Normalised spin-down luminosity (L) as a function of the magnetic inclination angle, α, as derived by LSTa (see their Figure 3). The solid curves represent three cases: the ON state (red), the OFF state (blue), and the vacuum state (purple). The model assumes a complete absence of plasma in the open-field-line region during the OFF state. In Section 3, we consider a modification of this model when the degree of depletion is less than complete; this is described by a ‘plasma filling factor’, η. Corresponding curves for η = 0.9 (dashed), 0.5 (dotted), and 0.1 (dashed dotted) are shown. See Sections 1 and 3 for details.