A Gaussian laser beam, propagating as an eigenmode through a low density plasma channel in the presence of an axial magnetic field, undergoes stimulated Raman back scattering, producing an upper hybrid wave and a radially localized electromagnetic sideband wave. The channel may be self created by the laser due to ponderomotive force or by a pre-pulse. The radial width of sideband is ≈ a and Langmuir wave of extent b ≈ (alambda;D)~(1/2) ≤a. The nonlocal effect arising, due to self generated magnetic field, modifies the electron response to these Eigen modes, reduces the region of nonlocal interaction and hence the growth rate. The growth rate decreases with the pump wave amplitude and it maximum for back scattering. A nonlocal theory of stimulated Raman back-scattering of a laser, propagating through a plasma channel in the presence of an axial magnetic field, is developed. The laser excites a forward propagating upper hybrid mode, that is strongly localized radially, and a backward propagating electromagnetic wave-sideband. The growth rate significantly decreases with the magnetic field.
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