In indirect-drive inertial confinement fusion (ICF), a millimeter-scale Au/U hohlraum filled with low-Z gas is used to convert laser energy into x rays, which uniformly irradiate a DT capsule that is placed at the hohlraum center.1 It was realized at the very beginning that laser plasma instabilities (LPIs)2 could be detrimental to the energy coupling from lasers to the hohlraum. For example, in low-gas-filled (0.3 mg/cm³) hohlraums, stimulated Brillouin scattering (SBS) is of great concern.3 This is because the scattered light can not only take energy away from the pump laser,4,5 but also potentially damage the optical components,6 thereby limiting the maximum output energy of the laser facility. Although a controlled fusion experiment exceeding the Lawson criterion has been achieved on the National Ignition Facility (NIF) with a low-gas-filled hohlraum,7 the laser power of the outer beams are ramped down at the end of the pulse, to avoid strong SBS.5,8 For achieving high-gain fusion in the future, longer laser pulses and higher-gas-filled hohlraums are required, which will inevitably lead to strong SBS.9–11 Therefore, studying SBS in a high-gas-filled hohlraum is still important for indirect-drive ICF research.

To study SBS under ICF conditions, a large number of experiments have been performed.12 Gas bag targets have been used to study SBS in the filled gas region, and it has been found that SBS reflectivity saturates at the 30% level for laser intensities above 5 × 10¹⁴ W/cm².13 Experiments with direct measurement of SBS light from ICF hohlraums have also been performed at different laser facilities, such as the Omega laser facility,14 the NIF,15 and the Shenguang laser facilities.16 These experiments have investigated in detail the factors influencing SBS in hohlraums, such as target geometry,14 gas fill,4 and laser smoothing techniques.16 However, given that the distribution of plasma parameters along the laser path inside an ICF hohlraum is quite complex, it is very difficult to determine the exact excitation region of SBS simply from the detected scattered light. To analyze the spatial growth of SBS, steady-state models have been developed to enable rapid calculations of the scattered light based on the plasma parameters provided by radiation-hydrodynamics simulations.17,18 These models have revealed some important mechanisms impacting on LPI, such as competition between SBS and stimulated Raman scattering (SRS),19 plasma heating via external magnetic fields20 and mixing between the filled gas and Au plasma from the hohlraum wall.21 Nonetheless, when these models were applied to the complex conditions in ICF hohlraums, discrepancies were found between calculations and experiments. For example, in our previous studies of SBS on the Shenguang-III prototype laser facility (SG-IIIp), the calculated SBS spectra always contained an extra component originating from the Au plasma, which was not observed in the experimental data.18 One of the possible explanations for this is that the neglect of ion–ion collisions in the calculation led to overestimation of the contribution of SBS in the Au plasma. However, this speculation has yet to be validated.

One way to experimentally study the spatial growth of SBS is to use collective Thomson scattering (TS)22 to diagnose the ion acoustic wave (IAW) driven by SBS locally.13 The TS diagnostic has been widely used in experiments with an open configuration (e.g., plate targets and gas bag targets), which have verified saturation mechanisms of SBS, such as ion trapping,23 detuning by the velocity gradient,24 and two-ion decay.25 However, owing to the requirement of a rigorous geometric relation between the SBS-driven IAW (determined by the pump laser), the TS probe beam, and the diagnostic system,26 TS has seldom been applied to experiments with a closed configuration, such as that of an ICF hohlraum target.

Taking advantage of a recently developed large-aperture TS diagnostic system,26 we apply TS to an ICF gas-filled hohlraum for the first time (to the best of our knowledge) to detect the driven IAW, so as to study the spatial growth of SBS. The results indicate that SBS primarily consists of two components, occurring respectively in the early and late phases of the laser pulse, both of which are primarily from the filled gas (CH) plasma. At early times, laser heating increases the electron density at the edges of laser channel, scattering high-intensity SBS light. At late times, the flow velocity in the hohlraum is relatively uniform, and hence produces strong SBS light. Owing to ion–ion collisional damping and the small size of the high-Z (Au) wall plasma, SBS in the wall plasma is weak. The additional TS probe beam in the experiment may suppress SBS, because of its perturbation of the local density distribution. These findings have improved the understanding of SBS in gas-filled hohlraums and may play an important role in mitigating SBS in the future experiments.

