Direct acceleration of electrons by a CO$_{2}$ laser in a curved plasma waveguide

Laser plasma interaction with micro-engineered targets at relativistic intensities has been greatly promoted by recent progress in the high contrast lasers and the manufacture of advanced micro- and nano-structures. This opens new possibilities for the physics of laser-matter interaction. Here we propose a novel approach that leverages the advantages of high-pressure CO$_{2}$ laser, laser-waveguide interaction, as well as micro-engineered plasma structure to accelerate electrons to peak energy greater than 1 GeV with narrow slice energy spread ($\sim1\%$) and high overall efficiency. The acceleration gradient is 26 GV/m for a 1.3 TW CO$_{2}$ laser system. The micro-bunching of a long electron beam leads to the generation of a chain of ultrashort electron bunches with the duration roughly equal to half-laser-cycle. These results open a way for developing a compact and economic electron source for diverse applications.