Dependence of the cutoff longitudinal wave number of a sausage oscillation on the internal Alfvén speed (and hence the potential well depth) for a fixed value of the external Alfvén speed and for different values of α. The long dashed line corresponds to α = 2, the triple-dot dashed line to α = 4, the dot dashed line to α = 6, the dashed line to α = 8, the dotted line to α = 10 and the solid line shows the step-function profile, i.e. α → ∞. The diamonds are the values for the cutoff in the case of a step-function profile, obtained analytically. The internal Alfvén speed is normalised such that the external Alfvén speed, CAe = 1, and the wavenumber is normalised such that the characteristic width of the slab, d = 1.
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