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“…The amplitude C j is determined by the frequency mismatch ω and the coupling coefficient W (3) a,b,c among the three modes satisfying (2) (where b = c for the case of the second-harmonic resonance). The latter W (3) a,b,c is measured by the cubic potential energy W (3) (ξ, ξ, ξ) associated with the nonlinear force term F (2) in (6) (see (12)). This formalism generally enables us to analyse nonlinear coupling of global MHD eigenmodes in a rigorous manner.…”

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“…The amplitude C j is determined by the frequency mismatch ω and the coupling coefficient W (3) a,b,c among the three modes satisfying (2) (where b = c for the case of the second-harmonic resonance). The latter W (3) a,b,c is measured by the cubic potential energy W (3) (ξ, ξ, ξ) associated with the nonlinear force term F (2) in (6) (see (12)). This formalism generally enables us to analyse nonlinear coupling of global MHD eigenmodes in a rigorous manner.…”

“…For q 0 = 1.0, q a0 = 5.0, ρ a0 /ρ 0 = 0.05 and R 0 /a 0 = 3.0, the numerically calculated AE spectra are shown in figure 1 for (m, n) = (1, 2), (2,4), (3,6). They satisfy the near resonance condition (2) …”