Mitigating wall plasma expansion and enhancing x-ray emission by using multilayer gold films as hohlraum material

The multilayer films are ablated layer by layer, and the generated plasma is not uniform during ablation (figure 1(a)). As laser energy deposits near the critical density surface, the heated plasma is blown off from the critical density surface, pushing and compressing inner colder plasma. The compressed plasma generates a shock wave and the wave propagates toward the inner of multilayer target. There is a narrow region of dense plasma between critical density surface and the shock wave front (hereinafter referred to as dense band, figure 1(b)). It is optically thick for soft x-ray. The emitted x-ray from the dense band transports into the inner of the target and heats the inner layer films before the shock wave propagates there: the radiation heat wave is supersonic (figure 1(c)), which is similar to the case of foam gold but different from the case of solid gold (subsonic) [13]. The dense band divides the plasma into two parts: the laser irradiated region (corona) and the x-ray ablated region. In the x-ray ablated region, the films expand and generate plasma jets. The plasma jets coming from adjacent layers collide with each other, forming regions of high density and high temperature. Afterward, the plasma in these regions spreads out and makes second collisions. Plasma motion is local compression and rarefaction, and there is no global plasma motion such as spraying out or moving inward. The plasma jets retain periodic structure of multilayer films until they are compressed by the shock wave and afterward sprayed into the corona. In the laser irradiated region, the plasma state is similar to that of solid target, as long as the plasma fluid velocity is referred to the critical density surface. Since the critical density surface moves inward for multilayer target but outward for solid target, the coronal plasma for multilayer target is slightly thinner and sprays out at lower speed compared with solid target (figure 2).

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The movement of laser spot changes the spatial distribution of the radiation field in the hohlraum, and makes the symmetry control difficult. The laser energy depositing position changes as the critical density surface moves, which indicates the movement of laser spot (figure 3). For multilayer target, the laser spot move into the inner of the target and its speed can be controlled by changing the gaps between films: smaller gaps result in lower inward speed. This is similar to changing the density of foam target. By adjusting the gaps, the movement of laser spot can be reduced to minimum.

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Here we derive a model to quantify the speed of critical density surface for planar multilayer film target, which can be used to estimate the speed of laser spot. In general, the shock wave is always faster than (or close to) the critical density surface, which means that the dense band may become wider. However, in the condition mentioned below, the shock wave speed and the critical surface speed are very close to each other (figure 1(b)), and they are assumed to be the same (v). The fluid velocity of the plasma before shock wave is assumed to be 0, since the global averaged velocity of local plasma motion is 0 according to momentum conservation. The momentum conservation condition of the shock wave discontinuity gives:

$$\begin{equation}\rho {v}^{2}+{p}_{1}={\rho }_{2}{v}_{2}^{2}+{p}_{2}.\end{equation} \tag{ 1 }$$

Here p₁ is the pressure before the shock wave while p₂ is the pressure of shocked material; ρ is the equivalent density of the multilayer films while ρ₂ is the density of the shocked material; v₂ is the velocity of shocked material relative to the shock wave surface (v₂ ≪ v in our condition). According to the mass flux condition ρv = ρ₂ v₂, we have$\rho {v}^{2}\gg {\rho }_{2}{v}_{2}^{2}$. The p₁ is also negligible compared with ρv². Ignoring the minor items, we have

$$\begin{equation}\rho {v}^{2}={p}_{2}.\end{equation} \tag{ 2 }$$

The plasma pressure in the dense band is uniform. The p₂ is driven by the laser (laser ablating pressure). It indicates the thermal energy density of the plasma near the critical density surface and it depends on the laser power. Equation (2) gives the relation between the speed of critical density surface v and the equivalent density ρ for a given laser power. According to simulation result, p₂ is approximately proportional to the laser power P_L. Therefore, the speed of critical density surface is:

$$\begin{equation}v=\text{const}\cdot \sqrt{\frac{{P}_{\mathrm{L}}}{\rho }},\end{equation} \tag{ 3 }$$

where const = 2.04 × 10⁻¹⁰ ns⁻¹ g^1/2 cm^1/2 W^−1/2 (this value is derived from curve fitting in figure 4).

