Self-regulated propagation of intense infrared pulses in elongated soft-x-ray plasma amplifiers

Increasing the electron density of collisionally pumped plasma-based soft-x-ray lasers offers promising opportunities to deliver ultrashort pulses. However, strong nonlinear effects, such as overionization-induced refraction and self-focusing, hinder the propagation of the laser beam and thus the generation of elongated volume of lasing ions to be pumped. Using a particle-in-cell code and a ray-tracing model we demonstrate that optically preformed waveguides allow for addressing those issues through a self-regulation regime between self-focusing and overionization processes. As a result, guiding intense pulses over several millimeters leads to the implementation of saturated plasma amplifiers.

Figure 1

(a) Intensity, (b) mean ionization, and (c) electron density at $z=0$. (d) Intensity, (e) mean ionization, and (f) electron density at $z=1.5Z_R.Z_R=0.0725\mathrm{cm}$. The temporal scale is the same in all six figures, but it is only depicted in (a) and (d) for the sake of visualization.

Figure 2

(a) Maximum intensity along the plasma channel. (b) Mean ionization along the plasma channel. $Z_R=0.0725\mathrm{cm}$.

Figure 3

Parameters for the two-parabola ray-tracing model [Eqs. (9) and (3)]. The electron-density radial profile at $z=0$ (blue circles) and $z=1.5Z_R$ (magenta crosses) as given by the pic code are depicted. Continuous lines (red and black) represent the parabolas that approximate the computed electron-density profile.

Figure 4

Maximum intensity as given by the pic simulation for $n_{e1}=1.4\times {10}^{16}{\mathrm{cm}}^{-3}$ (black diamonds) and $n_{e1}=1.4\times {10}^{18}{\mathrm{cm}}^{-3}$ (red circles) compared with the propagation of a Gaussian beam in vacuum (black line) and our ray-tracing model (red and magenta curves). Points A–C indicate a switch on the driving mechanism (overionization-induced refraction, channel guiding, diffraction, and relativistic self-focusing, respectively).