Observation of the colliding process of plasma jets in the double-cone ignition scheme using an x-ray streak camera

In recent years, various inertial confinement fusion research programs utilizing indirect and direct drive approaches have emerged.^1–7 Fusion ignition with an energy gain larger than one has been demonstrated at the National Ignition Facility (NIF).¹ However, the development of hydrodynamic instability and low coupling efficiency from lasers to fuels has created major challenges for robust ignition and high energy gain.^8–13 To achieve robust ignition and high gain fusion, the double-cone ignition (DCI) scheme^14–17 is proposed. The DCI scheme combines the advantages of fast ignition, direct-drive, and strong magnetic field guided ignition schemes. The compression and heating are decoupled in the DCI scheme. An optimized drive laser is used to implode the fuel shell within double gold cones to achieve quasi-isentropic compression.¹⁶ The high-density fuel is expelled from the cones at high speed and collides with each other, further improving the fuel temperature and density.¹⁷ A strong magnetic field is used to guide the fast electrons shooting into the colliding plasma to ignite the compressed fuel. The DCI scheme saves energy from the compression laser and ignition laser, thus, has the potential to achieve high-gain fusion.¹⁸ 

In the collision stage, the kinetic energy of the plasma is transformed into thermal energy, which leads to intense emission of x rays via bremsstrahlung radiation. The intensity of this spontaneous emission can reflect the temperature and density of the colliding plasma.^19,20 The duration and spatial size of collision plasma can indicate the effect of the plasma collision. The conditions of the colliding plasma strongly affect the subsequent fast ignition and fusion burning.^21,22 In addition, the formation and collision of high-density plasma jets created by the DCI scheme are also important to astrophysics. For example, in some young stellar objects (YSOs), active galactic nuclei (AGNs), and x-ray double stars, jets are very common and important phenomena.^23–25 Therefore, understanding the implosion dynamics of the DCI scheme is crucial for both inertial fusion and astrophysics.

In this study, a specialized experiment campaign was conducted to diagnose the evolution of implosion plasma. Temporally resolved self-emission signals were measured by an x-ray streak camera (XSC), enabling the observation of the changes in the spontaneous light with time. Due to the expense and complexity of manufacturing C₈D₈(CD) targets, the C₁₆H₁₄Cl₂ (CHCl) target was selected as a replacement in the experiment. Our experimental findings confirmed that the phenomena produced by CHCl and CD were generally similar, demonstrating the feasibility of using CHCl as a replacement in daily experiments.

Based on the experimental results of the 2021-R6 DCI experimental campaign on the Shenguang-II upgrade (SG-II UP) facility, the speed of the high-density jet could reach as high as 220 km/s. After collision, the x-ray self-emission was significantly enhanced, indicating a considerable increase in plasma temperature and density resulting from the collision. The duration and longitudinal space size of the collision plasma were 850 ps and 70 μm, respectively. These relatively large durations and space sizes of the colliding plasma provided good conditions for the subsequent fast heating with electrons generated by picosecond lasers.

This paper is organized as follows: Section II describes the experimental setup. Section III presents the experimental results and the analysis of the implosion dynamics. Section IV provides the preliminary two-dimensional simulation results of plasma implosion driven by lasers. Finally, a summary is given in Sec. V.

The experiments were carried out at the SG-II upgraded laser facility located at the Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences. As shown in Fig. 1, the target shells were placed in double gold cones with a wall thickness of 20 μm. A gold cone with a high opacity was selected to prevent the target from being heated by x rays emitted from the corona plasmas. The opening angle of the gold cone was 100°, coinciding with the laser configuration of the SG-II UP facility. The target was made of C₈D₈ (CD) or C₁₆H₁₄Cl₂ (CHCl) with an inner radius of 450 μm and a thickness of 45 μm. The initial densities of the CD target and CHCl target were 1.1 and 1.29 g/cc, respectively. The geometric center of the double-cone was centrally placed to coincide with the center of the target chamber.

As shown in Fig. 1(b), the laser pulse (R6-V1) was designed to obtain a quasi-isentropic compression by optimizing the strength and timing of the shocks via machine learning methods.¹⁶ The laser duration was approximately 4.7 ns. The picket prior to the main laser preheated the outer surface of the target and provided the first shock that determined the adiabat of the plasma. Notably, the experimental and designed waveforms exhibited remarkable similarity; thus, it was possible to more fully understand the experiments with the simulations. The laser operated at a wavelength of 351 nm and had an energy of 1.25 kJ per beam. The superimposed four laser beams were focused on the outer surface of the spherical shell on each side. Experiments using a single cone and double cones were conducted to study the implosion and collision of plasmas. Additionally, the geometric center of the double cone axis, placed vertically, was situated at the center of the target chamber.