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The speed of critical density surface given by equation (3) is consistent with 1D simulation result within 10% relative error (for 3.5 × 10¹⁴ W cm⁻² ⩽ P_L ⩽ 1.4 × 10¹⁵ W cm⁻², 0.01 g cm⁻³ ⩽ ρ ⩽ 0.2g cm⁻³, and $2{\times}1{0}^{15}\enspace \mathrm{W}\enspace \mathrm{c}\mathrm{m}\enspace {\mathrm{g}}^{-1}{\leqslant}\frac{{P}_{\mathrm{L}}}{\rho }{\leqslant}1.4{\times}1{0}^{17}\enspace \mathrm{W}\enspace \mathrm{c}\mathrm{m}\enspace {\mathrm{g}}^{-1}$). Equation (3) can also be applied to foam gold for the density range mentioned above, but cannot be applied to solid gold, since the shock wave propagates significantly faster than the critical density surface in solid gold and there is no such narrow dense band in plasma.

For hohlraum made of solid gold, significant portion of laser energy is converted into the kinetic energy of the plasma that expands from the wall, which is useless for ignition. For multilayer film target, the plasma kinetic energy is converted into internal energy during plasma collisions, and the heated and compressed plasma generates strong x-ray emission. Therefore, the radiative flux is increased by collisions. Compared with solid target, the radiative flux of multilayer target is about 12% higher (figure 5(a)). Figure 5(b) shows that the plasma kinetic energy of multilayer target is lower than that of solid target, while the plasma internal energy and radiation energy is higher. As figure 1(a) shows, there are two types of plasma collision in multilayer target: (1) the collision between plasma jets; (2) the collision between shock wave front and plasma jet. For the later, the plasma in the dense band are compressed (and therefore heated) by the collision, and strong x-ray is emitted out of the target since the corona is optically thin. The radiative flux reaches a peak each time the shock wave front collides with a plasma jet. For the former, the collisions are always accompanied by rarefactions. The effects of compressing and rarefaction cancel out. Therefore, they contribute little to the enhancement of x-ray emission. For multilayer target with smaller gaps, the radiation peaks are flatter (figure 5(a)). This can be explained as follow. The plasma jets tend to be less nonuniform after several collisions (collisions of type 1). The radiation peaks become flatter while the shock wave front collides with less nonuniform plasma jets. Smaller gaps lead to more frequent collisions between plasma jets, resulting in flatter radiation peaks. In practice, the plasma collisions are not synchronized for the whole surface of the wall. The 3D effect cannot be simulated by 1D program. Therefore, the practical radiation peaks are expected to be flatter than the simulation result. Furthermore, plasma collisions increase only soft x-ray rather than M-band x-ray which is harmful to ignition.

