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Radio Cherenkov radiation is arguably the most efficient mechanism fordetecting showers from ultra-high energy particles of 1 PeV and above. Showersoccuring in Antarctic ice should be detectable at distances up to 1 km. Wereport on electromagnetic shower development in ice using a GEANT Monte Carlosimulation. We have studied energy deposition by shower particles anddetermined shower parameters for several different media, finding agreementwith published results where available. We also report on radio pulse emissionfrom the charged particles in the shower, focusing on coherent emission at theCherenkov angle. Previous work has focused on frequencies in the 100 MHz to 1GHz range. Surprisingly, we find that the coherence regime extends up to tensof Ghz. This may have substantial impact on future radio-based neutrinodetection experiments as well as any test beam experiment which seeks tomeasure coherent Cherenkov radiation from an electromagnetic shower. Our studyis particularly important for the RICE experiment at the South Pole.Comment: 44 pages, 29 figures. Minor changes made, reference added, accepted  for publication in Phys. Rev.

Coherent radio pulses from GEANT generated electromagnetic showers in ice