Two-plasmon Decay Instability Research Articles

Multiple-beam laser–plasma interactions in inertial confinement fusion

The experimental evidence for multiple-beam laser-plasma instabilities of relevance to laser driven inertial confinement fusion at the ignition scale is reviewed, in both the indirect and direct-drive approaches. The instabilities described are cross-beam energy transfer (in both indirectly driven targets on the NIF and in direct-drive targets), multiple-beam stimulated Raman scattering (for indirect-drive), and multiple-beam two-plasmon decay instability (in direct drive). Advances in theoretical understanding and in the numerical modeling of these multiple beam instabilities are presented.

Nonuniformly driven two-plasmon-decay instability in direct-drive implosions.

Half-harmonic emission spectra and images taken during directly driven implosions show that the two-plasmon decay (TPD) instability is driven nonuniformly over the target surface and that multibeam effects dominate this instability. The images show a spatially limited extent of the TPD instability. A prominent spectral feature is used to determine the electron temperature in the corona. Near threshold the temperatures agree with one-dimensional hydrodynamic predictions but exceed them by ∼10% above the TPD threshold. Two-dimensional hydrodynamic simulations indicate that a significant part (∼20%) of the laser intensity must be locally absorbed by the TPD instability (i.e., by collisional damping of the electron plasma waves) to maintain these temperature islands.

Nonlinear development of the two-plasmon decay instability in three dimensions

Most recent experiments on the excitation of the two plasmon-decay (TPD) instability involve a three-dimensional (3D) array of overlapping laser beams. Our recent two dimensional (2D) simulations suggested that Langmuir cavitation and collapse are important nonlinear saturation mechanisms for TPD. There are important quantitative differences in the Langmuir collapse process in 2D and 3D. To address these and other issues, we have developed a 3D Zakharov code. It has been applied to study the evolution of TPD from absolute instabilities (arising from 3D laser geometries) to the nonlinear state (J. Zhang et al., Phys. Rev. Lett. (submitted)). The present paper concentrates on the nonlinear saturated state excited by the collective action of two crossed laser beams with arbitrary polarizations. Remarkable agreement between 3D and 2D simulations is found for several averaged physical quantities when the beams are polarized in their common plane. As in the previous 2D simulations, we find: (a) the collective, initially convectively unstable triad modes dominate after a sub-picosecond burst, (b) Langmuir cavitation and collapse are important nonlinearities, and (c) that the statistics of intense cavitons are characteristic of a Gaussian random process. The 3D steady-state saturated Langmuir energy level is about 30% higher than in 2D. The auto-correlation functions of the Langmuir envelope field and of the low-frequency electron density field yield the spatial shape of the strongest collapsing cavitons which are 3D ellipsoids whose orientation depends on the laser polarizations. This tilting of the caviton's strongest electric field direction away from the normal to the target surface is a major new 3D result. This tilting may deflect the hot electron flux and thereby mitigate target preheat.

Shock-ignition relevant experiments with planar targets on OMEGA

We report on laser-driven, strong-shock generation and hot-electron production in planar targets in the presence of a pre-plasma at shock-ignition (SI) relevant laser and pre-plasma conditions. 2-D simulations reproduce the shock dynamics well, indicating ablator shocks of up to 75 Mbar have been generated. We observe hot-electron temperatures of ∼70 keV at intensities of 1.4 × 1015 W/cm2 with multiple overlapping beams driving the two-plasmon decay instability. When extrapolated to SI-relevant intensities of ∼1016 W/cm2, the hot electron temperature will likely exceed 100 keV, suggesting that tightly focused beams without overlap are better suited for launching the ignitor shock.

Mitigation of two-plasmon decay in direct-drive inertial confinement fusion through the manipulation of ion-acoustic and Langmuir wave damping

The extended Zakharov model of the two-plasmon decay instability in an inhomogeneous plasma [D. F. DuBois et al., Phys. Rev. Lett. 74, 3983 (1995); D. A. Russell and D. F. DuBois, Phys. Rev. Lett. 86, 428 (2001)] is further generalized to include the evolution of the electron distribution function in the quasi-linear approximation [cf., e.g., K. Y. Sanbonmatsu et al. Phys. Plasmas 7, 2824 (2000); D. A. Russell et al., paper presented at the Workshop on SRS/SBS Saturation, Wente Vineyards, Livermore, CA, 2–5 April 2002]. This makes it possible to investigate anomalous absorption of laser light and hot electron production due to the two-plasmon decay instability of multiple overlapping electromagnetic waves. Scalings of hot-electron production in the (stationary) nonlinearly saturated regime relevant to recent experiments [B. Yaakobi et al., Phys. Plasmas 19, 012704 (2012); D. H. Froula et al., Phys. Rev. Lett. 108, 165003 (2012)] have been obtained. They indicate a sensitivity to ion-acoustic wave (IAW) damping and to the collisional absorption of Langmuir waves. Such a sensitivity might be exploited in inertial confinement fusion target design by the use of mid-Z ablators.

