Published online by Cambridge University Press: 09 July 2013
Brillouin backward scattering is investigated in the interaction of linearly polarized short laser pulse with a homogenous underdense transversely magnetized plasma by taking into account the relativistic and nonlinearity effects up to third order. The plasma is embedded in a uniform magnetic field perpendicular to both of propagation direction and electric vector of the radiation field. Temporal growth rate of instability is calculated by using of the nonlinear wave equation. Results are significantly different in comparison with lower order computations. The growth rate of Brillouin backward instability shows a decrease due to the presence of external magnetic field, while relativistic and higher order nonlinearities due to the external magnetic field, give rise the Brillouin backward scattering instability.