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Since M-band x-ray is mainly emitted from the laser irradiated coronal plasma, the XSC result can provide information of coronal plasma motion and laser energy deposition. Figure 7(a) shows the XSC frame recorded in experiment. Two bright areas appear in the frame, respectively corresponding to the two laser spots on the two sides of the target: the upper bright area is the image of multilayer films while the lower is of solid gold. Figure 8 shows how the plasma motion effects on the XSC frame. The image of multilayer films is dim, and it resolves the multilayer structure: the alternate bright and dark bands. This is caused by the plasma generated from the target margin (non-spot region, figure 8(d)) as the laser spot drills into the multilayer films. The M-band x-ray serves as the backlight source for the imaging of the target margin which does not emit but absorbs M-band x-ray. Indeed, the plasma in spot region losses its multilayer structure when it is sprayed into the corona (see section 2.1). The alternate bright and dark bands reflect the multilayer structure of plasma in the target margin. In the early stage, the bright bands correspond to the vacuum gaps and the dark correspond to the films. The pattern changes along with time: the bright become dark in the later stage while the dark become bright. The evolution of the pattern reflects the evolution of the plasma in the margin region. The non-spot region is ablated by the x-ray emitted from the spot region. The plasma in the non-spot region retains multilayer structure and behaves similarity to the plasma underneath shock wave front (see section 2.1: x-ray ablated region in 1D simulation): the plasma coming from each film expands and collides with each other (figure 8(b): local plasma motion in the target margin). The local plasma density changes along with plasma compression and rarefaction, resulting in the change of the pattern. In the later stage, the contrast ratio between the bright bands and dark bands decreases, because the local plasma density becomes less nonuniform after plasma collisions. For comparison, figure 7(b) shows the simulated XSC result. The detailed structure of alternate bright and dark bands on the two frames appears slight difference. The laser pulses are not ideal square wave and the laser beams are not ideal cone in experiment. Therefore, the behavior of plasma collisions in experiment is slightly different from that in simulation, introducing the difference mentioned above. The image of solid gold resolves a sharp inner boundary, which indicates the movement of critical density surface (see 'critical density surface' marked in figure 7): the laser reflecting surface is not exactly but very close to the critical density surface for non-perpendicularly incident laser, due to the high gradient of plasma density near critical density surface. It moves outwards with speed 60 ± 10 μm ns⁻¹ for experimental result. The 2D simulation result is 37 μm ns⁻¹ while 1D simulation is 18 μm ns⁻¹. For multilayer films, the inner boundary is not as sharp as that of solid gold, because the critical density surface is concaved during ablation (refer to figure 8). It moves inwards with speed 184 ± 30 μm ns⁻¹ for experimental result. The 2D simulation result is 180 μm ns⁻¹ while 1D simulation is 245 μm ns⁻¹, and the equation (3) gives 248 μm ns⁻¹. The 1D simulation result (as well as the result of equation (3)) is significantly higher than the results of 2D simulation and experiment for multilayer target but significantly lower for solid target, because in 1D case the laser power density near critical density surface is higher: (1) the 45° laser beams diverge when the critical density surface departs from the focus plane of the laser beams; (2) the optical thickness for perpendicularly incident laser to propagate to reflecting surface is shorter. It is difficult to compare the coronal plasma density between multilayer films and solid gold by analyzing the XSC result because of the influence of the plasma in non-spot region. In conclusion, wall plasma expansion is mitigated by replacing solid gold with multilayer gold films.

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The emitted x-ray flux was measured by 3 FXRDs and 3 MXRDs mounted on different view angles. In order to compare the x-ray flux between multilayer films and solid gold, the measured x-ray flux is normalized by the practical laser energy, since the practical laser energy differs from shot to shot (by ∼10%), and the x-ray emission is strongly correlated to the laser energy. The FXRDs obtained consistent result: the x-ray (full energy range) flux of multilayer films is about 30% higher than that of solid gold (figures 9(a)–(c)). The measured M-band x-ray flux of multilayer films is also higher (figures 9(e)–(g)). Although the percentage (0%–28%) differs from shot to shot, from MXRD to MXRD, it is overall lower than that of FXRD, indicating that the M-band fraction is lower. The 2D simulation result of full energy range x-ray flux of multilayer films is 16% higher than that of solid gold at 0° (180°) view angle and 6% higher at 30° (150°) view angle (figure 9(d)). The difference between experiment result and simulation result may due to the asymmetry structure of the film holder which restrains the plasma from transverse expansion (in the direction parallel to the target plane) on the three close boundaries of the square multilayer films. The multilayer target is concaved during ablation, forming a half chamber (figure 8). The half chamber decreases the escaped x-ray energy and increases the radiation temperature. However, the target margin obscures the emitted x-ray in large angle (angle to the target normal), especially when laser spot area is not sufficient large. Therefore, the emitted x-ray is anisotropic and the above result of XRDs is guaranteed by the view angle of the XRDs. The peaks on radiative flux curve caused by plasma collision in 1D simulation results cannot be characterized on the measured x-ray flux curve: the noise of the detector overrides the radiation peaks which are expected to be flatter than the results of 1D simulation.

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