The x-ray spontaneous light emitted by the plasma was captured using an XSC in conjunction with a pinhole, enabling the acquisition of the temporal evolution of the one-dimensional spatial profile.²⁶ The operational principles of the diagnostic system are shown in Fig. 2. In our experimental setup, an XSC Model 3200, fabricated by the Xi'an Institute of Optics and Precision Mechanics of the Chinese Academy of Sciences, was positioned on the horizontal plane of the target chamber for signal collection. The cathode material utilized in the XSC was cesium iodide (CsI), with a thickness of 150 nm, and it was deposited on an organic film. The vertically oriented slit used in the XSC had dimensions of 13 mm length and 100 μm width. Signal recording was accomplished using an optical scientific complementary metal–oxide semiconductor (sCOMS) camera with a resolution of 2048 × 2048 pixels. The full-time window was set to 21 ns to capture the temporal dynamics. The pinhole disk material consisted of 10 μm thick tantalum, with pinholes having an approximate diameter of 15 ± 1 μm. The configuration yielded a system magnification ratio of 5.5 times. The amplified image was directed through a slit on the XSC. Subsequently, the temporal evolution of the image along the vertical axis of the geometric center of the two gold cones was recorded, enabling the capture of the temporal evolution of the cone mouth and corona region in the one-dimensional spatial domain centered around the gold cone. The used setup provided a spatial resolution of 28 μm and a temporal resolution of 270 ps. The operating x-ray spectrum could be rather wide, ranging from 0.l to 10 keV and was determined by the filter and cathode materials (no filter was used in this experiment campaign).

Figure 3 shows the typical evolution process of spontaneous emission of CHCl plasma in a single cone experiment collected by XSC in shot 26. The horizontal axis represents time, and the vertical axis represents space. The backward-ejected ablated plasma and high-density imploding jet from the cone can be observed. The luminescence of the compressed plasma inside the cone cannot be observed because it is blocked by the gold cone wall. The plasma is ejected from the cone at approximately 975 ps after the laser is turned off, and the self-emission reaches its peak at approximately 1.2 ns. The self-emission intensity of the plasma ejection is 450. The imploding velocity of the jet is 220 ± 25 km/s.

Under the assumption of the same experimental conditions and targets, Z, A, ρ, $Γ B$, R, and $θ$ are fixed constants. Therefore, Eq. (3) indicates a positive correlation between bremsstrahlung emission P_br and laser power $P Laser$⁠; thus, the x-ray self-emission will align with the waveform of the laser power.

This relationship for self-emission and laser pulse power described by Eq. (3) is well supported by Fig. 3. The prepulse picket first ablates the target shell; thus, a small and weak spontaneous light is observed in the early stage. When the main pulse arrives, the plasma temperature in the coronal area sharply increases. When the coronal plasma expands into the vacuum, the density rapidly decreases, and the x-ray emission becomes increasingly weaker. After the laser is turned off, the intensity of spontaneous light begins to decline; therefore, the plasma temperature rapidly drops without laser heating. The compressed plasma continues to implode in the gold cone until it is ejected from the cone tip. The plasma temperature and density will increase during the implosion due to the shock heating and spherical convergent effect. Its temperature and density are sufficient to produce x-ray self-emission that can be captured by the XSC. The temperature of plasma ejected from the cone hole in this experiment can reach several hundred eV,^16,27 which can be well detected by the soft x-ray streak camera used in the experiments.

Two different materials, CD and CHCl, were used in the double-cone implosion experiments. Figure 4 shows the typical evolution process of self-emission signals during the collision of CHCl and CD plasma collected by XSC. Figure 4(a) shows the CHCl plasma results for shot 89, and the self-emission intensity of the colliding plasma was 1230. Figure 4(b) shows the results from the CD plasma for shot 94, and the self-emission intensity of the colliding plasma was 1980. In terms of laser energy, the 89th top four laser beams possessed an energy of 4824 J, while the bottom four lasers had an energy of 5041 J. For shot 94, the top four lasers had an energy of 4563 J, while the bottom four lasers had an energy of 4701 J. The conditions between the two experiments were similar; thus, the experimental results were generally similar.

In the experiment, as the plasma implodes along the inner wall of the gold cone, a small amount of gold is entrained into the colliding plasma. However, due to the smoothness of the cone's inner wall and the comparatively weak development of the Kelvin-Helmholtz instability, the amount of gold involved in the colliding plasma is extremely small. The maximum contribution of gold bremsstrahlung radiation is less than 1% of CD, which can be effectively disregarded.

