Mestel et al. (1985; MRΩ2) introduced an axisymmetric pulsar magnetosphere model in which electrons leave the star with non-negligible speeds and flow with moderate acceleration, and with poloidal motion that is closely tied to poloidal magnetic field lines, before reaching SL, a limiting surface near which rapid acceleration occurs. As well as these Class I flows, there exist Class II flows which do not encounter a region of rapid acceleration (Burman 1984, 1985b). The formalism introduced by MRΩ2 to describe the moderately accelerated flows can be interpreted in terms of a plasma drift across the magnetic field, following injection along it (Burman 1985a).

The MRΩ2 formalism fully incorporates the toroidal magnetic field generated by the poloidal flow. The general formalism leaves the poloidal magnetic field unspecified, but, in the detailed development of MRΩ2, and in my papers, that field was taken to be the dipolar field of the star.

Numerical work by Fitzpatrick & Mestel (1988a,b) suggested that the dipole approximation is inadequate. They developed a numerical technique for incorporating the modification to the poloidal magnetic field that is generated by the toroidal motions throughout the magnetosphere. They based their treatment on the hypothesis that those motions are such as to cancel the dipole field of the star, leaving a sextupole poloidal magnetic field at large distances.