van der Pol behavior of relaxation oscillations in a periodically driven thermionic discharge.

The nonlinear dynamics of the frequency entrainment process in periodically driven, self-oscillating thermionic discharges is investigated experimentally. The periodically interrupted frequency entrainment process, known as periodic pulling, is demonstrated to be an essential feature of the transition region between the quasiperiodic state and the entrained state. A detailed comparison of experimental findings with the analytical and numerical study of the driven van der Pol equation x\ifmmode\ddot\else\textasciidieresis\fi{}-\ensuremath{\epsilon}(1-\ensuremath{\beta}${\mathit{x}}^{2}$)${\mathrm{\ensuremath{\omega}}}_{0}$x\ifmmode \dot{}\else \.{}\fi{}+${\mathrm{\ensuremath{\omega}}}_{0}^{2}$x=${\mathrm{\ensuremath{\omega}}}_{0}^{2}$E cos(${\mathrm{\ensuremath{\omega}}}_{\mathit{i}}$t) confirms the relevance of this dynamical model for nonlinear plasma oscillations. A physical explanation is developed based on results from particle-in-cell simulations of periodic pulling in thermionic discharges.