Mode conversion in a weakly magnetized plasma with a longitudinal density profile

Motivated by conditions in the terrestrial foreshock, the mode conversion process in the inner region for a weakly magnetized plasma with a longitudinal linear density profile is examined. Coupled differential equations are employed to describe the wave energy coupling and the mode structure of electrostatic Langmuir and upper-hybrid branches, and electromagnetic O, X, and Z modes. For an incident electrostatic wave (the “inverse” problem), the coupled equations are solved using Green’s function method, and the mode conversion coefficient is determined from the asymptotic solutions. In the limit of a vanishing magnetic field, solutions converge to previous unmagnetized solutions. It is found that the magnetic field narrows the window of conversion and reduces the angles of propagation of electromagnetic waves with respect to the magnetic field, in agreement with results from previous solutions (of the “direct” problem) for a magnetized cold plasma. The narrowing of the window occurs at angles of propagation larger than the angle corresponding to the maximum conversion.