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Robustness of Key Parameters in Implosion of Multilayer Fuel Targets Against Change in Heavy-Ion Beam Parameters for Heavy-Ion Inertial Fusion
2026 年 21 巻 論文ID: 1404031
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2026 年 21 巻 論文ID: 1404031
This study investigated the effects of heavy-ion beam (HIB) pulse waveform and irradiation time on the implosion process of a multilayer fuel target designed for heavy-ion inertial fusion (HIF). Achieving high beam intensity, beam quality, and precise timing synchronization is challenging owing to the space charge effect. Multilayer fuel targets with low-density foam layers may alleviate these beam condition requirements and help achieve robust, uniform implosion. Using a 1-D spherical coordinate hydrodynamic model, this study evaluated implosion dynamics and variation using the coefficient of variation. Results showed that multilayer targets offer enhanced robustness against beam irradiation time variations compared to conventional designs. The Pb pusher configuration consistently demonstrated superior stability, attributed to the high density and atomic number of Lead that influences transport and hydrodynamics. The foam layer also plays a crucial role in mitigating the adverse effects of timing fluctuations. These findings suggest that multilayer fuel targets, particularly with a Pb pusher, provide a compelling advantage for practical applications by offering improved robustness and simplifying parameter optimization procedures compared to conventional HIF targets.
The process of energy deposition from the driver to the pellet in heavy-ion inertial fusion (HIF) has been extensively studied and is understood to follow the principles of classical physics [1]. Furthermore, heavy-ion beams (HIBs) offer flexibility to readily adjust energy deposition by modifying the ionic species and kinetic energy [2]. However, achieving high beam intensity, high beam quality, and precise timing synchronization for multibeam illumination presents a significant challenge owing to the impact of the space charge effect on HIBs [3]. Consequently, the stringent technical requirements for the ion source and accelerator supplying the HIB can potentially be relaxed by optimizing the beam conditions through meticulous design of the fuel target.
Furthermore, the potential of multilayer fuel targets with a low-density foam layer has been investigated to achieve robust and uniform implosion in HIF [4, 5]. Such targets are designed to promote robust and uniform implosion facilitated by radiation transport within the low-density foam layer. Moreover, such a target structure physically separates the ablation and pusher layers via the foam layer. In this configuration, the outer layer absorbs the HIBs and uniformly heats the inner fuel sphere via thermal radiation emitted from the outer shell. Alternatively, the inner layer may be imploded by plasma generated in the outer layer and expanding inwards, which can potentially enhance symmetry. Consequently, this configuration offers the potential to mitigate adverse effects stemming from the energy driver.
In this study, we numerically investigated the effects of HIB pulse waveform and irradiation time on the implosion process of multilayer fuel targets incorporating a foam layer.
We used a 1D spherical coordinate hydrodynamic model to solve the equations for compressible hydrodynamics coupled with the two-temperature model and radiation transport [6]. Figure 1 illustrates the fuel pellet structures investigated for HIF, with Figs. 1(a) and (b) depicting a multilayer target and conventional target, respectively. These fuel targets were comprised of a tamper layer, ablator layer, foam layer, pusher layer, and a fuel layer [7]. The mass densities for the tamper, ablator, foam, pusher, and fuel layers were 11.3, 2.69, 0.0269, 2.69, and 0.25 g/cm3, respectively. The pusher radius was set as 2.48 mm for the Al pusher and 2.43 mm for the Pb pusher to maintain consistent total mass and beam deposition profiles.
Figure 2 presents the input pulse waveforms of the HIBs utilized in this study. Specifically, a Pb ion beam species was employed, with a power of 6 TW for the foot pulse (Region I) and 320 TW for the main pulse (Region III). The total beam energy was 8.0 MJ, and the kinetic energy of the Pb ions was 8.0 GeV. The target and HIB parameters were carefully selected to ensure that the beam particles deposited their energy primarily within the tamper and ablator layers. The stopping range of the 8.0 GeV Pb ions from the outer surface of the target was calculated to be 0.35 mm. The beam irradiation time was controlled by adjusting the pulse widths of the foot-pulse (Region I) and ramping (Region II) phases. The total irradiation energy was maintained constant by calibrating the main pulse (Region III) width.
The effects of different irradiation schemes on the implosion characteristics were evaluated. Figure 3 shows the simulation results using the I + II + III irradiation scheme (I = 20, II = 4, III = 22.4 ns at each region), and Fig. 4 shows the results using only the III irradiation scheme (I = 0, II = 0, III = 24.9 ns). The results for multilayer fuel targets (Al Pusher and Pb Pusher) and a conventional fuel target (denoted “Without Foam” in the figure for clarity) were compared using Figs. 3 and 4. Within each condition, the results are indicated from left to right for the Al pusher, Pb pusher, and conventional (Without Foam) target, respectively. Figures 3 and 4(a)–(c) depict the radial position of each layer as a function of the normalized time (time/void close time), where the vertical axis represents the radial coordinate. Figures 3 and 4(d)–(f) in each subplot illustrate the temporal evolution of various key physical quantities as a function of the normalized time (time/void close time).
