  A plasma instability theory is presented for the prompt radiation from
gamma-ray bursts. In the theory, a highly relativistic shell interacts with the
interstellar medium through the filamentation and the two-stream instabilities
to convert bulk kinetic energy into electron thermal energy and magnetic field
energy. The processes are not efficient enough to satisfy the Rankine-Hugoniot
conditions, so a shock cannot form through this mechanism. Instead, the
interstellar medium passes through the shell, with the electrons radiating
during this passage. Gamma-rays are produced by synchrotron self-Compton
emission. Prompt optical emission is also produced through this mechanism,
while prompt radio emission is produced through synchrotron emission. The model
timescales are consistent with the shortest burst timescales. To emit
gamma-rays, the shell's bulk Lorentz factor must be greater than approximately
1000. For the radiative processes to be efficient, the interstellar medium
density must satisfy a lower limit that is a function of the bulk Lorentz
factor. Because the limits operate as selection effects, bursts that violate
them constitute new classes. In particular, a class of optical and ultraviolet
bursts with no gamma-ray emission should exist. The lower limit on the density
of the interstellar medium is consistent with the requirements of the Compton
attenuation theory, providing an explanation for why all burst spectra appear
to be attenuated. Several tests of the theory are discussed, as are the next
theoretical investigations that should be conducted.
