Potential drops above pulsar polar caps - Acceleration of nonneutral beams from the stellar surface

We develop a self-consistent, three-dimensional method for the calculation of the steady-state acceleration of nonneutral plasma at the surface of a rotating, magnetized, isolated neutron star. When the effects of surface work functions are negligible, there is a unique monotonic electrostatic potential and associated current profile. We obtain explicit solutions in the monopole and polar-cap geometries. In the latter, we neglect field-line curvature and consider only the aligned rotator. The maximum asymptotic particle energy in the polar-cap case, achieved along the central field line, is found to be Emax = 2.8 x l0 eV x (P/l s)-1(B/l012 gauss)112(R*/l06 cm)112(Zmlme)112. This result is in good accord with previous estimates made by Michel. The total luminosity of the pulsar in the form of each charged-particle beam from a polar cap is Lcap =4 x l027(Pll s)-3(B/l012 gauss)312(R*/l06 cm)912(m!Zme)'12 ergs -1 This luminosity is sufficient to explain radio pulsars if the beam energy can be converted to radio radiation with reasonably high efficiency, but is insufficient to explain pulsed y-ray emission from the Crab and other pulsars. In these numerical estimates, we assume that the closed magnetosphere extends to the light cylinder. We also investigate the rotation rate of the plasma, and show that on the open-field lines of the aligned rotator, the beam current induces a twist to the field lines such that an observer at infinity sees the plasma as nonrotating. We apply these results and point out the necessity of including the effects of field-line curvature in a realistic model. Subject headings: hydromagnetics - pulsars