  Shaping electron beams with the cycles of light provides femtosecond and
attosecond time resolution in electron microscopy and enables fundamental
quantum-coherent measurements. However, efficient light-electron control
requires a prolonged interaction between the two beams for cascaded transfer of
photon energy and momentum to the freely propagating electrons. Here we report
the use of traveling evanescent terahertz waves to achieve velocity matching
and thereby high acceleration gradients both in space and in time. With
experiment and simulations, we demonstrate attosecond streaking, temporal pulse
compression, acceleration and spatial focusing of sub-relativistic electron
pulses with a single evanescent-wave element under the control of selected
terahertz delays and phases. Based on these results, we propose to use a
symmetric arrangement with two evanescent terahertz waves to generate isolated
attosecond electron pulses in a beam with realistic parameters. These results
establish subluminal terahertz waves as a promising tool for ultrafast electron
pulse control.
