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“Bloch wave” modification of stimulated Raman by stimulated Brillouin scattering
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View: Figures


Image of FIG. 1.

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FIG. 1.

(a) is plotted showing the three modes that are coupled by Eq. (5) ; (b) a two-mode calculation (red) is compared with an eleven-mode calculation, both with . Near the band gap at and the solutions agree, but moving from away from this point can lead to an incorrect dispersion.

Image of FIG. 2.

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FIG. 2.

The Bloch wave frequency shift for three different values of LW wavenumber ( ) as a function of the IAW amplitude .

Image of FIG. 3.

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FIG. 3.

Spatial plot of the Bloch wave potential (blue curve) compared to the unmodulated LW (red curve) for and .

Image of FIG. 4.

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FIG. 4.

(a) The time-averaged reflectivities for SRS (blue) and SBS (red)are plotted as a function of the density scaling for two intensities:  W/cm2 and  W/cm2. BSBS reflectivity increases with increased intensity and as expected from linear gain-rate for the instability while the reflectivity for BSRS appears to decrease with increased intensity due to strong pump depletion by SBS reflectivities of more than 50%; (b) and (c) the time-dependent SRS and SBS reflectivities are shown for two cases: (b) and  W/cm2 and (c) and  W/cm2. The suppression of SRS by pump depletion of BSBS is clearly evident. The black lines show the temporal windows used in the FFT analyses.

Image of FIG. 5.

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FIG. 5.

Wave number spectrum for LWs for the case of Fig. 4(b) . Indicated are harmonics of the primary BSRS LW, LDI-produced LWs and its harmonics, and the Bloch wave harmonics with .

Image of FIG. 6.

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FIG. 6.

The electron velocity distribution function for the case of Fig. 4(b) indicating a hot electron tail associated with the primary BSRS LW. Initially, there are very few electrons in the Maxwellian distribution at the phase velocity of the primary BSRS-produced LW. LDI-initiated LW nucleation and collapse produce hot electrons that are further accelerated by and trapped in the primary BSRS-produced LW with .

Image of FIG. 7.

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FIG. 7.

The spectrum for the case of Fig. 4(c) , over plotted with Eq. (5) (black lines). Note the presence of band gaps at and a weak BSRS streak at the SRS matching condition of and . The weak frequency streak is downward (negative frequency shift), presumably due to trapping, beginning at the Bloch wave frequency.

Image of FIG. 8.

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FIG. 8.

(a) The spectrum from Fig. 4(b) at early times shows the negative frequency shift characteristic of electron trapping. (b) The late time spectrum from Fig. 4(b) shows a positive frequency shift relative to the unperturbed LW frequency, but a negative shift (as expected from trapping) relative to the Bloch wave frequency. The value for is taken from the simulations and used to calculate Eq. (5) . Although the band gaps are not visible, the dispersion relations match quite well at the SRS matching condition of and . (c) The time history of the IAW density amplitude at the SBS IAW wave number ( ) is shown in the solid curve. This amplitude is averaged over the timeinterval represented by the rectangular window ( ), which results in the time-averaged IAW density amplitude of used in Fig. 8(b) .

Image of FIG. 9.

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FIG. 9.

(a) The time-averaged SRS and SBS reflectivities as a function of . This parameter determines the IAW Landau damping, which is small for large ; (b) a low-damping case with significant Bloch wave harmonics where the negative frequency shift streak at the fundamental BSRS mode is strongly imprinted on the Bloch wave harmonics; (c) a case of highly damped BSBS where the Bloch wave harmonics are much weaker and a strong spectral streak from trapping appears only in the fundamental BSRS mode. Note that while the trapping streak in the primary BSRS LW in (b) is weaker (shorter) than in (c), the reverse is true for the streak in the Bloch wave harmonic.

Image of FIG. 10.

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FIG. 10.

The scattered light wave spectrum, averaged over the time interval , for the case shown in Fig. 4(c) . In addition to the backscatter light wave from BSRS and forward-scattered light wave from forward SRS, the self-Thomson-scattered light wave from the Bloch wave harmonic is also clearly observed. This observation suggests a possible scattered light wave diagnostic to provide experimental confirmation of the existence of Bloch wave distortion of the LW dispersion.


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Using the reduced-description particle-in-cell (RPIC) method, we study the coupling of backward stimulated Raman scattering (BSRS) and backward stimulated Brillouin scattering (BSBS) in regimes where the reflectivity involves the nonlinear behavior of particles trapped in the daughter plasma waves. The temporal envelope of a Langmuir wave (LW) obeys a Schrödinger equation where the potential is the periodic electron density fluctuation resulting from an ion-acoustic wave (IAW). The BSRS-driven LWs in this case have a Bloch wave structure and a modified dispersion due to the BSBS-driven spatially periodic IAW, which includes frequency band gaps at (kLW , k IAW , and k 0 are the wave number of the LW, IAW, and incident pump electromagnetic wave, respectively). This band structure and the associated Bloch wave harmonic components are distinctly observed in RPIC calculations of the electron density fluctuation spectra and this structure may be observable in Thomson scatter. Bloch wave components grow up in the LW spectrum, and are not the result of isolated BSRS. Self-Thomson scattered light from these Bloch wave components can have forward scattering components. The distortion of the LW dispersion curve implies that the usual relationship connecting the frequency shift of the BSRS-scattered light and the density of origin of this light may become inaccurate. The modified LW frequency results in a time-dependent frequency shift that increases as the IAW grows, detunes the BSRS frequency matching condition, and reduces BSRS growth. A dependence of the BSRS reflectivity on the IAW Landau damping results because this damping determines the levels of IAWs. The time-dependent reflectivity in our simulations is characterized by bursts of sub-picosecond pulses of BSRS alternating with multi-ps pulses of BSBS, and BSRS is observed to decline precipitously as soon as SBS begins to grow from low levels. In strong BSBS regimes, the Bloch wave effects in BSRS are strong and temporal anti-correlation with BSRS is due to pump depletion in addition to frequency detuning. In most cases studied, BSBS suppressed the time-averaged reflectivity of BSRS compared to the levels obtained with fixed ions (and therefore no BSBS). The strong spatial modulation of the Bloch Langmuir waves appears to weaken electron trapping and thereby lowers the inflated reflectivity levels of BSRS.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: “Bloch wave” modification of stimulated Raman by stimulated Brillouin scattering