I assume you mean off-axis detection? Because electron
beams are used to provoke semiconductor sensitivities,
if you hit them with it. Not the kind of energies normally
encountered by sane people, but still.
Electron beams in air do not have much range. I imagine
you might be able to pick up phosphorescence signatures
at N, O excitation wavelengths (see this being employed
for explosives detection, although they use UV source -
LINAC being a bit not-portable). Narrowband optical
filter and photodetector, then.
How much signature you can get, and whether you can
discriminate a random-time-of-arrival signature in the
same way as those detection folks can with their co-
situated pulsed source and detector (you can take a
baseline before the pulse, if you know when the pulse
is coming, and do a sample-sample subtraction and/or
zero the front end).