Tracking Particles in Accelerator Optics with Crystal Elements

Bent channeling crystals as elements of accelerator optics with extreme, 1000-Tesla intracrystalline fields can find many applications in accelerator world from TeV down to MeV energies. Situated in accelerator ring, they serve for beam scraping or extraction, e.g. in RHIC and IHEP U70. Crystal itself is a miniature beamline with its own "strong focusing", beam loss mechanisms etc. We describe the algorithms implemented in the computer code CATCH used for simulation of particle channeling through crystal lattices and report the results of tracking with 100-GeV/u Au ions in RHIC and with 70-GeV and 1-GeV protons in U70. Recent success of IHEP where a tiny, 2-mm Si crystal has channeled a 1012 p/s beam of 70-GeV protons out of the ring with efficiency 85% followed the prediction of computer model.