Non-local linear stability of ion beam eroded surfaces

► Extension of Bradley-Harper theory (BHT) avoiding gradient expansions. ► Extension of BHT including ion-induced surface mass redistribution. ► More complex scenarios of pattern formation than in BHT, including both type I and type II instabilities. ► Ion-beam induced pattern formation does not need erosion. ► Bifurcation scenarios depend sensitively upon statistical shapes of collision cascades.