Critical magnetic field strength for suppression of the Richtmyer-Meshkov instability in plasmas.

The critical strength of a magnetic field required for the suppression of the Richtmyer-Meshkov instability (RMI) is investigated numerically by using a two-dimensional single-mode analysis. For the cases of magnetohydrodynamic parallel shocks, the RMI can be stabilized as a result of the extraction of vorticity from the interface. A useful formula describing a critical condition for magnetohydrodynamic RMI is introduced and is successfully confirmed by direct numerical simulations. The critical field strength is found to be largely dependent on the Mach number of the incident shock. If the shock is strong enough, even low-ß plasmas can be subject to the growth of the RMI.

Observation of plasma inflows in laser-produced Sn plasma and their contribution to extreme-ultraviolet light output enhancement.

Plasma dynamics are governed by electron density (ne), electron temperature (Te), and radiative energy transfer as well as by macroscopic flows. However, plasma flow-velocity fields (vflow) inside laser-produced plasmas (LPPs) have rarely been measured, owing to their small sizes (< 1 mm) and short lifetimes (< 100 ns). Herein, we report, for the first time, two-dimensional (2D) vflow measurements of Sn-LPPs ("double-pulse" scheme with a CO2 laser) for extreme-ultraviolet (EUV) light sources for semiconductor lithography using the collective Thomson scattering technique, which is typically used to measure ne, Te, and averaged ionic charge (Z) of plasmas. Inside the EUV source, we observed plasma inflow speed exceeding 104 m/s magnitudes toward a plasma central axis from its peripheral regions. The time-resolved 2D profiles of ne, Te, Z, and vflow indicate that the plasma inflows maintain the EUV source at a temperature suitable (25 eV < Te < 40 eV) for EUV light emission at a high density (ne > 3 × 1024 m-3) and for a relatively long time (> 10 ns), resulting increment of total EUV light emission. These results indicate that controlling the plasma flow can improve EUV light output and that there is potential to increase the EUV output further.

Time-resolved two-dimensional profiles of electron density and temperature of laser-produced tin plasmas for extreme-ultraviolet lithography light sources.

Time-resolved two-dimensional (2D) profiles of electron density (n e) and electron temperature (T e) of extreme ultraviolet (EUV) lithography light source plasmas were obtained from the ion components of collective Thomson scattering (CTS) spectra. The highest EUV conversion efficiency (CE) of 4% from double pulse lasers irradiating a Sn droplet was obtained by changing their delay time. The 2D-CTS results clarified that for the highest CE condition, a hollow-like density profile was formed, i.e., the high density region existed not on the central axis but in a part with a certain radius. The 2D profile of the in-band EUV emissivity (ηEUV) was theoretically calculated using the CTS results and atomic model (Hullac code), which reproduced a directly measured EUV image reasonably well. The CTS results strongly indicated the necessity of optimizing 2D plasma profiles to improve the CE in the future.

Analytical and numerical study on a vortex sheet in incompressible Richtmyer-Meshkov instability in cylindrical geometry.

Motion of a fluid interface in the Richtmyer-Meshkov instability in cylindrical geometry is examined analytically and numerically. Nonlinear stability analysis is performed in order to clarify the dependence of growth rates of a bubble and spike on the Atwood number and mode number n involved in the initial perturbations. We discuss differences of weakly and fully nonlinear evolution in cylindrical geometry from that in planar geometry. It is shown that the analytical growth rates coincide well with the numerical ones up to the neighborhood of the break down of numerical computations. Long-time behavior of the fluid interface as a vortex sheet is numerically investigated by using the vortex method and the roll up of the vortex sheet is discussed for different Atwood numbers. The temporal evolution of the curvature of a bubble and spike for several mode numbers is investigated and presented that the curvature of spikes is always larger than that of bubbles. The circulation and the strength of the vortex sheet at the fully nonlinear stage are discussed, and it is shown that their behavior is different for the cases that the inner fluid is heavier than the outer one and vice versa.

