Abstract
The phenomenon of nonlinear second-harmonic generation of elliptically polarized electromagnetic Alfv\'en waves in compensated germanium and helicon waves in n-type indium antimonide has been studied theoretically. The Boltzmann transport equation has been solved to find the nonlinear response of electrons or holes in the semiconductor plasmas in the presence of external magnetic fields. For microwaves of power density \ensuremath{\sim}200 kW ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}2}$ and magnetic field \ensuremath{\sim}10 kG, the power conversion efficiencies of the second-harmonic waves generated turn out to be \ensuremath{\sim}50% and \ensuremath{\sim}2%, respectively, for the Alfv\'en and helicon waves.
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