The propulsion of surface ripples on SiO 2 by an ion beam was investigated by in situ electron microscopy. The observed propagation of the ripples contradicts existing models for ion-beam-induced ripple development. A new model based on the Navier-Stokes relations for viscous flow in a thin layer is introduced. It includes inhomogeneous viscous flow, driven by spatial variations in the deposition of the energy of the ion beam. The model explains the observed reversed propagation. The hitherto unknown propulsion mechanism is important for understanding nanoscale pattern formation by ion bombardment. DOI: 10.1103/PhysRevLett.96.107602 PACS numbers: 79.20.Rf, 61.80.Az, 68.35.Ct, 81.16.Rf Modification of surfaces is a widely explored and technologically highly relevant field of research. Surfaces bombarded by a beam of ions erode, but they may also develop specific nanoscale geometrical patterns [1]. These patterns have been studied intensively because they reveal details in the interaction of energetic particles with matter and because they have implications for ion-beam sputter erosion and deposition [2]. Recently, the formation of surface patterns by ion bombardment received appreciation as templates for the growth of low-dimensional nanostructures [3]. Various theories describe aspects of beaminduced pattern formation. Although they are widely applied, not all relevant processes are understood, not even qualitatively.A very common pattern is a series of ripples that can form under oblique incidence of kilo-electron-volt ions. Sigmund showed that the dependence of the material's erosion rate on the curvature of the surface leads to the growth of surface irregularities [4]. Bradley and Harper (BH) used Sigmund's model to explain the appearance of ripple patterns with a distinct wavelength [5]: Ripple formation is the result of a competition between curvaturedependent roughening and smoothing by thermal surface diffusion. The original BH model has been extended to include smoothening by beam-enhanced surface diffusion [6] and beam-enhanced viscous flow [7]. Carter suggested that viscous relaxation of a thin surface layer, compressively stressed by the ion bombardment, causes ripple formation [8], and Rudy and Smirnov used the NavierStokes relations to describe ion-beam-enhanced viscous flow [9]. Recently, Umbach, Headrick, and Chang showed that the enhanced viscous flow is limited to the ion penetration layer [10]. A common factor of all models is that only the ripples' growth rate has been tested experimentally. In contrast, the notion that ripples propagate across the surface is rarely outspoken [5,11] but always implicitly assumed. The overall surface erosion velocity is ÿ 0 ÿY f cos =n. Here Y is the number of removed atoms per incident ion, the angle between the ion beam and the surface normal, f the ion flux, and n the atomic density of the solid; the minus sign reflects the recession of the surface. Because of the increase of Y with up to 75 , the slopes that face the incident ion beam (the up slopes; se...