  A kinetic theory for radiation interacting with sound waves in an
ultrarelativistic electron-positron plasma is developed. It is shown that the
effect of a spatial spectral broadening of the electromagnetic pulse is to
introduce a reduction of the growth rates for the decay and modulational
instabilities. Such spectral broadening could be due to a finite pulse
coherence length, or through the use of random phase filters, and would
stabilize the propagation of electromagnetic pulses.
