We postulate that under realistic ionospheric conditions, barium ion clouds hundreds of meters in diameter can be long-lived, quasi-stable, nonbifurcating structures. These structures may resemble ''tadpoles,'' with a dense head, steep density gradients at the front, and a long, less dense tail. We assume that these structures are the final products of the recursive bifurcation of a considerably larger barium ion cloud, i.e., striations. The realistic ionospheric conditions to which we refer consist of a barium ion cloud with ion temperatures Ti of approximately 1000 ¿K, coupled electrically to a background ionosphere of lower compressibility than itself, i.e., an F region. We show analytically that this combination of finite Ti and relatively incompressible background, combined with the simplifying assumptions of equipotential magnetic field lines and of a uniform, altitude-invariant neutral wind, results in an effective diffusion of barium plasma but more importantly of total magnetic-field-line-integrated Pedersen conductivity &Sgr;p. The diffusion coefficient has a special form which allows the inner portions of the cloud to diffuse slowly, giving the cloud a long lifetime, and allows the outer, less dense portions of the cloud to diffuse rapidly, preventing cloud bifurcation. Numerical simulations of the full nonlinear dynamics are then used to show that this diffusion does in fact give rise to quasi-stable barium striations hundreds of meters in diameter. These findings are consistent with the linear analysis of Francis and Perkins (1975). The consequences of relaxing the above simplifying assumptions will be treated in subsequent papers in this series.