Light scattering by a dense ionization plasma wave with a tunable velocity

An optically-dense ionization wave (\textit{IW}) produced by two femtosecond laser pulses focused cylindrically and crossing each other is shown to be an efficient coherent $x$-ray converter. The resulting velocity of a quasi-plane \textit{IW} in the vicinity of pulse intersection increases with the angle between the pulses from the group velocity of ionizing pulses to infinity allowing an easy tuning the wavelength of $x$-rays. We study the conversion of a coherent light to x-rays by means of particle-in-cell simulation and by solution of continuous equation with the correct current. The x-ray spectra of a converted, lower frequency coherent light change from the monochromatic to a high order harmonic-like with the duration of ionizing pulses and the intensity of scattered pulses; the spectrum are not symmetrical at $Vc$.