The remainder of the paper is organized as follows. In Sec. II, we introduce the experimental setup and results. In Sec. III, we present the plasma parameters provided by radiation-hydrodynamics simulation. In Sec. IV, we introduce the models for SBS and TS calculations. In Sec. V, we analyze the factors affecting SBS in gas-filled hohlraums, including ion–ion collisions and transverse density variations caused by the interaction beam and the TS probe beam. Section VI provides a brief summary.

The experiment is conducted on the Shenguang-III prototype laser facility (SG-IIIp), as shown in Fig. 1. The target is a cylindrical Au hohlraum [see Fig. 1(a)] with a diameter of 1.4 mm and a length of 1.4 mm, and the open ends of the hohlraum serve as laser entrance holes (LEHs). The hohlraum is filled with pentane (C₅H₁₂) gas at a pressure of 0.6 atm, corresponding to an electron density of 6.3 × 10²⁰ cm⁻³ when fully ionized. The 1500 mg/cm³, 0.5 μm-thick polyimide covering membrane for gas filling is not shown. There is a 400 μm-diameter diagnostic hole on the wall of the hohlraum for injection of the TS probe beam. As shown in Fig. 1(a), eight 3ω (351 nm) beams enter the hohlraum through both ends, with an angle of 45° relative to the hohlraum axis, irradiating 200 μm below its waist. Each 3ω beam delivers an energy of 800 J in a 2 ns main pulse plus a 0.5 ns pre-pulse [see Fig. 1(b)]. All 3ω beams are smoothed by continuous phase plates (CPPs) and focused by f/5.4 lenses. Seven of them are used as heater beams and the other as an interaction beam. The heater beams are focused on the LEH plane, forming 500 μm-diameter focal spots. To drive strong SBS, the interaction beam forms a smaller focal spot with a diameter of 300 μm, which corresponds to an average intensity of ∼8 × 10¹⁴ W/cm². The energy and spectrum of the backscattered SBS light are diagnosed by a full-aperture backscattering station (FABS). The SBS-driven IAW with a wave vector (k⃗I=k⃗0−k⃗s≈2k⃗0) [see Fig. 1(c)] is detected by a 4ω (263.3 nm) TS probe beam. Routinely, the probe beam is synchronized with the main pulse of the 3ω beams, delivering 60 J energy in a 3 ns-square pulse. The probe beam is focused to a 70 μm-diameter spot by an f/7 lens. The TS light is collected by a large aperture (f/3) TS diagnostic system. The probe beam and the TS diagnostic system define a diagnostic volume (ϕ70 × 100 µm²), which is located at the center of the interaction beam, 400 μm from the upper LEH and 200 μm from the hohlraum axis, as shown by the green square in Fig. 1(a).

Figures 2(a) and 2(b) show the time-resolved spectra of the SBS light and the TS light off the SBS-driven IAW in the diagnostic volume shown in Fig. 1(a), respectively. The SBS reflectivity is about 4%. The SBS light consists of two components with comparable intensities, one in the early phase (0–0.7 ns) and the other in the late phase (1.2–1.9 ns) of the laser pulse. The TS light also contains two components similar to SBS light. TS light characterizes the SBS-driven IAW in the diagnostic volume, which correlates with the SBS light therein. Compared with the SBS spectrum, the two components of the TS spectrum have a greater contrast, with a much weaker signal in the early phase, which could come from two possible causes. One is that early SBS light primarily grows around the LEH, which is behind the TS diagnostic volume. The other is that SBS mainly occurs at the edge of the interaction beam, which the TS diagnostic volume does not cover.

The frequency shift of the TS spectrum relative to the probe beam is generally the same as that of the SBS spectrum relative to the interaction beam [see Figs. 2(c) and 2(d)], which demonstrates that the IAW detected by the TS diagnostic is indeed driven by the interaction beam and the SBS light. However, there are some minor differences between the two spectra. For example, at 0.4 ns, the SBS spectrum (0.4–1.6 THz) is narrower than the TS spectrum (0.1–2.2 THz), as shown in Fig. 2(c). A reasonable explanation is that the central part of the SBS spectrum experiences stronger amplification in the region from the TS diagnostic volume to the LEH, owing to its better coupling with the plasma parameters therein. The widths of the late (1.6 ns) SBS and TS spectra [see Fig. 2(d)] are both much narrower than the corresponding early spectra [see Fig. 2(c)], implying that the plasma parameters are more homogeneous in the late phase.

