The stability of a weakly ionized plasma column against a screw type perturbation in the presence of an applied axial electric field and a predominantly radial magnetic field—a linear Hall current accelerator—is investigated. The analysis is based on the ion and electron conservation equations and takes into consideration the effects of ionization. It is shown that the observed instability cannot be explained when the axial component of the magnetic field is identically zero even when one takes into consideration steady‐state solutions with both radial and axial dependence. On the other hand, when the axial component of the magnetic field is small, but not zero, the column is unstable in the absence of an axial density gradient to a right‐handed helical perturbation (m= −1). The resulting instability, which is of the Kadomtsev and Nedospasov type, is analyzed using a normal mode analysis. The results are in qualitative agreement with experiment.