Pulsar Magnetohydrodynamic Winds

The acceleration and collimation/decollimation of relativistic magnetocentrifugal winds are discussed concerning a cold plasma from a strongly magnetized, rapidly rotating neutron star in a steady axisymmetric state based on ideal magnetohydrodynamics. There exist unipolar inductors associated with the field line angular frequency, $\alpha$ , at the magnetospheric base surface, $S_{\mathrm{B}}$ , with a huge potential difference between the poles and the equator, which drive electric current through the pulsar magnetosphere. Any “current line” must emanate from one terminal of the unipolar inductor and return to the other, converting the Poynting flux to the kinetic flux of the wind at finite distances. In a plausible field structure satisfying the transfield force-balance equation, the fast surface, $S_{\mathrm{F}}$ , must exist somewhere between the subasymptotic and asymptotic domains, i.e., at the innermost point along each field line of the asymptotic domain of $\varpi_{\mathrm{A}}^2 / \varpi^2 \ll 1$ , where $\varpi_{\mathrm{A}}$ is the Alfvénic axial distance. The criticality condition at $S_{\mathrm{F}}$ yields the Lorentz factor, $\gamma_{\mathrm{F}} = \mu_{\varepsilon}^{1/3}$ , and the angular momentum flux, $\beta$ , as the eigenvalues in terms of the field line angular velocity, $\alpha$ , the mass flux per unit flux tube, $\eta$ , and one of the Bernoulli integrals, $\mu_{\delta}$ , which are assumed to be specifiable as the boundary conditions at $S_{\mathrm{B}}$ . The other Bernoulli integral, $\mu_{\varepsilon}$ , is related to $\mu_{\delta}$ as $\mu_{\varepsilon} = \mu_{\delta} [1-(\alpha^2 \varpi_{\mathrm{A}}^2 / c^2)]^{-1}$ , and both $\mu_{\varepsilon}$ and $\varpi_{\mathrm{A}}^2$ are eigenvalues to be determined by the criticality condition at $S_{\mathrm{F}}$ . Ongoing MHD acceleration is possible in the superfast domain. This fact may be helpful in resolving a discrepancy between the wind theory and the Crab-nebula model. It is argued that the “anti-collimation theorem” holds for relativistic winds, based on the curvature of field streamlines determined by the transfield force balance. The “theorem” combines with the “current-closure condition” as a global condition in the wind zone to produce a two-component “quasi-conical” field structure as one of the basic properties of MHD outflows of centrifugal origin in the pulsar magnetosphere.