  The double pulsar system PSR J0737-3039A/B offers exceptional possibilities
for detailed probes of the structure of the pulsar magnetosphere, pulsar winds
and relativistic reconnection. We numerically model the distortions of the
magnetosphere of pulsar B by the magnetized wind from pulsar A, including
effects of magnetic reconnection and of the geodetic precession. Geodetic
precession leads to secular evolution of the geometric parameters and
effectively allows a 3D view of the magnetosphere. Using the two complimentary
models of pulsar B's magnetosphere, adapted from the Earth's magnetosphere
models by Tsyganenko (ideal pressure confinement) and Dungey (highly resistive
limit), we determine the precise location and shape of the coherent radio
emission generation region within pulsar B's magnetosphere. We successfully
reproduce orbital variations and secular evolution of the profile of B, as well
as subpulse drift (due to reconnection between the magnetospheric and wind
magnetic fields), and determine the location and the shape of the emission
region. The emission region is located at about 3750 stellar radii and has a
horseshoe-like shape, which is centered on the polar magnetic field lines. The
best fit angular parameters of the emission region indicate that radio emission
is generated on the field lines which, according to the theoretical models,
originate close to the poles and carry the maximum current. When considered
together, the results of the two models converge and can explain why the
modulation of B's radio emission at A's period is observed only within a
certain orbital phase region. Our results imply that the wind of pulsar A has a
striped structure only 1000 light cylinder radii away. We discuss the
implications of these results for pulsar magnetospheric models, mechanisms of
coherent radio emission generation, and reconnection rates in relativistic
plasma.
