Brillouin backscattering instability in inhomogeneous collisional plasma

Brillouin backscattering instability is investigated in inhomogeneous colli sional plasma. The slow-coupling equations for the instability in a medium with linear density ramp are obtained. For large inhomogeneity scale length , the homogeneous growth rate is found to be modified by a factor of 1/root2 root omega (2)(0)/omega (2)(0) + nu (2)(e) + omega (0)/root omega ( 2)(0) + nu (2)(e) . For the convective instability, the amplification factor is found to be Lambda = /gamma (0)(B)/(2)/2 beta omega (2)(0)/omega (2)(0) + nu (2)(e). The presence of collisions leads to a reduction in both the growth rate and the amplification factor, where the threshold intensity for the instabilit y to occur increases.