Hydrodynamic simulations of long-scale-length two-plasmon–decay experiments at the Omega Laser Facility

Direct-drive–ignition designs with plastic CH ablators create plasmas of long density scale lengths (Ln ≥ 500 μm) at the quarter-critical density (Nqc) region of the driving laser. The two-plasmon–decay (TPD) instability can exceed its threshold in such long-scale-length plasmas (LSPs). To investigate the scaling of TPD-induced hot electrons to laser intensity and plasma conditions, a series of planar experiments have been conducted at the Omega Laser Facility with 2-ns square pulses at the maximum laser energies available on OMEGA and OMEGA EP. Radiation–hydrodynamic simulations have been performed for these LSP experiments using the two-dimensional hydrocode draco. The simulated hydrodynamic evolution of such long-scale-length plasmas has been validated with the time-resolved full-aperture backscattering and Thomson-scattering measurements. draco simulations for CH ablator indicate that (1) ignition-relevant long-scale-length plasmas of Ln approaching ∼400 μm have been created; (2) the density scale length at Nqc scales as Ln(μm)≃(RDPP×I1/4/2); and (3) the electron temperature Te at Nqc scales as Te(keV)≃0.95×I, with the incident intensity (I) measured in 1014 W/cm2 for plasmas created on both OMEGA and OMEGA EP configurations with different-sized (RDPP) distributed phase plates. These intensity scalings are in good agreement with the self-similar model predictions. The measured conversion fraction of laser energy into hot electrons fhot is found to have a similar behavior for both configurations: a rapid growth [fhot≃fc×(Gc/4)6 for Gc < 4] followed by a saturation of the form, fhot≃fc×(Gc/4)1.2 for Gc ≥ 4, with the common wave gain is defined as Gc=3 × 10−2×IqcLnλ0/Te, where the laser intensity contributing to common-wave gain Iqc, Ln, Te at Nqc, and the laser wavelength λ0 are, respectively, measured in [1014 W/cm2], [μm], [keV], and [μm]. The saturation level fc is observed to be fc ≃ 10–2 at around Gc ≃ 4. The hot-electron temperature scales roughly linear with Gc. Furthermore, to mitigate TPD instability in long-scale-length plasmas, different ablator materials such as saran and aluminum have been investigated on OMEGA EP. Hot-electron generation has been reduced by a factor of 3–10 for saran and aluminum plasmas, compared to the CH case at the same incident laser intensity. draco simulations suggest that saran might be a better ablator for direct-drive–ignition designs as it balances TPD mitigation with an acceptable hydro-efficiency.

Observation of parametric instabilities in the quarter critical density region driven by the Nike KrF laser

The krypton-fluoride (KrF) laser is an attractive choice for inertial confinement fusion due to its combination of short wavelength (λ=248 nm), large bandwidth (up to 3 THz), and superior beam smoothing by induced spatial incoherence. These qualities improve the overall hydrodynamics of directly driven pellet implosions and should allow use of increased laser intensity due to higher thresholds for laser plasma instabilities when compared to frequency tripled Nd:glass lasers (λ=351 nm). Here, we report the first observations of the two-plasmon decay instability using a KrF laser. The experiments utilized the Nike laser facility to irradiate solid plastic planar targets over a range of pulse lengths (0.35 ns≤τ≤1.25 ns) and intensities (up to 2×1015 W/cm2). Variation of the laser pulse created different combinations of electron temperature and electron density scale length. The observed onset of instability growth was consistent with the expected scaling that KrF lasers have a higher intensity threshold for instabilities in the quarter critical density region.

