Fig. 4

Regions of resonance in (equatorial pitch angle \(\alpha_{\text{eq}}\), magnetic latitude \(\lambda\)) space for resonance (n = 4) between magnetosonic waves and ring current protons at L = 3 (inside the plasmasphere) and at L = 6 (outside the plasmasphere) for six energies (from top to bottom: 3 keV, 10 keV, 30 keV, 100 keV, 300 keV, and 1 MeV) and for two wave normal angles (from left to right \(\theta = 87^{\circ }\) and \(\theta = 89^{\circ }\)). The wave frequency band is adopted as 0.0026 < \(\omega /\left( {\varOmega_{ce} } \right)_{\text{eq}}\) < 0.0044, corresponding to a frequency range of 83–141 Hz at L = 3 and 10–18 Hz at L = 6