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Hysteresis and Bifurcation for the Axisymmetric Waves in a Nonneutral Electron Plasma

The hysteresis phenomena of the axisymmetric waves in a nonneutral electron plasma were observed by sweeping frequencies of the externally applied sinusoidal oscillations. The nonlinear response for the fundamental mode showed distinct hysteresis phenomenon with positive frequency shift. The response profile was obtained in the three-dimensional control space and compared with the theoretical stationary one. The bifurcation was also observed for the mode. The frequency shift changed its sign from positive to negative when the waves increased in the axial wavenumber. The observed responses for higher modes exhibited hysteresises with negative frequency shifts accompanied by sawtooth-like behavior due to the mode transitions. The mechanism was examined based on the ponderomotive force including the finite effect of the plasma column length.