  The detection of ultra-high energy (UHE, >10 PeV) neutrinos via detectors
designed to utilize the Askaryan effect has been a long-time goal of the
astroparticle physics community. The Askaryan effect describes radio-frequency
(RF) radiation from high-energy cascades. When a UHE neutrino initiates a
cascade, cascade properties are imprinted on the radiation. Thus, observed
radiation properties must be used to reconstruct the UHE neutrino event.
Analytic Askaryan models have three advantages when used for UHE neutrino
reconstruction. First, cascade properties may be derived from the match between
analytic function and observed data. Second, analytic models minimize
computational intensity in simulation packages. Third, analytic models can be
embedded in firmware to enhance the real-time sensitivity of detectors. We
present a fully analytic Askaryan model in the time-domain for UHE
neutrino-induced cascades in dense media that builds upon prior models in the
genre. We then show that our model matches semi-analytic parameterizations used
in Monte Carlo simulations for the design of IceCube-Gen2. We find correlation
coefficients greater than 0.95 and fractional power differences < 5% between
the the fully analytic and semi-analytic approaches.