To obtain plasma parameters for SBS analysis, a 2D cylindrically symmetric radiation-hydrodynamics simulation for the SG-IIIp gas-filled hohlraum is performed using the code LARED.27 This code has already been benchmarked in an almost identical experiment, by comparing the simulated plasma parameters inside the hohlraum with those measured by TS.28 Restricted by the cylindrical symmetry, the diagnostic hole and the probe beam are absent in the simulation, and all 3ω lasers, including the interaction beam, have the same focal spots with diameters of 500 μm in the R direction. The 0.5 μm-thick covering membrane used in the experiment is too thin to be simulated, and so it is replaced by a mass-equivalent membrane with a greater thickness (50 μm) and a lower density 15 mg/cm³. As will be shown below, these differences between the experiment and the simulation cannot be ignored in the SBS analysis.

Figure 3 shows the spatial distributions of the simulated plasma parameters for two typical times: 0.4 and 1.6 ns. Owing to the laser heating, the plasma temperature inside the laser channel is higher than that outside, while the electron density inside is lower than that outside, as shown by the profile at 0.4 ns (red line) in Fig. 4. This is because at early times, the transverse pressure caused by laser heating pushes the initially static plasma out from the laser channel, resulting in a low density at the center and a high density at the edges. As the heating continues, the transverse electron density distribution around the channel becomes flat, as shown by the blue line in Fig. 4. The density increase at the channel center at 0.7 ns is due to the expansion of the Au bubble, which compresses the CH plasma inside the hohlraum.

Based on the plasma parameters from the LARED simulation, we calculate the SBS light of different rays in the interaction beam using the 1D steady-state model from Ref. 19. The total SBS light of the interaction beam is then obtained by summing the scattered light of these rays. Specifically, along each ray in the 300 μm-diameter interaction beam, the model solvesdlI0(l)=−κ0I0−I0∫dωsω0ωs(τ1+Γis),(1)−∂lis(l,ωs)=−κsis+Σ+I0(τ1+Γis).(2)Here, l is the distance along the ray of the interaction (pump) beam. ω₀ and I₀ are respectively the frequency and intensity of the interaction beam. It should be noted that although the average intensity of the interaction beam in experiment is ∼8 × 10¹⁴ W/cm², a value of I₀ = 2 × 10¹⁵ W/cm² is used in SBS calculations for considering the high-intensity speckles in the focal spot.16i_s dω_s is the intensity of the SBS light within the frequency interval between ω_s and ω_s + dω_s. κ₀ and κ_s are the inverse bremsstrahlung absorption coefficients of the interaction beam and the SBS light, respectively. I₀τ₁ represents the noise source from TS and Σ the noise source from bremsstrahlung. The absorption coefficients and noise sources are basically the same as those used in Ref. 17, except that the effects of whole-beam focusing are omitted. The coupling coefficient Γ is expressed asΓ=−kI2e2me2c22πksk0ω0Imχe(1+χi)ε,(3)where e and m_e are respectively the charge and mass of the electron, and k_I is the wavenumber of the SBS-driven IAW. χ_e and χ_i are the collisionless electron and ion susceptibilities, respectively. ɛ = 1 + χ_e + χ_i is the plasma dielectric function. The computational domain ranges from n_e = 0.001n_c to n_e = 1n_c. Because SBS light is treated as a broadband signal in this model, its spectrum at a given moment can be obtained by solving the coupled Eqs. (1) and (2) based on the corresponding plasma parameters. Doing this calculation for the whole duration of the interaction beam, one then obtains the time-resolved SBS spectra.