Hot-electron production and suprathermal heat flux scaling with laser intensity from the two-plasmon–decay instability

The fully kinetic reduced-description particle-in-cell (RPIC) method has been applied to simulations of two-plasmon–decay (TPD) instability, driven by crossed laser beams, in an inhomogeneous plasma for parameters consistent with recent direct-drive experiments related to laser-driven inertial fusion. The nonlinear saturated state is characterized by very spiky electric fields, with Langmuir cavitation occurring preferentially inside density channels produced by the ponderomotive beating of the crossed laser beams and the primary TPD Langmuir waves (LWs). The heated electron distribution function is, in all cases, bi-Maxwellian, with instantaneous hot-electron temperatures in the range 60–100 keV. The net hot-electron energy flux out of the system is a small fraction (∼1% to 2%) of the input laser intensity in these simulations. Scalings of the hot-electron temperature and suprathermal heat flux as functions of the laser intensity are obtained numerically from RPIC simulations. These simulations lead to the preliminary conclusion that Langmuir cavitation and collapse provide dissipation by producing suprathermal electrons, which stabilize the system in saturation and drive the LW spectrum to the small dissipation scales at the Landau cutoff. The Langmuir turbulence originates at an electron density 0.241× the laser's critical density, where the crossed laser beams excite a “triad” mode—a common forward LW plus a pair of backward LWs. Remnants of this “triad” evolve in k-space and dominate the time-averaged energy spectrum. At times exceeding 10 ps, the excited Langmuir turbulence spreads toward lower densities. Comparisons of RPIC simulations with the extended Zakharov model are presented in appropriate regimes, and the necessary requirements for the validity of a quasi-linear Zakharov model (where the spatially averaged electron-velocity distribution is evolved) are verified by RPIC simulation results.

Hot-electron generation by “cavitating” Langmuir turbulence in the nonlinear stage of the two-plasmon–decay instability

The kinetic reduced-description particle-in-cell simulation technique has been applied to study the nonlinear stage of two-plasmon–decay (TPD) instability in an inhomogeneous plasma driven by crossed laser beams. The TPD instability is found to be a prolific generator of “cavitating” Langmuir turbulence. Langmuir “cavitons”—localized longitudinal electric fields, oscillating near the local electron plasma frequency, trapped in ponderomotive density depressions—collapse to dimensions of a few electron Debye lengths, where the electric field energy is collisionlessly transferred to electron kinetic energy. The resulting hot electrons can attain instantaneous temperatures up to 100 keV with net suprathermal heat flux out of the system of up to a few percent of the input laser energy. Scaling laws for this hot-electron generation by TPD, in regimes motivated by recent experiments on the Omega laser, were presented recently by Vu et al. (H. X. Vu, D. F. DuBois, D. A. Russell, and J. F. Myatt, Phys. Plasmas 19, 102703 (2012)). This paper concentrates on the microscopic mechanisms for hot-electron generation. The spatial distribution of the maxima of the electric field envelope modulus is found to be very spiky, with the distribution of electric field envelope maxima obeying Gaussian statistics. The cavitons are produced in density-depletion trenches produced by the combined ponderomotive interference of the crossed laser beams and the ponderomotive beats of the primary backward-going TPD Langmuir waves (LWs) resulting from the crossed beams. The Langmuir turbulence is strongest in the electron-density region near 0.241× the laser's critical density, where the forward LWs from the crossed-beam TPD are degenerate. Nucleation of cavitons is assisted by the modulation of the electron density in the trenches, which in turn is caused by the beating of the common forward-going LW and the pair of backward-going LWs. The autocorrelation function of the LW envelope field provides a near-universal shape for intense cavitons—in the neighborhood of the local field maxima. The hot-electron temperature is found to be approximately a linear function of the “caviton temperature” determined from the Gaussian distribution of caviton maxima. These diagnostics provide strong evidence for the importance of Langmuir caviton collapse in the generation of hot electrons by TPD. Extended Zakharov model predictions for TPD exhibit the same qualitative phenomena.

Measurements of hohlraum-produced fast ions

We report the first fast ion measurements in indirect-drive experiments, which were taken on OMEGA hohlraum and halfraum shots using simple filtered CR-39, a nuclear track detector, and a charged-particle spectrometer. Protons are observed in two energy regimes that are associated with different fast ion production mechanisms. In the first, resonance absorption at the hohlraum wall early in the laser pulse accelerates runaway electrons. In the second, fast electrons are produced with high energy from the two-plasmon decay instability in the exploding laser entrance hole, or from stimulated Raman scattering in the underdense gas fill. In both cases, the runaway electrons set up a strong electrostatic field that accelerates the measured ions. The former mechanism is observed to have an energy conversion efficiency ∼(0.6-4)×10-4 into fast protons depending on the hohlraum and drive. The latter mechanism has an estimated conversion efficiency from the main drive of ∼(0.5-2)×10-5 depending on the assumptions made.

