AbstractThe velocity distribution of the ions in the positive column of the free‐fall type discharge is derived by means of the method of characteristics from collisionless Boltzmann equation extended by a source term in plane and cylindrical geometries. A homogeneous axial magnetic field and the initial distribution of ion velocities is taken into account. The formula of Tonks and Langmuir for ion density is reproduced in case of vanishing initial velocity of the ions and vanishing magnetic fiel