Investigation of ion instability exhibiting a broadband continuous spectrum in electron cyclotron resonance magnetic nozzle

Instabilities in electron cyclotron resonance (ECR) magnetic nozzles are investigated through both theoretical analysis and experimental observation. An analytical dispersion relation for instabilities is derived using a two-fluid model. Experimentally, an instability measurement system employing fixed probe pairs is utilized to detect the presence of instabilities within the magnetic nozzle. Additionally, time-averaged plasma parameters inside the magnetic nozzle are measured for theoretical analysis of instabilities. By integrating the theoretical dispersion analysis with experimental instability measurements and plasma diagnostics, the influence of electromagnetic fields on the observed azimuthal instabilities is examined. The results reveal that the maximum growth rate (γ_max) of the azimuthal instability decreases while the corresponding wavelength increases with the divergence angle of the magnetic field, defined as tan⁻¹(B_x/B_z). As for the electric field effects, γ_max increases with a stronger parallel electric field E_∥ along the magnetic field lines, whereas the corresponding wavelength becomes shorter. In contrast, the perpendicular electric field E_⊥ shows negligible influence on the instability. These findings suggest that maintaining the magnetic field divergence angle between 30°and 45°, along with reducing the magnetic field gradient, can effectively suppress azimuthal instabilities in ECR magnetic nozzles.