Hydrodynamic evolution of plasma waveguides for soft-x-ray amplifiers

High-density, collisionally pumped plasma-based soft-x-ray lasers have recently delivered hundreds of femtosecond pulses, breaking the longstanding barrier of one picosecond. To pump these amplifiers an intense infrared pulse must propagate focused throughout all the length of the amplifier, which spans several Rayleigh lengths. However, strong nonlinear effects hinder the propagation of the laser beam. The use of a plasma waveguide allows us to overcome these drawbacks provided the hydrodynamic processes that dominate the creation and posterior evolution of the waveguide are controlled and optimized. In this paper we present experimental measurements of the radial density profile and transmittance of such waveguide, and we compare them with numerical calculations using hydrodynamic and particle-in-cell codes. Controlling the properties (electron density value and radial gradient) of the waveguide with the help of numerical codes promises the delivery of ultrashort (tens of femtoseconds), coherent soft-x-ray pulses.

Figure 1

Experimental setup for the creation and diagnosis of a high-density plasma waveguide. The ignitor and heater beams have, respectively, an energy of $E_1=130$ mJ and $E_2=690$ mJ, a duration of 30 fs and 600 ps and are separated by a delay of $\mathrm{\Delta }t=600$ ps.

Figure 2

Electron density at the central region of the 5-mm-long gas jet at different ignitor-probe delays, showing the creation and evolution of the plasma waveguide. The ignitor and heater pulse delay and duration are shown in the figure (the time at which the peak of the pulse arrives is shown in orange). Their relative intensities are not scaled for the sake of clarity.

Figure 3

Energy distribution of the IR pump beam ($I=3\times {10}^{18}$ W ${\mathrm{cm}}^{-2}$), at its focal spot in vacuum (a) and focused at the end of the 5-mm-long high-density plasma amplifier without (b) and with (c) the plasma waveguide, injected 1.55 ns after the arrival of the ignitor pulse.

Figure 4

Transmission of the IR beam through the plasma waveguide as a function of the gas jet length (which is similar to that of the plasma waveguide). The dashed green line denotes the best fit.

Figure 5

Radial profile of electron density as measured experimentally (red continuous line) and as given by our modeling (blue circles) at different ignitor-probe delays.

Figure 6

Density maps of krypton ion species, as given by CalderCirc, generated focusing a IR beam with I = $3\times {10}^{18}$ W ${\mathrm{cm}}^{-2}$ into a high-density 5-mm-long plasma waveguide, which corresponds to experimental conditions. Each subfigure shows the density of the corresponding ion species.

Figure 7

Fraction of the energy of the IR beam propagating through the waveguide, as computed by WAKE-EP, guided (blue circles) and unguided (magenta squares) for different axial electron densities: (a) $n_{e0}={10}^{18}{\mathrm{cm}}^{-3}$, (b) $n_{e0}=3\times {10}^{18}{\mathrm{cm}}^{-3}$, (c) $n_{e0}=5\times {10}^{18}{\mathrm{cm}}^{-3}$, and (d) $n_{e0}=8\times {10}^{18}{\mathrm{cm}}^{-3}$. The sum of both is depicted by the red continuous line.