Because of the pressure and magnetic-field gradients and curvature of the magnetic field lines in a bundle divertor of a tokamak device, the plasma may be unstable to local interchange modes. Turbulent transport could be quite large and lead to a thick scrape-off layer which is as large as the radius of curvature of the diverted flux bundle. Such turbulence would be beneficial for lowering the energy and particle fluxes on the collector in a bundle divertor. The effect of a bundle divertor on the β-limit resulting from the ballooning modes of instability in the central plasma is also estimated. The critical β is reduced by less than one percent.