Hydrodynamic optical-field-ionized plasma channels

We present experiments and numerical simulations which demonstrate that fully ionized, low-density plasma channels could be formed by hydrodynamic expansion of plasma columns produced by optical field ionization. Simulations of the hydrodynamic expansion of plasma columns formed in hydrogen by an axicon lens show the generation of 200 mm long plasma channels with axial densities of order $n_{\mathrm{e}}\left(0\right)=1\times {10}^{17}{\mathrm{cm}}^{-3}$ and lowest-order modes of spot size $W_{\mathrm{M}}\approx 40\mu \mathrm{m}$. These simulations show that the laser energy required to generate the channels is modest: of order 1 mJ per centimeter of channel. The simulations are confirmed by experiments with a spherical lens which show the formation of short plasma channels with $1.5\times {10}^{17}{\mathrm{cm}}^{-3}\lesssim n_{\mathrm{e}}\left(0\right)\lesssim 1\times {10}^{18}{\mathrm{cm}}^{-3}$ and $61\mu \mathrm{m}\gtrsim W_{\mathrm{M}}\gtrsim 33\mu \mathrm{m}$. Low-density plasma channels of this type would appear to be well suited as multi-GeV laser-plasma accelerator stages capable of long-term operation at high pulse repetition rates.

Figure 1

Calculated retained kinetic energy distributions $f\left(E_{\mathrm{k}}\right)$ of electrons produced by optical field ionization of molecular hydrogen with laser fields of various ellipticity $\epsilon$. For these simulations the laser pulse was assumed to have a Gaussian temporal profile of 40 fs FWHM, a peak intensity $2.5\times {10}^{14}{\mathrm{W}\mathrm{cm}}^{-2}$, and a center wavelength of $\lambda =800\mathrm{nm}$.

Figure 2

Schematic diagram of the experimental layout employed to measure low-density plasma channels. Symbols: Half-wave plate (HWP); quarter-wave plate (QWP); plano-convex lenses ($L1$–$L3$); dichroic mirror ($DM$); 50/50 beamsplitter (BS). The inset shows the interference fringes observed when a plasma channel is formed.

Figure 3

Measured transverse electron density profiles at delays $t$ after the arrival of the channel-forming pulse focused into 50 mbar of hydrogen gas. Each profile is obtained from analysis of a single interferogram and is shown in a square of side $280\mu \mathrm{m}$. The delay $t$ is indicated for each plot.

Figure 4

Measured transverse electron density profile for hydrogen plasma after OFI by a circularly polarized pulse. The solid lines show the mean rotationally averaged profile for 5–10 shots while the associated colored band shows the RMS error in the measurement. (a) The temporal evolution of a plasma channel from an initial fill pressure of 50 mbar; (b) the electron density profile 3.9 ns after ionization for a range of different cell fill pressures.

Figure 5

Comparison of measured and simulated temporal evolution of the shock front. Blue circles show the average of the major and minor axes of an ellipse fitted to a half-max contour of the measured electron density profiles; the same data binned by time interval are shown as open red circles. The results of a HELIOS simulation (dotted purple) and a fit of the data to the Sedov-Taylor solution [Eq. (2), dashed black) are also shown.

Figure 6

Simulated evolution of the transverse density profile $n_{\mathrm{e}}\left(r\right)$ of the hydrodynamic expansion of an OFI plasma produced in molecular hydrogen of pressure 60 mbar by an axicon with $\alpha =2.5^{\circ }$ and $R=18\mathrm{mm}$. (a) $n_{\mathrm{e}}\left(r\right)$ at 1 ns intervals after the formation of the initial plasma column (dashed line). (b) The calculated electron density surface, overlaid with the shock front position $r_s\left(t\right)$ expected from the Sedov-Taylor solution (red) and the calculated matched spot size $W_{\mathrm{M}}$ of the lowest-order mode of the plasma channel (dotted white). For these simulations the incident channel-forming pulses were assumed to be circularly polarized, of top-hat incident transverse profile, of energy 22 mJ, and 40 fs FWHM duration.

Figure 7

(a) The spot size (solid red line) $W_{\mathrm{M}}$ of the lowest-order mode plotted against the axial electron density $n_{\mathrm{e}}\left(0\right)$ of the plasma channel for the plasma channel shown in Fig. 6 during the interval $0\le t\le 10\mathrm{ns}$. The channel starts at the bottom right of the plot and evolves towards the top left, corresponding to a decreasing on-axis density and an increasing matched spot size. Also shown is the evolution of ${\lambda }_{\mathrm{p}}$ (dashed black); to remain in the quasilinear regime with $a_0\approx 1$ and $P<P_{\mathrm{c}}$, a guided pulse should have a spot size less than this value. (b) Temporal evolution of the 1/e power attenuation length $L_{\mathrm{att}}$ of the lowest-order mode.