Laser-driven Rayleigh-Taylor instability: Plasmonic effects and three-dimensional structures

The acceleration of dense targets driven by the radiation pressure of high-intensity lasers leads to a Rayleigh-Taylor instability (RTI) with rippling of the interaction surface. Using a simple model it is shown that the self-consistent modulation of the radiation pressure caused by a sinusoidal rippling affects substantially the wave vector spectrum of the RTI, depending on the laser polarization. The plasmonic enhancement of the local field when the rippling period is close to a laser wavelength sets the dominant RTI scale. The nonlinear evolution is investigated by three-dimensional simulations, which show the formation of stable structures with “wallpaper” symmetry.

Figure 1

(a) The geometry used in the model calculations. (b) Phase matching between surface waves (SWs) and an EM plane wave at normal incidence on a grating. The thick lines give the dispersion relation of SWs in the $\left(\omega ,k_y\right)$ plane, folded into the Brillouin zone $|k_y|<\pi /a$. The oblique dashed lines give the ${\omega }_p/\omega \to \infty$ limit of the SW dispersion relation. The vertical arrow represents the incident wave, i.e., $\left(\omega ={\omega }_0,k_y=0\right)$.

Figure 2

Two-dimensional simulations of plane wave reflection from a grating surface. The figures show the temporal average (over one laser period) of $B_t^2$, where $B_t$ is the transverse magnetic field (in arbitrary units) for the cases of $S$ and $P$ polarization, i.e., for the electric field of the plane wave perpendicular and parallel to the simulation plane, respectively. For the $P$-polarization case, the field amplitude is locally enhanced in the valleys of the grating, while for $S$ polarization enhancement occurs at the grating peaks.

Figure 3

RTI growth rate of a thin foil for $S,P$, and circular (C) polarization. The dashed curve ${\gamma }_{\text{RT}}={\left(P_{0}q/\sigma \right)}^{1/2}$ gives the rate for the standard RTI of a “flat” thin foil, to which all curves are reduced for $q<k$, i.e., when ${\kappa }_1$ is imaginary. The parameter ${\gamma }_0={\left(P_{0}k/\sigma \right)}^{1/2}$.

Figure 4

Analysis of the transverse modes in 2D plane wave simulations. (a), (c) Charge density $\left(t=20\lambda /c\right)$ of electrons and ions. For each time step the longitudinal position $x=x(y,t)$ of the vacuum-plasma interface was reconstructed as a function of the transverse coordinate $y$. (b) Temporal evolution of the Fourier transform $\tilde{x}(q,t)$ for electrons. (d) Comparison of $\tilde{x}$ for electrons (thick line) and carbon ions (dashed line) at $t=20$.

Figure 5

A 3D snapshot image of the density of both proton (dark green tones) and carbon (light blue tones) densities at $t=30T$. In order to make the carbon ion density visible, the proton density is shown only on the left part $(y\ge 0)$ of the image.

Figure 6

Areal density of carbon ions at $t=15T$ in 3D simulations with the same parameters as in Fig. 5 but for a plane wave, for circular (CP) and linear (LP) polarization.