  In this work we demonstrate the inelastic scattering of slow-electron
wavepackets at a propagating Hermite-Gaussian light beam. The pulsed
Hermite-Gaussian beam thereby forms a ponderomotive potential for the electron
with large enough momentum components, leading to the inelastic scattering of
electrons and their bunching along the longitudinal direction. We show that the
resulting energy-gain spectra after the interaction is strongly influenced by
the self-interference of the electron in this ponderomotive potential. It is
shown that this effect is observable for various optical wavelengths and
intensities and further discuss how the variation of the electron velocity and
the light intensity allow to control the energy modulation of the electron
wavepacket. This effect opens up a new platform for manipulating the electron
wavepacket by utilizing the vast landscape of structured electromagnetic
fields.
