Convection in protoneutron stars and the structure of surface magnetic fields in pulsars

We consider generation and evolution of small-scale magnetic fields in neutron stars. These fields can be generated by small-scale turbulent dynamo action soon after the collapse when the protoneutron star is subject to convective and neutron finger instabilities. After instabilities stop, small-scale fields should be frozen into the crust that forms initially at high density similar to10(14) g/cm(3) and then spreads to the surface. Because of high crustal conductivity, magnetic fields with the lengthscale similar to1-3 km can survive in the crust as long as 10-100 Myr and form a sunspot-like structure at the surface of radiopulsars.