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The radio pulsar models based on the existence of an inner accelerating gaplocated above the polar cap rely on the existence of a small scale, strongsurface magnetic field $B_s$. This field exceeds the dipolar field $B_d$,responsible for the braking of the pulsar rotation, by at least one order ofmagnitude. Neither magnetospheric currents nor small scale field componentsgenerated during neutron star's birth can provide such field structures in oldpulsars. While the former are too weak to create $B_s \gtrsim 5\times10^{13}$G$\;\gg B_d$, the ohmic decay time of the latter is much shorter than$10^6$ years. We suggest that a large amount of magnetic energy is stored in atoroidal field component that is confined in deeper layers of the crust, wherethe ohmic decay time exceeds $10^7$ years. This toroidal field may be createdby various processes acting early in a neutron star's life. The Hall drift is anon-linear mechanism that, due to the coupling between different components andscales, may be able to create the demanded strong, small scale, magnetic spots.Taking into account both realistic crustal microphysics and a minimal coolingscenario, we show that, in axial symmetry, these field structures are createdon a Hall time scale of $10^3$-$10^4$ years. These magnetic spots can belong-lived, thereby fulfilling the pre-conditions for the appearance of theradio pulsar activity. Such magnetic structures created by the Hall drift arenot static, and dynamical variations on the Hall time scale are expected in thepolar cap region.

Hall drift in the crust of neutron stars - necessary for radio pulsar activity?