Simple dynamical model that leads to sputter cone formation

We introduce a model for sputter cone formation that includes only the angular dependence of the sputter yield and a fourth-order smoothing effect like surface diffusion. In one dimension, a sputter cone is a particular kind of shock wave that is known as an undercompressive shock. Simulations of our model show that a wide variety of initial conditions lead to the formation of sputter cones and that the opening angle of the cones does not depend on the detailed form of the initial condition. In two dimensions, a sputter cone is a higher-dimensional analog of an undercompressive shock. For two particularly simple choices of parameters, a sputter cone is a four-sided pyramid with rounded edges that is produced by the superposition of two orthogonal, one-dimensional undercompressive shocks.