We describe the scientific motivation, experimental basis, design methodology, and simulated performance of the ExaVolt Antenna (EVA) mission, and planned ultra-high energy (UHE) particle observatory under development for NASAs suborbital super-pressure balloon program in Antarctica. EVA will improve over ANITAs integrated totals - the current state-of-the-art in UHE suborbital payloads - by 1-2 orders of magnitude in a single flight. The design is based on a novel application of toroidal reflector optics which utilizes a super-pressure balloon surface, along with a feed-array mounted on an inner membrane, to create an ultra-large radio antenna system with a synoptic view of the Antarctic ice sheet below it. Radio impulses arise via the Askaryan effect when UHE neutrinos interact within the ice, or via geosynchrotron emission when UHE cosmic rays interact in the atmosphere above the continent. EVAs instantaneous antenna aperture is estimated to be several hundred square meters for detection of these events within a 150-600 MHz band. For standard cosmogenic UHE neutrino models, EVA should detect of order 30 events per flight in the EeV energy regime. For UHE cosmic rays, of order 15,000 geosynchrotron events would be detected in total, several hundred above 10 EeV, and of order 60 above the GZK cutoff energy
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