As shown in Fig. 4, the self-emission of the plasma demonstrates a significant increase due to the collision. For the CHCl target, the self-emission brightness increases from 450 (shot 26, single cone) to 1230 (shot 89, double-cone). This result indicates a substantial increase in the density and temperature of the plasma due to the efficient conversion of the kinetic energy into internal energy. Notably, during the head-on collision between the two high-density plasma jets, a substantial deceleration occurs, leading to a significant reduction in velocity. This stagnation process has a duration of approximately 100 ps; this stagnation is comparable to or even shorter than the typical growth time of hydrodynamic instability. In addition, no central gas that stagnates the high-density plasmas as in the traditional central ignition scheme is present. As a result, the hydrodynamic instability of the colliding plasma is unable to develop and is effectively suppressed.

The coasting time (t_coast) is a crucial parameter in laser-driven fusion and exerts a significant influence on the implosion. In the ICF experiment, the t_coast is defined as the difference in bang-time and the time of end of the laser pulse, which is mainly used to characterize the implosion performance. In indirect-drive ICF, the bang-time is the time of peak neutron production, whereas in the DCI experiments without fast heating process, it represents the time of peak x-ray self-emission. In the DCI experiments, both the peak time of neutron yield and the peak time of x-ray self-emission are essentially simultaneous, occurring around the peak time of collision density. In indirect-drive ICF, reducing the coasting time has the advantage of increasing the implosion velocity and ablation pressure because of the reduced hohlraum cooling. Therefore, reducing the coasting time can lead to significant increases in stagnation pressure and fusion yield, which are critical for fusion.^27–29, t_coast is defined as the time interval between the time of plasma collision and when the laser power is turned off. In the NIF experiments, a shorter coasting time leads to an increased implosion velocity (V_imp) and higher ablation pressure (P_abl).^28–30 The stagnation pressure (P_stag) is the energy density of the stagnation plasma and can be expressed as P_stag ∼ P_abl ×  $M a 3,$²⁹ where M_a represents the Mach number of the fuel plasma. Consequently, increasing the implosion velocity and ablation pressure is helpful to increase the stagnation pressure. In our experiments, we specifically measured the coasting time for the CHCl and CD targets. The coasting time of CHCl and CD plasma was clearly different, which was observed in many experiments, as shown in Fig. 5. The average coasting time for CHCl was measured to be approximately 1.30 ns, while it was approximately 0.98 ns for CD. The coasting time of CD was 25% shorter than that of CHCl. The shorter coasting time observed for CD indicated a faster implosion speed compared to that of CHCl, resulting in higher temperature increases due to its implosion velocity. This discrepancy accounted for the stronger spontaneous radiation observed in CD colliding plasma compared to CHCl. Compared to the typical coasting time of ∼600 ps³⁰ in the NIF experiments, the coasting time in the 2021-R6 DCI campaign was slightly longer. In the future, the laser pulse could be optimized to reduce the coasting time and hopefully increase the stagnation pressure.

The full width at half maximum (FWHM) durations of CHCl and CD were measured to be 655 and 660 ps, respectively. Similarly, the FWHM longitudinal dimensions were found to be 70 and 60 μm for CHCl and CD, respectively, showing no significant difference. The lack of noticeable difference could be attributed to the close proximity of the two cones since they were separated by only 100 μm. Consequently, the longitudinal expansion of the colliding plasma was constrained, resulting in a limited impact on the overall observation. However, the transverse expansion size of the colliding plasma could vary due to differences in stagnated pressure.

In summary, the collision phenomena between CHCl and CD exhibited many similarities; however, differences in terms of coasting time and other specific details were observed. Notably, the duration time (>650 ps) for both CD and CHCl targets was sufficient for injecting a picosecond laser for subsequent fast heating to increase the plasma temperature.

To better understand the implosion dynamics of the plasmas, extensive simulations of the position and velocity of the imploding plasma are performed with the hydrodynamic code MULTI-2D, as shown in Fig. 6. MULTI-2D^31,32 solves radiation hydrodynamic equations in axial-symmetric geometry with unstructured grids. The laser is assumed to uniformly irradiate the target shell. The interaction between the laser and plasma is modeled by a ray-tracing method considering the inverse bremsstrahlung absorption and refraction. The arbitrary Lagrangian–Eulerian (ALE) module is activated to relax the grid distortion. The shell is made of CD or CHCl plastic as in the experiments. According to the symmetry of the target, only a quarter of the target is calculated. The grid is divided into 250 mesh in the radial direction and 40 mesh in the azimuthal grid. Since the Rayleigh–Taylor instability is not included in the simulations, the simulated plasma density would be slightly higher than the experimental plasma density. However, the overall implosion dynamics of the plasma should be the same in experiments.

