The migration of intense ionization created in helium buffer gas under the influence of applied electric fields is considered. First the chemical evolution of the ionization created by fast heavy-ion beams is described. Straight forward estimates of the lifetimes for charge exchange indicate a clear suppression of charge exchange during ion migration in low pressure helium. Then self-consistent calculations of the migration of the ions in the electric field of a gas-filled cell at the National Superconducting Cyclotron Laboratory (NSCL) using a Particle-In-Cell computer code are presented. The results of the calculations are compared to measurements of the extracted ion current caused by beam pulses injected into the NSCL gas cell.