Normalized wavenumber of first three harmonics of sausage waves (blue – first harmonic, green – second harmonic, dark red – third harmonic) vs. width to length ratio of the magnetic tube from Eq. (9). The red dashed lines show the cut-off wavenumbers for three different values of the ratio of internal and external densities, d = ρ0/ρe = 5, 10, and 20.
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