Vortex core dynamics and singularity formations in incompressible Richtmyer-Meshkov instability.

Motion of a fluid interface in Richtmyer-Meshkov instability is examined as a vortex sheet with the use of Birkhoff-Rott equation. This equation coupled with an evolution equation of the strength of the vortex sheet can describe all inviscid and incompressible fluid instabilities, i.e., Kelvin-Helmholtz, Rayleigh-Taylor, and Richtmyer-Meshkov instabilities, when Atwood numbers and initial distribution of vorticities are given. With these equations, detailed motion of a vortex core in the Richtmyer-Meshkov instability is investigated. For the Kelvin-Helmholtz and Rayleigh-Taylor instabilities, it is known that the curvature of a vortex sheet diverges at a finite time t=tc. This fact indicates that the solution loses its analyticity at tc. We show that the singularity formation also occurs in the Richtmyer-Meshkov instability and at the same time, accumulation of vorticity to some points where singularities are formed develops to the roll-up of a sheet when the sheet is regularized. We investigate motion of these accumulation points, i.e., vortex cores, and present that their trajectories and the strengths depend on the Atwood numbers.

Fully nonlinear evolution of a cylindrical vortex sheet in incompressible Richtmyer-Meshkov instability.

Fully nonlinear motion of a circular interface in incompressible Richtmyer-Meshkov instability is investigated by treating it as a nonuniform vortex sheet between two different fluids. There are many features in cylindrical geometry such as the existence of two independent spatial scales, radius and wavelength, and the ingoing and outgoing growth of bubbles and spikes. Geometrical complexities lead to the results that nonlinear dynamics of the vortex sheet is determined from the inward and outward motion rather than bubbles and spikes, and that the nonlinear growth strongly depends on mode number.

Saturation and postsaturation phenomena of Rayleigh-Taylor instability with adjacent modes.

A weakly nonlinear theory has been developed for the classical Rayleigh-Taylor instability with a finite bandwidth taken into account self-consistently. The theory includes up to third order nonlinearity, which results in the saturation of linear growth and determines subsequent weakly nonlinear growth. Analytical results are shown to agree fairly well with two-dimensional hydrodynamic simulations. There are generally many local peaks of a perturbation with a finite bandwidth due to the interference of modes. Since a local amplitude is determined from phases among the modes as well as the bandwidth, we have investigated an onset of the linear growth saturation and the subsequent weakly nonlinear growth for different bandwidths and phases. It is shown that the saturation of the linear growth occurs locally, i.e., each of the local maximum amplitudes (LMAs) grows exponentially until it reaches almost the same saturation amplitude. In the random phase case, the root mean square amplitude thus saturates with almost the same amplitude as the LMA, after most of the LMAs have saturated. The saturation amplitude of the LMA is found to be independent of the bandwidth and depends on the Atwood number. We derive a formula of the saturation amplitude of modes based on the results obtained, and discuss its relation with Haan's formula [Phys. Rev. A 39, 5812 (1989)]. The LMAs grow linearly in time after the saturation and their speeds are approximated by the product of the linear growth rate and the saturation amplitude. We investigate the Atwood number dependence of both the saturation amplitude and the weakly nonlinear growth.

Nonlinear evolution of an interface in the Richtmyer-Meshkov instability.