The dynamics of hot-electron heating in direct-drive-implosion experiments caused by two-plasmon-decay instability

Two-plasmon-decay (TPD) instability is identified as a potential source of target preheat in direct-drive-implosion experiments on OMEGA. A physical model of electron heating is developed that relies on extended Zakharov simulations to predict the nonlinearly saturated Langmuir wave spectrum. Hot electron generation is estimated via a test-particle approach. It is noted that because of the relatively low areal density of the targets during the time of TPD instability, hot-electron recirculation and reheating are potentially important effects. This is modeled by a particular form of boundary conditions on the test particles. Such boundary conditions might prove useful in other kinetic simulations of particle heating where recirculation is a possibility.

On possibility of low-threshold two-plasmon decay instability in 2ndharmonic ECRH experiments at toroidal devices

The effects o f the parametric decay of the 2 nd harmonic X-mode into two short wave-length UH plasmons propagating in opposite directions is considered. The possibility of the absolute instability excitation is demonstrated in the case of the density profile possessing local maximum slightly exceeding the UH resonance value. The threshold of the absolute instability is shown to be substantially smaller than t hat provided by the standard theory for monotonous density profile.

Kinetic simulations of stimulated Raman backscattering and related processes for the shock-ignition approach to inertial confinement fusion

A detailed description of stimulated Raman backscattering and related processes for the purpose of inertial confinement fusion requires multi-dimensional kinetic simulations of a full speckle in a high-temperature, large-scale, inhomogeneous plasma. In particular for the shock-ignition scheme operating at high laser intensities, kinetic aspects are predominant. High- (Iλo2~5×1015Wμm2/cm2) as well as low-intensity (Iλo2~1015Wμm2/cm2) cases show the predominance of collisionless, collective processes for the interaction. While the two-plasmon decay instability and the cavitation scenario are hardly affected by intensity variation, inflationary Raman backscattering proves to be very sensitive. Brillouin backscattering evolves on longer time scales and dominates the reflectivities, although it is sensitive to the intensity. Filamentation and self-focusing do occur for all cases but on time scales too long to affect Raman backscattering.

The linear regime of the two-plasmon decay instability in inhomogeneous plasmas

A linear fluid code solving the equations for the two-plasmon decay (TPD) instability has been developed and used to study the TPD instability. Both absolute and convective modes are observed in the simulations using this code, which show that the absolute modes are located close to the quarter-critical-density surface while the convective modes are located in the lower-density region. The maximum growth rates of the absolute modes measured in the simulations agree well with the theoretical results in the limits of large and small values of the parameter β∝Te2/(Iλ2), where Te is the electron temperature, I is the laser intensity, and λ is the laser wavelength. The simulation results also agree with the β-dependent threshold for absolute TPD. A derivation of the convective gain that retains the dependence on electron temperature and perpendicular mode number is presented and it is in good agreement with the simulation results.

Growth and Saturation of Convective Modes of the Two-Plasmon Decay Instability in Inertial Confinement Fusion

Particle-in-cell (PIC) and fluid simulations of two-plasmon decay (TPD) instability under conditions relevant to inertial confinement fusion show the importance of convective modes. Growing at the lower density region, the convective modes can cause pump depletion and are energetically dominant in the nonlinear stage. The PIC simulations show that TPD saturates due to ion density fluctuations, which can turn off TPD by raising the instability threshold through mode coupling.

Two-plasmon-decay instability in direct-drive inertial confinement fusion experiments

The two-plasmon-decay (TPD) instability in direct-drive irradiation OMEGA [J. M. Soures, R. L. McCrory, C. P. Verdon, et al., Phys. Plasmas 3, 2108 (1996)] experiments is seen in the half-integer harmonic emission. Experimental time-resolved ω/2 and 3ω/2 spectra indicate that the linear theory for the absolute TPD instability reasonably predicts TPD thresholds. The plasma wave spectra do not, however, agree at all with the predictions of the linear theory. This is most likely a consequence of the nonlinear evolution of this instability once it is above threshold. This is demonstrated with spectral data obtained from spherical implosion experiments as well as planar target experiments. In the latter, Thomson scattering shows the importance of the Landau cutoff. For the TPD instability, the Landau cutoff is found to be respected in all spherical and planar target experiments. In addition, the maximum plasma wave amplitudes appear to occur near the Landau cutoff.