As mentioned in Sec. I, the neglect of collisional damping in SBS calculations may overestimate the SBS growth in the Au plasma. Collisions in an ICF plasma include electron–electron, electron–ion, and ion–ion collisions, whose mean free paths are given by λ_ee = v_Teτ_ee, λ_ei = v_Teτ_ei, and λ_ii = v_Tiτ_ii, respectively, where vTe=Te/me and vTi=Ti/mi are the thermal velocities of electrons and ions, respectively. τ_ee, τ_ei, and τ_ii are the corresponding collision times.29 The collisional effects on the IAW depend on the parameter k_Iλ, where λ denotes λ_ee, λ_ei, or λ_ii for the respective collisions. If the parameter k_Iλ is not much greater than 1, the collisions provide non-negligible damping on the IAW. We consider two typical hohlraum plasmas, namely, an Au plasma (with n_e = 0.12n_c, T_e = 1400 eV, T_i = 1200 eV, and Z = 39) and a CH (C₅H₁₂) plasma (with n_e = 0.09n_c, T_e = 1200 eV, T_i = 1000 eV, and Z̄=∑iZi2ni/∑iZini≈4.57). The parameters k_Iλ for the Au and CH plasmas are shown in Table I. Here, the quantities for the CH plasma are calculated by treating it as a single-ion-species plasma with Z̄=4.57. For the electron–electron and electron–ion collisions, the parameters k_Iλ_ee and k_Iλ_ei are much greater than 1 in both the Au and CH plasmas. This means that these collisions are quite weak and have little effect on SBS. On the other hand, for the ion–ion collisions, k_Iλ_ii is much less than 1 in the Au plasma and not much greater than 1 in the CH plasma. Therefore, ion–ion collisional damping is considered in the following calculations of SBS. This is realized by correcting the ion susceptibility:30χic=ZTeTiα2−1xi2−53xi4+i109kIλiixi3,kIλii≤0.1,ZTeTiα2−1xi2−1151xi4+i16251kIλiixi5+iπ2xie−xi2/2,0.1<kIλii<10,ZTeTiα2−1xi2−3xi4+i851kIλiixi5+iπ2xie−xi2/2,kIλii≥10,(4)where α=(kIλD)−1, λ_D is the the electron Debye length, x_i = ω_I/k_Iv_Ti, and ω_I is the frequency of the IAW. This corrected ion susceptibility χic is then substituted into Eq. (3), to solve the coupled Eqs. (1) and (2).

To calculate the TS spectra, the electron density fluctuation δn_e of the IAW is required. In stimulated scattering, the electron density fluctuations are driven by the ponderomotive force, which can be described by the following equation:19,31δne(kI,ωI)=−12kI2e2neme2c2ωpe2χe(1+χic)εa0as*.(5)Here, ω_pe is the electron plasma frequency, and a₀ and a_s are respectively the complex envelopes of the pump laser (0) and the scattered light (s). The complex envelopes and laser intensities are related by I0=vg0ω02|a0|2/8πc2 for the interaction beam and isdωs=vgsωs2|as|2/8πc2 for the SBS light within the frequency interval between ω_s and ω_s + dω_s, where v_g0 and v_gs are respectively the group velocities of the interaction beam and the SBS light in the plasmas. The TS light (I_TS) off SBS-driven IAWs can be obtained from the electron density fluctuation:32ITS(k⃗TS,ωTS)=Iprre2ΔΩ∫VdVδne(k⃗I,ωI)2×∝[Vδn̄e(k⃗I,ωI)]2.(6)Here I_pr is the intensity of the probe beam, ΔΩ is the solid angle of the TS light, and V is the TS diagnostic volume. The wave vector and frequency of the TS light are k⃗TS=k⃗pr±k⃗I and ω_TS = ω_pr ± ω_I, respectively, where ω_pr is the frequency of the probe light and the sign ± depends on the specific geometric relationship. For a given moment, with the intensities of the interaction beam and SBS light in the diagnostic volume provided by the SBS calculation, the TS spectrum can be calculated by Eqs. (5) and (6). The time-resolved TS spectra are then obtained by doing the calculation for the whole duration of the probe beam.

