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This note deals with steadily rotating nonaxisymmetric pulsar magnetospheres, with the effects of particle inertia fully incorporated. It is pointed out that the equations of motion for the component species of a relativistically streaming nondissipative plasma can be considerably simplified by using the steady-rotation constraint together with a fluxoid conservation law and Endean's Bernoulli-type integral..The canoniCal pulsar model consists of a rotating magnetized neutron star with its magnetic axis inclined to the rotation axis, but a self-consistent model of the pulsar magnetosphere is still lacking. Both the vacuum model, in which the particles are regarded as test charges in the vacuum field, and the zero-inertia model are unacceptable: the plasma is not only a source of the electromagnetic field, but also carries energy and angular momentum.For the axisymmetric vacuum model, Goldreich and Julian (1969) pointed out that the component Ell of the electric field E parallel to the magnetic field B is sufficiently powerful near the star to pull charges out of it, so creating a charged magnetosphere. The solution for the nonaxisymmetric vacuum model with a dipolar magnetic field on. the stellar surface was obtained by Deutsch (1955), in the context of the theory of normal magnetic stars: This enabled Mestel (1971) and Cohen and Toton (1971) to extend the argument of Goldreich and Julian to the oblique rotator model, in which the magnetic and rotation axes are not aligned or anti parallel. Subsequent investigations of the physics of neutron star surfaces have suggested that, for most pulsars, the Goldreich-Julian mechanism might not be sufficiently powerful to extract positive ions (Ruderman 1971).The -argument of Goldreich and Julian (1969) poses the problem of studying magneto spheres that are sufficiently dense near the star to make Ell R! 0 there. Various authors have investigated charge-separated plasmas with inertial and other non-electromagnetic terms neglected, so that the equation of motion is justwhere c and v are the vacuum speed of light and the plasma's fluid velocity. But in the last few years it has become clear that inertial effects are crucial in pulsar magnetospheres: the need for the fields to be nonsingular at the light cylinder leads to difficulties when inertial effects are neglected.

Aust. J. Phys., 1985,38,749-61 Mestel et al. (1985 have recently introduced an axisymmetric pulsar magnetosphere model in which electrons leave the star with speeds that are non-negligible, but not highly relativistic, and flow with moderate acceleration, and with poloidal motion that is closely tied to the poloidal magnetic field lines, before reaching a limiting surface, near which rapid acceleration occurs. This paper presents an analysis of flows which either encounter the limiting surface beyond the light cylinder or do not meet it at all.

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It is pointed out that inertial drift of a species will become important, corresponding to development of vorticity, as its number density becomes small. Hence, regions of inertial development of vorticity will form natural boundary layers to domains in which a species is concentrated.