The linear theory of the Richtmyer-Meshkov instability derived by Wouchuk and Nishihara [Phys. Plasmas 4, 3761 (1997)] indicates that the instability is driven by the nonuniform velocity shear left by transmitted and reflected rippled shocks at a corrugated interface. In this work, the nonlinear evolution of the interface has been investigated as a self-interaction of a nonuniform vortex sheet with a density jump. The theory developed shows the importance of the finite density jump and the finite initial corrugation amplitude of the interface. By introducing Lagrangian markers on the interface with proper kinematic boundary conditions, it is shown that stretching and shrinking of the interface occur locally even in the tangential direction. This causes deformation of bubble and spike profiles depending on the Atwood number. The vorticity on the interface for a finite density jump is not conserved in the nonlinear regime. Our results suggest that the spiral structure of the spike is due to local increase and decrease of the vorticity on the interface. Nonlinear analysis shows that the large initial amplitude of the corrugation results in rapid increase of the vorticity, which may also explain the fast roll up motion of the spiral for large amplitudes. With the use of the asymptotic linear growth rate, the nonlinear evolution of the instability is uniquely determined from the initial corrugation amplitude of the interface, the Atwood number, and the incident shock intensity. There is no need to use an impulsive formulation. The analytical nonlinear growth agrees well with the experiment [Dimonte et al., Phys. Plasmas 3, 614 (1996)]. The theory reveals nonlinear properties of the instability, such as the time evolution of the interface profiles and the vorticity on the interface, and also their dependence on the Atwood number and the corrugation amplitude.

Opacity effect on extreme ultraviolet radiation from laser-produced tin plasmas.

Opacity effects on extreme ultraviolet (EUV) emission from laser-produced tin (Sn) plasma have been experimentally investigated. An absorption spectrum of a uniform Sn plasma generated by thermal x rays has been measured in the EUV range (9-19 nm wavelength) for the first time. Experimental results indicate that control of the optical depth of the laser-produced Sn plasma is essential for obtaining high conversion to 13.5 nm-wavelength EUV radiation; 1.8% of the conversion efficiency was attained with the use of 2.2 ns laser pulses.

Ablation effects on weakly nonlinear Rayleigh-Taylor instability with a finite bandwidth.

A weakly nonlinear but numerically tractable model (to third order in amplitude and including bandwidth effects) has been developed for the ablative Rayleigh-Taylor (RT) instability. Model results clearly show growth reduction from linear ablative RT values and even amplitude saturation in some realistic cases. For excitation of a band of wave numbers near the cutoff for growth, the behavior is dominated by the mode with the largest linear growth rate, and not by the mode with the largest initial amplitude. This type of model is likely to be important for the future assessment of the RT effects on specific target designs of the inertial confinement fusion.

Soliton synchrotron afterglow in a laser plasma.

Coherent synchrotron radiation can be emitted by relativistic electromagnetic subcycle solitons dwelling in a low-temperature collisionless plasma. Using three-dimensional particle-in-cell simulations we show that solitons, left in a wake of a relativistically intense short circularly polarized laser pulse in the plasma, emit spiral electromagnetic wave, as a result of charge density oscillations in the wall of the soliton cavity. This high-frequency afterglow persists for tens of Langmuir periods.

Three-dimensional relativistic electromagnetic subcycle solitons.

Three-dimensional (3D) relativistic electromagnetic subcycle solitons were observed in 3D particle-in-cell simulations of an intense short-laser-pulse propagation in an underdense plasma. Their structure resembles that of an oscillating electric dipole with a poloidal electric field and a toroidal magnetic field that oscillate in phase with the electron density with frequency below the Langmuir frequency. On the ion time scale, the soliton undergoes a Coulomb explosion of its core, resulting in ion acceleration, and then evolves into a slowly expanding quasineutral cavity.

Suppression of the Rayleigh-Taylor instability due to self-radiation in a multiablation target.

A scheme to suppress the Rayleigh-Taylor instability has been investigated for a direct-drive inertial fusion target. In a high-Z doped-plastic target, two ablation surfaces are formed separately-one driven by thermal radiation and the other driven by electron conduction. The growth of the Rayleigh-Taylor instability is significantly suppressed on the radiation-driven ablation surface inside the target due to the large ablation velocity and long density scale length. A significant reduction of the growth rate was observed in simulations and experiments using a brominated plastic target. A new direct-drive pellet was designed using this scheme.