Figure 5 shows the spectra of SBS and TS calculated with ion–ion collisions either ignored or considered. The spectra from the ion–ion collisionless calculation [see Figs. 5(a) and 5(b)] reproduce the main features observed in the experiment [see Figs. 2(a) and 2(b)], with two components: one in an early phase during 0–0.6 ns and the other in a later phase during 1.2–1.9 ns. However, there is an extra strong signal during 0.5–1.5 ns with a wavelength shift of 0–0.2 nm, which was routinely seen in the previous calculations,18 but was not measured in the experiment. The SBS spatial spectrum during 1.0 ns [Fig. 6(c)] clearly shows that the strong signal is from the Au plasma. In the collisionless case, the SBS growth rate in the Au plasma is larger than that in the CH plasma by one to two orders of magnitude [see Fig. 6(a)], and so SBS grows rapidly in the Au plasma, as shown in Fig. 6(c). In the calculated TS spectrum [Fig. 5(b)], there is also a strong TS signal near the 4ω during 0.5–1.5 ns, which demonstrates that a large-amplitude IAW is driven in the diagnostic volume by the pump laser and the SBS light from the Au plasma. When ion–ion collisions are considered, the spatial growth rate of SBS in the Au plasma broadens, with its peak value decreased by about an order of magnitude [see Fig. 6(b)]. As a result, the intensities of SBS light at the CH/Au interface and the left boundary both decrease by four orders of magnitude, as shown in Fig. 6(e). The SBS and TS spectra [see Figs. 5(c) and 5(d)] in this case basically agree with the experimental spectra, indicating that ion–ion collisions in the Au plasma may not be ignored in the analysis of SBS growth.

With ion–ion collision considered, the calculation [see Fig. 5(c)] shows that SBS is mainly from the late phase of the laser pulse (1.2–1.9 ns), weakly from the early phase (0–0.7 ns), and negligibly from the middle phase (0.7–1.2 ns). This behavior is primarily caused by the longitudinal (along the laser path) distributions of flow velocity and material (filled gas or covering membrane), as shown in Fig. 7(a) for three typical times (0.4, 1.0, and 1.6 ns). At 1.6 ns, the flow velocity is relatively uniform, which facilitates the growth of SBS; as a result, the SBS growth rate at this time is larger than those at the other two times, as shown in Fig. 7(b). Although the velocity gradient at 0.4 ns is greater than that at 1.0 ns, the former growth rate is larger than the latter. This is because the higher-Z membrane plasma at 0.4 ns makes a great contribution to the SBS growth, as can be seen by comparing the growth rates with (solid green line) and without (dashed green line) the membrane plasma in Fig. 7(b). This contribution is negligible at 1.0 and 1.6 ns, because the later flow velocity of the membrane plasma (R < −600 µm) deviates from that of the interior plasma, causing the membrane plasma to decouple from the SBS light from the CH and Au plasmas.

Although the calculated SBS and TS spectra basically agree with the experimental results once ion–ion collisions have been considered, a quantitative discrepancy still exists. In the calculation, the early (0–0.7 ns) SBS light only accounts for 3% of the total SBS energy, whereas it accounts for 30% in the experiment. This discrepancy could result from two factors that are not well treated in the radiation-hydrodynamics simulation. First, the use of a mass-equivalent membrane in the simulation would lead to a lower membrane density than in the experiment, which may lead to underestimation of the SBS in the membrane plasma. Second, restricted by the cylindrical symmetry of the simulation, the focal spot of the interaction beam (of diameter 300 μm in the experiment) is set to be the same as that of the heater beams (of diameter 500 μm in the experiment). This may underestimate the density piled up at the edges of the laser channel caused by laser heating, which would then lead to an underestimation of SBS from the channel edge in the early phase. In the following subsections, we will discuss these two factors in detail.

The covering membrane has a much higher initial density than the filled gas. It can generate a high-density membrane plasma at the beginning of the pulse, which may lead to strong SBS. However, since the it is difficult to simulate ultrathin and high-density materials in LARED, a low-density membrane of equal mass is used. This treatment could lead to a low plasma density around the LEH and thus an underestimation of SBS at early times (0–0.7 ns). To examine this hypothesis, we calculate the SBS and TS spectra by doubling the membrane plasma density in 0–0.7 ns, as shown in Fig. 8. The higher-density in membrane plasma does produce stronger SBS light at early times, which makes the temporal behavior of SBS light closer to that in the experiment [green dashed lines in Figs. 2(a) and 8(a), respectively]. However, the early TS spectrum is almost completely suppressed as the membrane plasma density increases, which deviates from the experimental data [green dashed lines in Figs. 2(b) and 8(b), respectively]. According to the calculation, this suppression is caused by the pump depletion effect.33 The stronger SBS in the membrane plasma around the LEH scatters more pump laser energy, leaving less energy arriving at the hohlraum interior; as a result, a weaker IAW is driven in the TS diagnostic volume, and hence weaker TS spectra are detected. As the membrane plasma density further increases, the deviation of the calculated early TS spectrum becomes greater. Therefore, the disagreement in the calculated and experimental TS spectra excludes the possibility that the relatively strong SBS in the early phase is from the dense membrane plasma.

