We propose a dielectric-based, crossed-laser-beam electron linear accelerator structure operating in a vacuum that is capable of providing 1 TeV electrons in approximately 1 km. The accelerator structure employs cylindrical laser focusing that allows for simplifying the fabrication process, accelerating more electrons, reducing the electron phase slip, minimizing the transverse wake-fields, and spreading the structural thermal loading. We present a 0.7 GeV/m average-gradient accelerator structure, repeated every 390 μm, subject to the laser damage fluence 2 J/cm2 on the optical components for 100 fs laser pulses.