Research ArticlePHYSICS

Ultrafast optical field–ionized gases—A laboratory platform for studying kinetic plasma instabilities

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Science Advances  06 Sep 2019:
Vol. 5, no. 9, eaax4545
DOI: 10.1126/sciadv.aax4545
  • Fig. 1 Initial EVD of OFI helium plasma.

    EVDs (A) for CP and (B) for LP laser pulse from 3D OSIRIS simulations. The solid blue lines in (A) and (B) show the projected distributions. In the CP case (A), the projected distribution deviates significantly from a Maxwellian distribution having the same root-mean-sqaure (rms) temperature of 470 eV, as shown by the red dashed line. In the LP case (B), the projected distribution can be well approximated by a two-temperature (1D Maxwellian) distribution with THe1+=60eV and THe2+=60eV = 214 eV. The blue lines in (C) and (D) show the measured TS spectrum for CP (C) and LP (D) for an initially fairly low plasma density of 6.6 × 1017 cm−3. The red dashed lines in (C) and (D) are fits to the measured spectrum (see the main text).

  • Fig. 2 2D simulations show OFI-triggered kinetic streaming and filamentation instabilities in a helium plasma.

    The plasma (ne = 5 × 1018 cm−3) is ionized by a CP laser (τ = 50 fs, w0 = 8 μm, I = 1.6 × 1017 W/cm2). The Ey field, Bx field, and density fluctuations associated with the instability are shown in (A), (B), and (C), respectively. (D) and (E) are zoom in of the regions marked by the boxes in (C). The corresponding k-space of these density fluctuations is shown in (F) and (G), where the two dots mark the k of the waves being measured in experiments and where the 400-nm (800 nm) probe is used for CP (LP) pump pulses. (H and I) and (J and K) show the transverse phase space of He1+ and He2+ electrons ionized by CP and LP lasers, respectively. These results are from simulations with higher resolutions. The color bars represent the density of the electrons [in arbitrary units (a.u.)]. The simulation box is 35 μm wide in y. Because the laser only ionizes the central 20 μm of He, a 30-μm window is shown in these plots. In all cases, the electrons inside a Δz = 2-μm slab at z = 20 μm are used to show the phase space. (H) and (I) are taken 0.14 ps while (J) and (K) are taken 1.9 ps after the laser has passed the slab. The gray dashed lines mark the locations of the thin sheaths. The direction of the arrows indicates the shift of the momentum distributions.

  • Fig. 3 TS diagram and examples of measured TS spectra.

    (A) k-matching diagram where a helium plasma produced by a 50-fs, 800-nm CP (LP) pump laser is diagnosed by a 400-nm, probe 1 (800-nm, probe 2) laser traversing through the plasma with a variable delay. The measured time-resolved TS spectra are shown in (B) and (C) for the CP and LP pump, respectively. Note that the time scales for the two polarizations are different. The dashed lines mark the position of the expected plasma frequency corresponding to the plasma density. The entire dataset is obtained by scanning the timing in 50- to 200-fs steps, and each step is the average of 20 individual scattering events. Time t = 0 is defined as the time when pump and probe overlap with one another (determined by locating the position of the ionization front seen in a shadowgram formed by the probe at the same location as the probe beam).

  • Fig. 4 Streaming, filamentation, and Weibel instabilities induced by circular polarization.

    (A) The blue circles show the measured magnitude of the electron feature as a function of time (derived from Fig. 3B) for a plasma density of 6 × 1018 cm−3. The red line shows temporal evolution of the density fluctuation magnitude (instability wave amplitude) for the same probed value of k obtained from a 2D PIC simulation. The black dashed line shows the exponential growth of a linear wave from kinetic theory. The horizontal error bars mark the uncertainty in determining the t0 when ionization is completed. The vertical error bars represent the ±2σ confidence level. (B) Measured (magenta circles), predicted (blue line), and simulated (green squares) growth rates of the instability. (C) Measured (magenta circles) and predicted (blue line) frequencies of the streaming instability for the same range of densities as in (B). (D) Measured magnitude of the zero-frequency feature (green) and the electron feature (blue) within the first 2 ps. (E) The measured (circles) and calculated (green line) initial growth rates of the filamentation instability. The horizontal error bars show the uncertainty of density measurement, and the vertical error bars represent the ±σ confidence interval of the deduced growth rate. The blue dashed line shows the growth rate of the zero-frequency mode of the streaming instability. (F) Measured magnitude of the zero-frequency feature as a function of time (green squares, derived from Fig. 3B). The solid (dashed) purple line shows the evolution of the amplitude of the electron (ion) density fluctuation at the same k that is being probed in the experiment. The red dotted-dashed line shows the maximum growth rate of the Weibel instability calculated using the simulated EVD at t = 1 ps.

  • Fig. 5 Evolution of the temperature anisotropy of the OFI plasma.

    The upper (lower) row in (A) shows the py (pz) distribution function of electrons at t = 0, 1, and 6 ps. The dashed gray line is a Gaussian fit to the distribution. The initial distribution can be approximated by four drifting Maxwellian beams in the transverse plane as indicated by the red line and the arrows. The red dashed line is a Gaussian fit to the pz distribution. (B) The blue line shows the anisotropy from the same simulation as in (A), which does not include collisions. The red line shows the simulation of anisotropy evolution of a preionized plasma with only Coulomb collisions included. (C) The average magnetic field energy as a function of time shows two distinct growth phases corresponding to filamentation and Weibel regimes, respectively.

  • Fig. 6 Instabilities in a plasma ionized by an LP laser.

    (A) Measured (blue) and simulated (red) evolutions of the magnitude of the electron density fluctuations of the streaming instability. (B) The measured magnitude of the zero-frequency mode as a function of time, displaying an oscillatory behavior with a roughly ion acoustic period.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/9/eaax4545/DC1

    Supplementary Text

    Fig. S1. A time sequence of snapshots of electron density fluctuations.

    Fig. S2. Comparison of PIC simulations without and with e-e collisions.

    Fig. S3. Relaxation of nonthermal plasma due to Coulomb collisions.

    Fig. S4. Recurrence of the streaming mode and the fixed phase relationship between the streaming and the filamentation modes.

  • Supplementary Materials

    This PDF file includes:

    • Supplementary Text
    • Fig. S1. A time sequence of snapshots of electron density fluctuations.
    • Fig. S2. Comparison of PIC simulations without and with e-e collisions.
    • Fig. S3. Relaxation of nonthermal plasma due to Coulomb collisions.
    • Fig. S4. Recurrence of the streaming mode and the fixed phase relationship between the streaming and the filamentation modes.

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