Laser heating leads to transverse plasma inhomogeneity, with the formation of a high-temperature, low-density plasma at the center of the laser channel and a low-temperature, high-density plasma at the edges and outside, similar to the features shown in Figs. 3 and 4. As stated above, the 300 μm-diameter interaction beam is replaced by a 500 μm-diameter beam in the radiation-hydrodynamics simulation. This difference in beam diameter will lead to an overestimation of the distance from the piled-up region to the beam axis and hence an underestimation of the density at the edges of the 300 μm-diameter interaction beam. On the other hand, in the SBS calculation, the interaction is limited to a region with a transverse size of 300 μm in diameter, so as to be consistent with the experiment. This means that as long as the original plasma parameters from the simulation are used in the SBS calculation, the interaction in the high-density piled-up region will be underestimated. Therefore, to better reproduce the experiment, the transverse distribution of the plasma parameters should be corrected. Similarly, the TS probe beam can also perturb the plasma, which should also be considered in the SBS calculations.

As shown in Fig. 4, owing to the plasma evolution, the transverse inhomogeneity of plasma parameters inside the laser channel lasts only for a short time interval. After t = 0.7 ns, the plasma becomes uniform. Hence, the correction of plasma parameters caused by the interaction beam only applies to the early phase (0–0.7 ns) in the following calculations. To quantitatively correct the plasma parameters, we use the energy deposition and transport model from Ref. 20. In this model, the energy deposited into the plasma by the inverse bremsstrahlung process and the energy lost from the plasma via the transverse electron thermal transport are in equilibrium. Thus, the electron temperature T_e satisfies the following equation:ωpe2ω02νeivg0fLfscI0r=−κQ1r∂Ter∂r,(7)where ν_ei is the electron–ion collision frequency, r is the distance from the beam axis, and f_L and f_sc are the Langdon absorption-reduction factor and ion screening correction factor, respectively, as given in Ref. 34. The local thermal conductivity is κQ=β(Z̄)neTe/meνei, where β(Z̄) is a coefficient related to the average ion charge Z̄,35 given approximately by β(Z̄)=3.2(0.24+Z̄)/(1+0.24Z̄)≃7.34. The electron density is considered to satisfy thermal pressure equilibrium, n_e(0)T_e(0) = n_e(r)T_e(r) = ⋯ = n_e(∞)T_e(∞). Since the f_L and f_sc depend on T_e, Eq. (7) has to be solved numerically. The boundary electron density n_e(∞) is set as the initially fully ionized electron density of the filled gas (∼0.07nc). The boundary electron temperature T_e(∞) is set as 0.4 keV, which is the electron temperature outside the laser channel at 0.2 ns from the LARED simulation.

Figure 9 shows the calculated transverse profiles of the electron temperature and density for two laser intensity profiles corresponding respectively to the interaction beam with a diameter of 300 μm and the heater beam with a diameter of 500 μm. The laser intensity profiles used here are tenth-order super-Gaussian distributions. As can be seen, at the edges of the interaction beam (gray region in Fig. 9), the plasma heated by the interaction beam has ∼30% higher electron density and ∼20% lower electron temperature than the plasma heated by the heater beam. These relative variations in electron density and temperature are applied to the simulated plasma parameters for correction.

In principle, the plasma flow should also be corrected when the smaller-size interaction beam is considered. However, this correction has a negligible impact on the SBS calculation for two reasons. First, the perturbation caused by the interaction beam is primarily along its transverse direction, whereas the 1D SBS calculation depends only on the plasma flow along the longitudinal direction. Second, the transverse perturbation quickly spreads out of the interaction beam channel. By contrast, the TS probe beam propagates across the interaction beam at an angle of 45°, and so its heating effect will lead to a correction of plasma parameters (including electron density, electron temperature, and plasma flow velocity) not only within the probe beam channel, but also along the interaction beam channel as the perturbation spreads. Consequently, this correction should be taken into account in the SBS calculation throughout the presence of the TS probe beam. In this case, the energy deposition and transport model used above is no longer applicable.

