  Giant radio pulses of the millisecond pulsar B1937+21 were recorded with the
S2 VLBI system at 1.65 GHz with NASA/JPL's 70-m radio telescope at Tidbinbilla,
Australia. These pulses have been observed as strong as 65000 Jy with widths <=
15 ns, corresponding to a brightness temperature T_b >= 5 x 10^39 K, the
highest observed in the universe. The vast majority of these pulses occur in a
5.8 mcs and 8.2 mcs window at the very trailing edges of the regular main pulse
and interpulse profiles, respectively. Giant pulses occur in general with a
single spike. Only in one case out of 309 was the structure clearly more
complex. The cumulative distribution is fit by a power law with index -1.40 +/-
0.01 with a low-energy but no high-energy cutoff. We estimate that giant pulses
occur frequently but are only rarely detected. When corrected for the
directivity factor, 25 giant pulses are estimated to be generated in one
neutron star revolution alone. The intensities of the giant pulses of the main
pulses and interpulses are not correlated with each other nor with the
intensities or energies of the main pulses and interpulses themselves. Their
radiation energy density can exceed 300 times the plasma energy density at the
surface of the neutron star and can even exceed the magnetic field energy
density at that surface. We therefore do not think that the generation of giant
pulses is linked to the plasma mechanisms in the magnetosphere. Instead we
suggest that it is directly related to discharges in the polar cap region of
the pulsar.
