  The advent of ultrafast science with pulsed electron beams raised the need in
controlling the temporal features of the electron pulses. One promising
suggestion is the nano-selective quantum optics with multi-electrons, which
scales quadratically with the number of electrons within the coherence time of
the quantum system. Terahertz (THz) radiation from optical nonlinear crystals
is an attractive methodology to generate the rapidly varying electric fields
necessary for electron compression, with an advantage of an inherent temporal
locking to laser-triggered electrons, such as in untrafast electron
microscopes. Longer (picosecond-) pulses require sub-THz field for their
compression, however, the generation of such low frequencies require pumping
with energetic optical pulses and their focusability is fundamentally limited
by their mm-wavelength. This work proposes electron-pulse compression with
sub-THz fields directly in the vicinity of their dipolar origin, thereby
avoiding mediation through radiation. We analyze the merits of nearfields for
compression of slow electrons particularly in challenging regimes for THz
radiation, such as small numerical apertures, micro-joule-level optical pump
pulses, and low frequencies. This sheme can be implemented within the tight
constraints of electron microscopes and reach fiels of a few kV/cm below 0.1
THz at high repetition rates. Our paradigm offers a realistic approach for
controlling electron pulses spatially and temporally in many experiments,
opening the path of flexible multi-electron manipulation for analytic and
quantum sciences.
