In recent works we discussed the feasibility of the radar detection technique as a new method to probe high-energy cosmic-neutrino induced plasmas in ice. Using the different properties of the induced ionization plasma, an energy threshold of several PeV was derived for the over-dense scattering of a radio wave off the plasma. Next to this energy threshold the radar return power was determined for the different constituents of the plasma. It followed that the return signal should be detectable at a distance of several hundreds of meters to a few kilometers, depending on the plasma constituents and considered geometry. In this article we describe a more detailed modeling of the scattering process by expanding our model to include the full shower geometry, as well as the reflection off the under-dense plasma region. We include skin-effects, as well as the angular dependence of the scattered signal. As a first application of this more detailed modeling approach, we provide the effective area and sensitivity for a simplified detector setup. It follows that, depending on the detailed plasma properties, the radar detection technique provides a very promising method for the detection of neutrino induced particle cascades at energies above several PeV. Nevertheless, to determine the feasibility of the method more detailed information about the plasma properties, especially its lifetime and the free charge collision rate, are needed.
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