Aurorae often break down into elongated, cylindrically symmetric space-charge filaments (with radius r) parallel to the local uniform geomagnetic field. We study the ion kinetic theory in auroral plasmas in the presence of the strong electric field (E) produced by the filaments. A method of characteristics is used to solve both the collision-free and collisional Boltzmann equation under different E and initial ion density (n). If E is constant in time (t) but proportional to r and n is uniform, the collision-free ion distribution function (f) pulsates in t and transport properties oscillate. If collisions are introduced, f takes a horseshoe shape symmetric to the E direction while the bulk parameters evolve from pulsating to steady states. When E changes radially, the collision-free f has various shapes and bulk parameters change accordingly. Results are also obtained in the presence of collisions and initial density inhomogeneities when E is constant in t and proportional to r. Finally, when E is unable to stay constant and is modulated by in-coming charged particles (i.e., the Bolzmann-Vlasov problem), several plasma wave modes are excited under different initial conditions.