The weak resonance-overlapping multiple-n TAE (β_h = 1.81%) (a) and the relatively strong resonance-overlapping multiple-n TAE (γ_h = 6%) (b). Fast ion trajectories in the phase space of canonical momentum P_ϕ and energy E in the presence of multiple-n TAE modes at t = 0–2000τ_A. Only the initially resonant particles are plotted in the figure. The particles which initially resonate with the different components of the multiple-n mode are represented by colors: n = 1 (red), n = 2 (green), n = 3 (black), n = 4 (blue). Since the particles are trapped by the n = 1, 2, 3, 4 modes, the positions of resonant particles in phase space can be regarded as the eigenmodes. Namely, the eigenmodes are represented by colors: n = 1 (red), n = 2 (green), n = 3 (black), n = 4 (blue). The frequencies of ω₁, ω₂, ω₃, ω₄ stand for the mode frequencies of n = 1, 2, 3, 4, respectively, in the multiple-n case.