A theoretical formalism is developed to obtain the mode structure of right circularly polarized nonlinear laser Eigen mode in a self created plasma channel in the presence of an axial magnetic field. The nonlinearity in electron response arises due to relativistic mass effect and ponderomotive force induced density redistribution. The Eigen mode is seen to be unstable to stimulated Raman backscattering involving an electrostatic quasi-mode and a scattered electromagnetic wave. The growth rate increases with ambient magnetic field.
