  In this paper, the nonlinear mode conversion of extraordinary waves in
nonuniform magnetized plasmas is studied using the variational symplectic
particle-in-cell simulation. The accuracy of the nonlinear simulation is
guaranteed by the long-term accuracy and conservativeness of the symplectic
algorithm. The spectra of the electromagnetic wave, the evolution of the wave
reflectivity, the energy deposition profile, and the parameter-dependent
properties of radio-frequency waves during the nonlinear mode conversion are
investigated. It is illustrated that nonlinear effects significantly modify the
physics of the radio-frequency injection in magnetized plasmas. The evolutions
of the radio-frequency wave reflectivity and the energy deposition are
observed, as well as the self-interaction of the Bernstein waves and mode
excitations. Even for waves with small magnitude, nonlinear effects can also
become important after continuous wave injections, which are common in the
realistic radio-frequency wave heating and current drive experiments.
