Cross-field charge transport by the diocotron instability in pulsar magnetospheres with gaps

In a previous work, we have shown by linear analysis that a thin charged disk in differential rotation in the magnetosphere of a neutron star with vacuum gaps is unstable to a collisionless instability induced in non-neutral plasmas by differential rotation, the diocotron instability. In this paper we study the long-time-scale evolution of this instability in the non-linear regime by means of both direct numerical simulations and a quasilinear model. We show that, when the disk is externally fed with charged particles produced by a moderate pair creation activity in the magnetosphere, the diocotron instability causes diffusion of the charged particles across the magnetic field lines outwards. An equatorial cross-field electric current is observed to form, carrying a net charge flux radially outwards. This constitutes a hitherto ignored charge transport mechanism in the pulsar magnetosphere. We briefly discuss how this turbulent charge transport mechanism could bear on the problem of electric current closure in pulsarʹs magnetospheres.