A reduced dispersion relation for multibeam laser–plasma instability is derived. The dispersion relation includes the combined effects of self-coupling and interaction with other beams by sharing a common scattered light (SL modes) and by sharing a common plasma wave (SP modes). The latter two have the most prominent collective effects of all. We have solved the dispersion relation numerically for stimulated Raman scattering, and set different beam configurations and polarizations to discuss the spatial distributions of the temporal growth rate. The instability in the beam overlapping region is complicated, but there are still a few simple rules that govern the system, such as the dominancy of SL modes and subdominancy of backscattering and SP modes. The maximum growth rate always occurs at these special modes, or a new mode formed by combining two or three of the special modes. The reduced model provides us with the ability to understand the underlying physics of multibeam instabilities under general laser and plasma conditions.
