Proper Lindblad modes appearing in a ring confined at the 1/3 SOR. The outputs of the run shown in Fig. 6 have been used to detect normal modes in the confined rings between times 250 000 and 250 200, with steps ∆T = 0.05. The Lomb normalized periodogram power spectra of the modes described by Eq. (13) are displayed in the upper six panels as a function of ω_m/Ω_B for |m| = 1 to 6. Consistent with Eq. (15), the maximum power (red squares) is reached at the frequency ω_m = (1 + |m|)Ω_B/3. This is illustrated in the lower left panel. The lower middle panel shows the rapid decrease in the amplitude A_m of the modes with |m|, while the right panel shows the distribution of phases ϕ_m.