To investigate the effect of the probe beam on the plasma parameters, a separate simulation is performed with LARED. In this simulation, a cup-shaped Au hohlraum with a diameter of 1 mm and a length of 1.5 mm is initially filled with pentane (C₅H₁₂) at a pressure of 0.6 atm. The initial electron temperature of the filled gas is set as 10 eV, which corresponds to the electron temperature outside the interaction beam at −0.1 ns in the above-mentioned simulation case. The probe beam with the same settings as the experiment (60 J energy, a 70 μm-diameter spot, and a 3 ns-square pulse) is injected into the hohlraum along its axis from the open end and terminates at the closed end, as shown in Fig. 10(a). As expected, the probe beam heats the nearby plasma to 0.3–0.4 keV, and also forms a density valley and density peaks at the center and the edges of the beam, respectively, as displayed in Figs. 10(b)–10(d). The density peak moves transversely outward at a speed of 1.2 × 10⁷ cm/s. Along with the outward movement of the density peak, the local plasma flow is also perturbed. To take these impacts into account, the previously simulated electron density around the probe beam is corrected by multiplying by the normalized density profile n_e(s, t)/n₀ obtained here, and the plasma flow velocity and electron temperature along the transverse direction of the probe beam are corrected by adding the velocity V(s, t) and temperature T_e(s, t) obtained here. n₀ is the initial electron density, and s denotes the coordinate along the transverse direction of the probe beam, which corresponds to the direction along the hohlraum axis in the previous simulation. Unlike the correction resulting from the interaction beam, which works only in the early phase (0–0.7 ns), the correction resulting from the probe beam lasts for the whole interaction period (2 ns), because it continues to affect the SBS process.

The heating effects of the 300 μm-diameter interaction beam and the probe beam affect SBS by perturbing the flow velocity, temperature, and density. The longitudinal distributions of electron temperature and flow velocity with the corrections for the heating effect of the TS probe beam are shown in Fig. 11 (solid lines). As can be seen, compared with the uncorrected results (dashed lines), the plasma flow velocity is only weakly affected. Although the electron temperature near the probe beam (−1200 µm ≤ l ≤ −650 µm) rises slightly from 1.3 to 1.7 keV, this is not sufficient to have a noticeable effect on SBS. The temperature and velocity corrections caused by the probe beam will red-shift the SBS light by ∼0.05 nm and attenuate it by ∼5%. Similarly, the temperature drop caused by the interaction beam has a minor effect on SBS.

The interaction beam and probe beam affect SBS primarily by perturbing the electron density. Figure 12 shows the spatial distributions of electron density and SBS reflectivity with (solid lines) and without (dashed lines) the corrections due to the heating effect. The electron density at the edge of the interaction beam increases by ∼30% [see Fig. 12(a), red lines] in the early phase (0–0.7 ns), resulting in the intensity of the SBS light at the left boundary rising by about an order of magnitude [see Fig. 12(a), blue lines]. The probe beam attenuates SBS by reducing the density near the diagnostic volume. In the early phase, the lengths of plasma affected by the probe beam are less than 350 μm, and so the impact on SBS is weak (∼5% reduction in SBS intensity). As the perturbed region spreads out, more of the plasma is depressed, and the impact then becomes prominent. At 1.6 ns, the depressed region is ∼600 μm along the interaction beam, and hence the SBS light at the left boundary is attenuated by ∼65%, as shown in Fig. 12(b). The probe light reduces the average SBS reflectivity by about 50% within the interaction beam duration.

The corrections caused by the heating effects of the 300 μm-diameter interaction beam and the probe beam greatly affect the temporal behavior of the SBS, as shown in Fig. 13(a). The SBS light calculated based on the original simulated plasma parameters [blue line in Fig. 13(a)] mainly appears in the late phase of the pulse, with negligible signal in the early phase, which is quite different from the experimental result [black line in Fig. 13(a)]. The calculated average SBS reflectivity in this case is 6%, which is also larger than the experimental result (∼4%). After considering the correction (mainly density increases at the channel edges) caused by the 300 μm-spot interaction beam, the early SBS light grows to an appreciable intensity [green line in Fig. 13(a)], and the SBS reflectivity raises to ∼7%. The additional perturbation (mainly density drop) caused by the probe beam then attenuates the late SBS, resulting in comparable intensities of early and late SBS, and a smaller overall reflectivity of ∼3%, as shown by the red line in Fig. 13(a). With these corrections, the calculated SBS spectrum [see Fig. 13(c)] agrees very well with the experimental result [see Fig. 2(a)].

