We present time-domain Monte Carlo simulations of radio emission from cosmic ray air showers in the scheme of coherent geosynchrotron radiation. Our model takes into account the important air shower characteristics such as the lateral and longitudinal particle distributions, the particle track length and energy distributions, a realistic magnetic field geometry and the shower evolution as a whole. The Monte Carlo approach allows us to retain the full polarisation information and to carry out the calculations without the need for any far-field approximations. We demonstrate the strategies developed to tackle the computational effort associated with the simulation of a huge number of particles for a great number of observer bins and illustrate the robustness and accuracy of these techniques. We predict the emission pattern, the radial and the spectral dependence of the radiation from a prototypical 10^17 eV vertical air shower and find good agreement with our analytical results (Huege & Falcke 2003) and the available historical data. Track-length effects in combination with magnetic field effects surprisingly wash out any significant asymmetry in the total field strength emission pattern in spite of the magnetic field geometry. While statistics of total field strengths alone can therefore not prove the geomagnetic origin, the predicted high degree of polarisation in the direction perpendicular to the shower and magnetic field axes allows a direct test of the geomagnetic emission mechanism with polarisation-sensitive experiments such as LOPES. Our code provides a robust, yet flexible basis for detailed studies of the dependence of the radio emission on specific shower parameters and for the inclusion of additional radiation mechanism in the future.
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