Theoretical study on the resonant interaction between helicon waves and electrons

Whistler mode waves within bounded plasmas manifest as helical phase fronts rather than plane waves, and are simply called helicon waves in this paper. To compare wave-particle resonant interactions between helicon waves and plane waves, we present the Hamiltonian describing electron motion based on the eigenmode of helicon waves in a cylindrical coordinate system. For the m = 0 azimuthal mode helicon wave, Hamiltonian theory is used to derive the Poincaré maps of electrons at different initial positions. The results show that electrons can undergo three types of resonances: Landau resonance, cyclotron resonance, and subcyclotron resonance. Unlike plane whistler waves, the spatial distribution of helicon waves leads to a strong dependence of electron resonance behavior on the radial position. As the electron’s position moves from the center to the boundary, the widths of the Landau resonance island and the cyclotron resonance island vary. Particularly, the cyclotron resonance island vanishes when the gyroharmonic-resolved coupling coefficient approaches zero. The island centers can undergo an abrupt change from near Ψ = 0 (π) to Ψ = π (0) owing to a sign change in the gyro-averaged force. The Hamiltonian model established in this paper provides a new theoretical framework for understanding the resonance interaction between helicon waves and electrons in plasmas.