Vacuum gaps in pulsars and PSR J2144-3933
  In this paper we revisit the radio pulsar death line problem within the framework of curvature radiation and/or inverse compton scattering induced vacuum gap model above neutron star polar caps. Our special interest is in the recently detected pulsar PSR J2144-3933 with extremal period 8.5 seconds, which lies far beyond conventional death lines. We argue, that formation of vacuum gaps requires a complicated multipolar surface magnetic field, with a strenght $B_s$ much higher than the surface dipolar component $B_d$, and radii of curvature ${\cal R}$ much smaller than the neutron star radius $R=10^6$ cm. Such a multipolar surface field is also consistent with death lines including the extremal pulsar PSR J2144-3933. Since vacuum gap models produce sparks, our paper naturally supports the spark related models of subpulse drift phenomenon as well as to the spark associated models of coherent pulsar radio emission. 
Janusz Gil (J. Kepler Astronomical Centre), Dipanjan Mitra (Raman   Research Institut)