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Web extra: View animations of the simulation described in this article.Download QuickTime or Windows media playerFigure 3. Spatial coordinate (x, y, z) view of volume-rendered particle density, based on a 512 3 mapping of 300 million particles.Figure 4. Phase space (x, px, z) view of volume-rendered particle density, based on a 512 3 mapping of 300 million particles.Particle accelerators play an increasingly important role in basic and applied science. Several countries are involved in efforts aimed at developing accelerator related technologies to support different application domains, including high-energy and nuclear physics, material science, biological science, and military use.The technological challenges associated with designing the next generation of accelerators will require numerical modeling capabilities far beyond those normally used within the accelerator community. For example, future high-average-power linear accelerators will have to operate with extremely low beam loss (of the order 0.1 nanoamperes per meter) to prevent unacceptably high levels of radioactivity. Meeting this requirement demands very high-resolution simulations using hundreds of millions to billions of particles in which the beam propagates through kilometers of complicated accelerating structures. These calculations require computational performance of billions of floating-point operations per second (GFLOPS) to teraFLOPS (TFLOPS) and core memory requirements of hundreds of gigabytes.