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Based on the exact dipolar solution of the pulsar equation theself-consistent two-fluid model of the pulsar magnetosphere is developed. Weconcentrate on the low-mass limit of the model, taking into account theradiation damping. As a result, we obtain the particle distributions sustainingthe dipolar force-free configuration of the pulsar magnetosphere in case of aslight velocity shear of the electron and positron components. Over most partof the force-free region, the particles follow the poloidal magnetic fieldlines, with the azimuthal velocities being small. Close to the Y-point,however, the particle motion is chiefly azimuthal and the Lorentz-factor growsunrestrictedly. This may result in the very-high-energy emission from thevicinity of the Y-point and may also imply the magnetocentrifugal formation ofa jet. As for the first-order quantities, the longitudinal acceleratingelectric field is found to change the sign, hinting at coexistence of the polarand outer gaps. Besides that, the components of the plasma conductivity tensorare derived and the low-mass analogue of the pulsar equation is formulated aswell.

Two-fluid model of the pulsar magnetosphere represented as an axisymmetric force-free dipole