Generating coherent, ultrashort, and ultraintense Langmuir wave trains via two-plasmon decay instability

In plasmas, a Langmuir wave is a bridge connecting external sources with waves or particles, whose properties are mainly determined by the shape, amplitude, dispersion relation, or phase of the Langmuir wave. Here we propose a scheme to generate coherent Langmuir wave trains with width as short as submicrons and field amplitude of hundreds of GV/m. An initial seed Langmuir wave interacting with a pump laser can generate a backward Langmuir wave as long as the three waves satisfy the matching condition of two-plasmon decay instability. The backward Langmuir wave evolves into a self-similar regime and forms small pulses trailing behind. The ultrashort duration and ultraintense amplitude are predictable by scaling laws from the self-similar theory, making the generation process controllable. Unlike backward Raman amplification of light waves, Langmuir wave amplification is inherently two dimensional and more efficient. The coherent and structured Langmuir wave has potential applications in generating energetic and ultrashort electron beams.