The calculated TS spectrum [see Fig. 13(d)] is also favorably consistent with the experimental result. Since the TS diagnostic volume is at the center of the interaction beam channel, the TS spectrum is not affected by the plasma parameter correction at the channel edges caused by the heating effect of the interaction beam. As a result, when the heating effect of the interaction beam is considered, the temporal behavior of the TS light [case B, green line in Fig. 13(b)] is identical with that from the uncorrected calculation case (case A, blue line). The electron density drop near the TS diagnostic volume caused by the probe beam reduces the amplitude of the SBS-driven IAW, leading to reductions in the intensity of TS light by ∼35% in the early phase (0–0.7 ns) and by ∼50% in the late phase (1.2–1.9 ns), respectively. Consequently, the contrast between the early and late components decreases, as shown by the red line in Fig. 13(b), which agrees better with the experimental result (black line).

The calculations also reveal a significant difference between the SBS light from the edges and from the center of the interaction beam, as shown in Fig. 14. The SBS light at the lower edge of the interaction beam (region I, red in Fig. 14) contributes ∼92% to the total energy, and ∼100% in the early component (0–0.7 ns). The SBS light near the center of the interaction beam (region II, green in Fig. 14) contributes ∼8% to the total energy, and ∼13% to the late component (1.2–1.9 ns). The SBS light at the upper edge of the interaction beam (region III, blue in Fig. 14) is very weak, contributing less than 1% to the total SBS energy. Such different contributions are primarily due to effective plasma lengths (with 0.01n_c ≤ n_e < 1n_c) and electron densities in the different regions. The effective plasma lengths of the three regions are respectively 2040 μm (I), 1890 μm (II), and 1720 μm (III). At 1.6 ns, the average electron densities in regions I, II, and III are 0.093n_c, 0.065n_c and 0.040n_c, respectively. The high density in region I is a result of compression around the hohlraum axis caused by the expansion of the hohlraum wall, while the low density in region III is due to rarefaction around the LEH caused by the outward flow.

It should be noted that the ion trapping effect is not taken into account in the analysis, because it is not an important factor here. For the typical parameters in our experiment, the threshold for ion trapping to cause SBS saturation is n_th/n_e ∼ 2.5%,23,36 whereas in the calculations, even at the moment with the strongest SBS, the IAW amplitude δn_e/n_e is less than 1.5%. Therefore, the ion trapping effect may not lead to SBS saturation, and neglecting it is acceptable.

The TS technique has been used in a gas-filled hohlraum for the first time to study the spatial growth of SBS by detecting the SBS-driven IAW. The time-resolved SBS and TS spectra obtained in the experiment have been analyzed with a steady-state code based on a ray-tracing model. The analysis indicates that ion–ion collisions may play an important role in suppressing SBS growth in the Au plasma, as a result of which the SBS excited in the gas-filled region dominates. In the early phase of the main pulse (0–0.7 ns), the heating effect of the interaction beam piles up plasma at its channel edges, which could be responsible to the early strong SBS. In the middle phase (0.7–1.2 ns), SBS is detuned by inhomogeneity of the plasma flow velocity, resulting in a negligible contribution. In the late phase (1.2–1.9 ns), the plasma flow velocity along the interaction beam is relatively uniform, which facilitates the growth of SBS. The presence of the TS probe beam in the experiment might mitigate SBS by perturbing the density distribution around the region overlapping with the interaction beam. This impact increases as the perturbed region spreads with time. The results of the experiment and analysis presented in this work will help comprehension of the SBS growth in gas-filled hohlraums, and could be valuable for future ignition target design.

Acknowledgment. This work is supported by the Natural Science Foundation of China (Grant Nos. 11905204, 11975215, 12105270, 12205272, 12205274, 12275032, 12275251, and 12035002), and the Laser Fusion Research Center Funds for Young Talents (Grant No. RCFPD3-2019-6).