A plasma instability theory is presented for the prompt radiation from gamma-ray bursts. In the theory, a highly relativistic shell interacts with the external 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 external 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 or similar to 10(3). For the radiative processes to be efficient, the external 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. Efficient gamma-ray emission requires an external medium of relatively high density. Several tests of the theory are discussed, as are the next theoretical investigations that should be conducted.
