The effects of the nonlinear polarization in a partially stripped plasma on stimulated Brillouin scattering （SBS） process of a strong laser are discussed. A set of nonlineax mode coupling equations and the linear growth rate of SBS instability is derived, respectively. When the intensity of an incident laser Io > 1017 W/cm2, the third order susceptibility X（3） will reduce the above mentioned linear growth rate enormously. If taking the maximum value of the second order susceptibility X（2）, the growth rate may be decreased observably when Io > 1014W/cm2. Furthermore, the nonlinear susceptibility can affect the nonlinear evolution of SBS much extensively.
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