Abstract
The propagation of an extraordinary wave in a weakly inhomogeneous collisionless magnetoplasma is first studied in the cold plasma approximation. As the cold plasma theory breaks down near the upper hybrid resonance, a fourth-order warm plasma field equation is derived and its solutions obtained in integral form. Connection formulas based on the asymptotic expansion of the integral solutions by the method of saddle-point integration are deduced. These connection formulas are then applied to the problem of mode conversion between extraordinary waves and electrostatic plasma waves across the upper hybrid resonance.
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