  Current advances in ultrafast electron microscopy make it possible to combine
optical pumping of a nanostructure and electron beam probing with
sub{\aa}ngstrom and femtosecond spatiotemporal resolution. We present a theory
predicting that this technique can reveal a rich out-of-equilibrium dynamics of
plasmon excitations in graphene and graphite samples. In a disruptive departure
from the traditional probing of nanoscale excitations based on the
identification of spectral features in the transmitted electrons, we show that
measurement of angle-resolved, energy-integrated inelastic electron scattering
can trace the temporal evolution of plasmons in these structures and provide
momentum-resolved mode identification, thus avoiding the need for
highly-monochromatic electron beams and the use of electron spectrometers. This
previously unexplored approach to study the ultrafast dynamics of optical
excitations can be of interest to understand and manipulate polaritons in 2D
semiconductors and other materials exhibiting a strong thermo-optical response.
