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 ${\kappa }_{\infty }$, 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 ${\kappa }_{\infty }$, 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 ${\kappa }_{\infty }$, 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 (Reissner-Nordström) solution for a charged black hole.

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