  A component of space weather, electron beams are routinely accelerated in the
solar atmosphere and propagate through interplanetary space. Electron beams
interact with Langmuir waves resulting in type III radio bursts. Electron beams
expand along the trajectory, and using kinetic simulations, we explore the
expansion as the electrons propagate away from the Sun. Specifically, we
investigate the front, peak and back of the electron beam in space from derived
radio brightness temperatures of fundamental type III emission. The front of
the electron beams travelled at speeds from 0.2c--0.7c, significantly faster
than the back of the beam that travelled between 0.12c--0.35c. The difference
in speed between the front and the back elongates the electron beams in time.
The rate of beam elongation has a 0.98 correlation coefficient with the peak
velocity; in-line with predictions from type III observations. The inferred
speeds of electron beams initially increase close to the acceleration region
and then decrease through the solar corona. Larger starting densities and
harder initial spectral indices result in longer and faster type III sources.
Faster electron beams have higher beam energy densities, produce type IIIs with
higher peak brightness temperatures and shorter FWHM durations. Higher
background plasma temperatures also increase speeds, particularly at the back
of the beam. We show how our predictions of electron beam evolution influences
type III bandwidth and drift-rates. Our radial predictions of electron beam
speed and expansion can be tested by the upcoming in situ electron beam
measurements made by Solar Orbiter and Parker Solar Probe.
