Harmonic generation by Gould–Trivelpiece modes propagating into an axial density gradient

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Abstract
Prior experiments on the propagation of electrostatic waves on a plasma column (Gould–Trivelpiece modes) have shown linear wave reflections from an adjustable axial density gradient which scaled according to the predictions of WKB theory. For finite amplitude incident waves at radian frequency ω<ωpo, we have observed strong harmonic production at frequencies nω<ωpo where n in an integer and ωpo is the mean electron plasma frequency in the axially uniform part of the column. The harmonic production appeared to originate in the axially nonuniform plasma, and decreased markedly as the gradient was reduced experimentally. No threshold for harmonic production was observed, thus suggesting that parametric effects were not important. Second‐order perturbation theory based on the cold plasma equations is applied to an axially nonuniform plasma in a strong uniform axial magnetic field. The results show that nonlinear source terms enter into the governing differential equation for the second‐harmonic potential which are larger than the customary nonlinear terms for an axially uniform column, by a factor as large as (ωpR/ωL)4 where R is the plasma radius and L is the scale length of the inhomogeneity. Enhancement in harmonic production predicted by this model is in quantitative agreement with the experiment.