In this paper, the nonlinear interaction of ultra-high power laser beam with fusion plasma at relativistic regime in the presence of obliquely external magnetic field has been studied. Imposing an external magnetic field on plasma can modify the density profile of the plasma so that the thermal conductivity of electrons reduces which is considered to be the decrease of the threshold energy for ignition. To achieve the fusion of Hydrogen–Boron(HB) fuel,the block acceleration model of plasma is employed. Energy production by HB isotopes can be of interest, since its reaction does not generate radioactive tritium. By using the inhibit factor in the block model acceleration of plasma and Maxwell's as well as the momentum transfer equations, the electron density distribution and dielectric permittivity of the plasma medium are obtained. Numerical results indicate that with increasing the intensity of the external magnetic field, the oscillation of the laser magnetic field decreases, while the dielectric permittivity increases. Moreover, the amplitude of the electron density becomes highly peaked and the plasma electrons are strongly bunched with increasing the intensity of external magnetic field. Therefore, the magnetized plasma can act as a positive focusing lens to enhance the fusion process. Besides, we find that with increasing θ-angle(from oblique external magnetic field) between 0 and 90°, the dielectric permittivity increases, while for θ between 90° and 180°, the dielectric permittivity decreases with increasing θ.
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