  At the KATRIN experiment, the electron antineutrino mass is inferred from the
shape of the $\beta$-decay spectrum of tritium. Important systematic effects in
the Windowless Gaseous Tritium Source (WGTS) of the experiment include the
energy loss by electron scattering, and the extended starting potential. In the
WGTS, primary high-energy electrons from $\beta$-decay produce an extended
secondary spectrum of electrons through various atomic and molecular processes
including ionization, recombination, cluster formation and scattering. In
addition to providing data essential to the simulation of energy loss
processes, the electron spectrum also provides information important in the
simulation of plasma processes. These simulations will then provide an insight
on the starting potential. Here, a Monte Carlo approach is used to model the
electron spectrum in the source for a given magnetic and electric field
configuration. The spectrum is evaluated at different positions within the
WGTS, which allows for a direct analysis of the spectrum close to the rear wall
and detector end of the experiment. Alongside electrons, also ions are tracked
by the simulation, resulting in a full description of the currents in the
source.
