The transverse acceleration of ions by fast lower hybrid waves in the topside auroral ionosphere has remained elusive. The linear and nonlinear propagation and evolution of lower hybrid waves are essentially a three-dimensional problem. Analytical treatment of this problem, including the essential kinetic effects for particle acceleration, is a formidable task if not impossible. We have treated this problem by a fully three-dimensional particle-in-cell simulation. It is found that a fast lower hybrid pump wave undergoes a parametric decay generating secondary waves over a broad frequency range from the ion cyclotron frequency &OHgr;i to just above the lower hybrid frequency &ohgr;lh. These secondary waves are instrumental in the accelerations of both cold ions and electrons perpendicular and parallel to the ambient magnetic field B_, respectively. ¿ American Geophysical Union 1996