Analytic study of traveling-wave velocity variation in line-focusing schemes for plasma x-ray lasers

Efficient amplification of coherent short-wavelength pulses along a plasma gain column requires traveling-wave excitation with the sweep velocity matched to the signal group velocity. Through simulations incorporating the gain dynamics of the system, we show that the group velocity is not constant but increases monotonically along the line focus due to strong saturation. We demonstrate a line-focusing configuration that results in traveling wave excitation with the sweep velocity well matched to the spatially varying group velocity. Moreover, we show through numerical simulations that the improved velocity matching yields a significant improvement in signal amplification.