The distributions of plasma density for the CD target at different times are presented in Fig. 6. The plasma shells are compressed and accelerated by the laser ablation pressure. After the drive laser is turned off at 4.7 ns, the plasma shells become thicker due to the effects of rarefaction. The main body of the imploding plasmas exits the gold cone at 5.55 ns with a density of approximately 27 g/cc and a velocity of 218 km/s. The plasma jets collide with each other, and a pair of reflected shock waves propagates outward at 5.95 ns. Since no central gas is present inside the imploding plasma shell and opening space is available for the collisions, the colliding plasma forms an isochoric structure with a maximum density greater than 100 g/cc.

The evolution of the mass-averaged temperature in the center and the areal density in the horizontal direction is plotted in Fig. 7. The peak temperatures during collision for the CD target and CHCl target are approximately 402 and 370 eV, respectively. The peak areal density of the CD target (0.37 g/cm²) is higher than that of the CHCl target (0.36 g/cm²). The coasting time is approximately 1.07 ns for the CD target and 1.35 ns for the CHCl target. The differences can be partially explained by the faster implosion of the CD target (∼218 km/s) than the CHCl target (∼206 km/s). When the implosion velocity is faster, the coasting time becomes shorter, and the Mach number (M_a = V/C_s), representing the plasma compressibility, becomes higher. In addition, the areal density reaches the peak value later than the temperature. This is caused by low-density precursor plasma in front of the high-density imploding plasma. The precursor plasma is generated when the shocks pass through the inner surface of the plastic shell.

Compared to the experimental results, the simulations can effectively capture the primary implosion dynamics in the DCI scheme. For example, the target shell can be accelerated to more than 200 km/s before collision, and the imploding kinetic energy is converted to thermal energy during the collision. In addition, the CD target implodes faster than the CHCl target because the CD target has a smaller initial density. However, some differences are also observed between the experimental and simulation results. For example, the coasting time in the simulations is slightly longer than that in the experiments. These differences potentially occur because the hydrodynamic instabilities and a multigroup radiation transport model are needed to better reproduce the experiments. In addition, the accuracy of the equation of state and opacity can also cause differences between the simulations and experiments. In the future, we will perform more accurate simulations to better understand the implosion dynamics of the plasma in the experiments.

In this study, the self-emission signals of one-dimensional space with respect to time obtained by an x-ray streak camera in the 2021-R6 DCI experimental campaign were analyzed. A high-density jet with a velocity of 220 ± 25 km/s could be created in the experiments. Notably, the self-emission intensity dramatically increased after the collision, indicating that the plasma density and temperature significantly increased during the collision. Furthermore, the coasting time of CHCl was observed to be later than that of CD, with respective durations of 1.30 and 0.98 ns. The collision between CHCl and CD plasma resulted in a collision plasma duration of 850 ps. While differences persisted in coasting time and other specific details, the overall implosion dynamics exhibited similarities between CHCl and CD. Hence, CHCl could be used as a viable alternative to CD in initial experiments, thereby reducing experimental complexity and cost. These experimental results were found to agree well with the two-dimensional fluid simulations. The extensive plasma, characterized by high density and temperature, has promise for subsequent fast electron heating experiments and astrophysics. However, further investigations are needed to refine our understanding of the physical processes involved during the implosion phase.

We are very grateful to the staff of the Shenguang Laser facility in Shanghai and the researchers at Xi'an Institute of Optics and Precision Mechanics for their support of the XSC. This work was supported by the National Key R&D Program of China (Grant No. 2022YFA1603203), the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant Nos. XDA25030700 and XDA25051200), the National Natural Science Foundation of China (Grant Nos. 12205185, 12325305, and 12135001), and the Shanghai Municipal Science and Technology Key Project (No. 22JC1401500).

The authors have no conflicts to disclose.

Zhengdong Liu and Fuyuan Wu contributed equally to this work.

Zhengdong Liu: Conceptualization (equal); Data curation (equal); Methodology (equal); Software (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Fuyuan Wu: Conceptualization (equal); Software (equal); Validation (equal); Writing – original draft (equal); Writing – review & editing (equal). Yapeng Zhang: Methodology (equal); Software (equal); Supervision (equal); Visualization (equal); Writing – review & editing (equal). Xiaohui Yuan: Methodology (equal); Resources (equal); Supervision (equal); Writing – review & editing (equal). Zhe Zhang: Methodology (equal); Resources (equal); Supervision (equal); Writing – review & editing (equal). Xiangyan Xu: Resources (equal); Software (equal). Yanhua Xue: Resources (equal); Software (equal). Jinshou Tian: Resources (equal); Software (equal). Jiayong Zhong: Conceptualization (equal); Methodology (equal); Resources (equal); Supervision (equal); Writing – review & editing (equal). Jie Zhang: Conceptualization (lead); Resources (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.