Study of nonlinear mode–mode couplings between Alfvénic modes by the Fourier bicoherence and Lissajous-curve technique in HL-2A

Nonlinear couplings of various Alfvén modes driven by energetic particles in HL-2A are addressed by employing the Fourier bicoherence and Lissajous-curve technique. Long-lived modes and high-frequency coherent modes are presented. Then the squared bicoherence of three waves establishes the existence of three-wave coupling. Lissajous-curves of those waves manifest that their phases are locked, which again confirms that they are nonlinearly coupled to each other. Moreover, coupled modes triggered by supersonic molecular beam injection are investigated. The phase evolution of them is given by the Lissajous-curve. Further details of phase-flip and phase-slip are presented and discussed.