  In recent years, the freely available Monte Carlo code REAS for modelling
radio emission from cosmic ray air showers has evolved to include the full
complexity of air shower physics. However, it turned out that in REAS2 and all
other time-domain models which calculate the radio emission by superposing the
radiation of the single air shower electrons and positrons, the calculation of
the emission contributions was not fully consistent. In this article, we
present a revised implementation in REAS3, which incorporates the missing radio
emission due to the variation of the number of charged particles during the air
shower evolution using an "end-point formalism". With the inclusion of these
emission contributions, the structure of the simulated radio pulses changes
from unipolar to bipolar, and the azimuthal emission pattern becomes nearly
symmetric. Remaining asymmetries can be explained by radio emission due to the
variation of the net charge excess in air showers, which is automatically taken
into account in the new implementation. REAS3 constitutes the first
self-consistent time-domain implementation based on single particle emission
taking the full complexity of air shower physics into account, and is freely
available for all interested users.
