self-similarity reminiscent of that observed in critical
collapse. Below the continuum threshold kappa_oo, and except at the discrete
values kappa_n, the baryonic fluid drops through the Cauchy horizon, and in
this case undergoes a shock, downstream of which the solution terminates at an
irregular sonic point where the proper acceleration diverges, and there is no
consistent self-similar continuation to zero radius. As far as the solution can
be followed inside the Cauchy horizon, the radial direction is timelike. If the
radial direction remains timelike to zero radius (which cannot be confirmed
because the self-similar solutions terminate), then there is presumably a
spacelike singularity at zero radius inside the Cauchy horizon, which is
distinctly different from the vacuum solution for a charged black hole.
