Threshold analysis of lower hybrid and ion Bernstein wave instability driven by ring-like energetic ions

This paper numerically investigates the instability of lower hybrid and ion Bernstein waves driven by ring-like energetic ions, focusing on the energetic-ion density for their excitation. We systematically analyze how this threshold density depends on crucial parameters, namely, the lower hybrid resonance frequency (ωLH) and the velocity of energetic ions. It is shown that the threshold density tends to decrease significantly when ωLH approaches integer multiples of the ion cyclotron frequency. However, this tendency depends on the energetic-ion velocity. We also find that a higher energetic-ion velocity does not always result in a smaller threshold density; depending on the value of ωLH, the threshold density can be smaller when the energetic-ion velocity is small or intermediate. We discuss the instability mechanism theoretically and compare the theoretical predictions with the numerical results.