High-resolution imaging spectrometer for recording absolutely calibrated far ultraviolet spectra from laser-produced plasmas

An imaging spectrometer was designed and fabricated for recording far ultraviolet spectra from laser-produced plasmas with wavelengths as short as 155 nm. The spectrometer implements a Cassegrain telescope and two gratings in a tandem Wadsworth optical configuration that provides diffraction limited resolution. Spectral images were recorded from plasmas produced by the irradiation of various target materials by intense KrF laser radiation with 248 nm wavelength. Two pairs of high-resolution gratings can be selected for the coverage of two wavebands, one grating pair with 1800 grooves/mm and covering approximately 155-175 nm and another grating pair with 1200 grooves/mm covering 230-260 nm. The latter waveband includes the 248 nm KrF laser wavelength, and the former waveband includes the wavelength of the two-plasmon decay instability at 23 the KrF laser wavelength (165 nm). The detection media consist of a complementary metal oxide semiconductor imager, photostimulable phosphor image plates, and a linear array of 1 mm(2) square silicon photodiodes with 0.4 ns rise time. The telescope mirrors, spectrometer gratings, and 1 mm(2) photodiode were calibrated using synchrotron radiation, and this enables the measurement of the absolute emission from the laser-produced plasmas with temporal, spatial, and spectral resolutions. The spectrometer is capable of measuring absolute spectral emissions at 165 nm wavelength as small as 5x10(-7) J/nm from a plasma source area of 0.37 mm(2) and with 0.4 ns time resolution.

Time-resolved absorption in cryogenic and room-temperature direct-drive implosions

Time-dependent and time-integrated absorption fractions are inferred from scattered-light measurements in room-temperature and cryogenic direct-drive-implosion experiments on OMEGA. The measurements agree reasonably well with hydrodynamic simulations that include nonlocal electron-heat transport. Discrepancies in the time-resolved scattered-light spectra between simulations and experiments remain for complex laser pulse shapes, indicating beam-to-beam energy transfer and commensurate coupling losses. Time-resolved scattered-light spectra near ω∕2 and 3ω∕2 as well as time-resolved hard-x-ray measurements indicate the presence of a strongly driven two-plasmon-decay (TPD) instability at high intensities that may influence the observed laser light absorption. Experiments indicate that energetic electron production due to the TPD instability can be mitigated with high-Z-doped plastic shells.

Laser plasma instability experiments with KrF lasers

Deleterious effects of laser-plasma instability (LPI) may limit the maximum laser irradiation that can be used for inertial confinement fusion. The short wavelength (248nm), large bandwidth, and very uniform illumination available with krypton-fluoride (KrF) lasers should increase the maximum usable intensity by suppressing LPI. The concomitant increase in ablation pressure would allow implosion of low-aspect-ratio pellets to ignition with substantial gain (>20) at much reduced laser energy. The proposed KrF-laser-based Fusion Test Facility (FTF) would exploit this strategy to achieve significant fusion power (150MW) with a rep-rate system that has a per pulse laser energy well below 1 MJ. Measurements of LPI using the Nike KrF laser are presented at and above intensities needed for the FTF (I∼2×1015W∕cm2). The results to date indicate that LPI is indeed suppressed. With overlapped beam intensity above the planar, single beam intensity threshold for the two-plasmon decay instability, no evidence of instability was observed via measurements of 32ωo and 12ωo harmonic emissions.

Absolutely calibrated vacuum ultraviolet spectra in the 150–250-nm range from plasmas generated by the NIKE KrF laser

High-resolution vacuum ultraviolet (VUV) spectra were recorded from plasmas generated by the NIKE KrF laser for the purpose of observing emission from the two-plasmon decay instability (TPDI) at 2∕3 the NIKE wavelength (165nm). The targets were irradiated by up to 43 overlapping beams with intensity up to ≈1014W∕cm2 and with beam smoothing by induced spatial incoherence (ISI). The targets consisted of planar foils of CH, BN, Al, Si, S, Ti, Pd, and Au. Titanium-doped silica aerogels in Pyrex cylinders were also irradiated. The spectra of the target elements were observed from charge states ranging from the neutral atoms to five times ionized. The spectrometer was absolutely calibrated using synchrotron radiation, and absolute VUV plasma emission intensities were determined. Emission from the TPDI at 165-nm wavelength was not observed from any of the irradiated targets. An upper bound on the possible TPDI emission was less than 4×10−8 the incident NIKE laser energy. The NIKE laser radiation backscattered from the silica aerogel targets at 248nm was typically 6×10−6 the incident NIKE laser energy, and the spectral broadening corresponded to the 1-THz bandwidth of the ISI smoothing. The spectra from the moderately charged plasma ions (up to five times ionized), spectral linewidths, absolute continuum emission level, and slope of the continuum were consistent with plasma temperatures in the 100–300-eV range.