The “void close time” is defined as the time at which the central void within the pellet collapses, signifying the point of maximum fuel compression. Typically, initial fuel pellets in inertial confinement fusion contain a central void. As the implosion progresses, this void region shrinks and ultimately collapses at maximum compression. Normalizing the time axis by the void close time facilitates the comparison of simulation results across varying implosion timescales. As depicted in (a)–(c) in Figs. 3 and 4, the radii of the ablator, pusher, and fuel layers gradually decrease over time. This signifies the process where the ablator layer is vaporized and ablated owing to beam irradiation, and the resulting reaction force compresses the inner pusher and fuel layers. Notably, a rapid reduction in the fuel radius is observed around time/void close time = 1. This signifies the moment of peak compression and correlates strongly with the peak behavior of the compression ratio and ion temperature observed in (d)–(f) in Figs. 3 and 4. Figures 3(d)–(f) and 4(d)–(f) display the temporal evolution of the compression ratio, ion temperature (in keV), and maximum implosion velocity (in km/s) against the horizontal axis, labeled “Time/Void close time”.
In Figs. 3 and 4, the I + II + III irradiation scheme is designed to control the initial phases of the implosion using the foot pulse (Region I) and ramp pulse (Region II), to facilitate efficient high compression during the main pulse (Region III). However, the data reveals that, for multilayer fuel targets, the III-only irradiation scheme yields higher compression ratios. This suggests that, for multilayer targets, the intense irradiation delivered solely by the main pulse is sufficient to achieve substantial compression. Consequently, the energy delivered during the foot and ramp pulses may not contribute significantly to the final compression efficiency, which is directly reflected by the achieved compression ratio, considering the constant total input energy. Indeed, the foot and ramp pulses might even exert a detrimental effect by causing excessive preheating of the ablator layer, potentially hindering the compression efficiency achieved by the subsequent main pulse and compromising the radiation confinement capability of the foam layer. In other words, the I + II + III irradiation scheme appears suboptimal from an energy efficiency perspective for multilayer fuel targets, suggesting that further detailed investigation is warranted to fully clarify this aspect.
Conversely, the disparity in performance between the I + II + III and III-only irradiation schemes is comparatively more pronounced for conventional fuel targets (those without a foam layer). This indicates that the main pulse alone is insufficient to achieve adequate compression in these conventional target configurations. Therefore, the initial implosion shaping provided by the foot and ramp pulses plays a crucial role in achieving the desired final compression in a conventional target.
Figure 5 illustrates the peak performance of key implosion parameters as a function of the HIB irradiation time for different target configurations: the multilayer targets with Al and Pb pushers, and the conventional target (denoted as “Without Foam” for consistency). The evaluated parameters are defined as follows: (a) compression ratio, representing the degree of fuel volume reduction, which achieves its maximum value at the void close time. (b) Areal density, defined as the integrated mass density along the radial coordinate (
By contrast, conventional targets exhibited distinct temporal responses to varying irradiation times. The compression ratio and areal density displayed a pulse-like behavior, reaching maximum values at approximately 45 ns irradiation time. The increase towards these peak values was relatively gradual, whereas the subsequent decline was considerably steeper. The maximum ion temperature generally exhibited a decreasing trend with longer irradiation times. However, a transient increase was noticeable in the 40–50 ns range, coinciding with the time of peak compression ratio and areal density. The maximum implosion velocity remained remarkably stable across the investigated range of irradiation times, exhibiting minimal temporal variation.
Delving deeper into the interplay between these physical quantities, the striking similarity in the temporal behavior of the compression ratio and areal density strongly suggests a tight correlation. This fundamental relationship is rooted in the physics of compression, where achieving a higher volumetric compression inherently leads to an increase in areal density. Furthermore, the transient increase in the maximum ion temperature observed around the time of peak compression and areal density hints at a potential mechanism: maximizing fuel compression and areal density might effectively mitigate energy dissipation processes during implosion. The relative insensitivity of the maximum implosion velocity to variations in irradiation time may indicate that it is a physical quantity largely independent of the specifics of the HIB irradiation time and pulse shaping.
These findings underscore the profound impact of HIB irradiation conditions, particularly the irradiation time, on the resulting compression performance. The pulse-like response of the compression ratio and areal density observed in conventional targets highlights the potential for achieving peak performance through precise control of the HIB irradiation timing. However, this behavior also implies a critical vulnerability: even minor deviations from the optimal irradiation time can lead to significant performance degradation, thereby emphasizing the crucial need for stringent control. Therefore, dedicated parameter optimization efforts are essential to identify the optimal irradiation time for consistently achieving high compression and areal density in conventional targets.
Conversely, the monotonic decline observed in multilayer fuel targets, while seemingly indicating reduced peak performance at longer irradiation times, offers a different perspective. This characteristic suggests that relatively high-performance levels can still be attained even with shorter irradiation durations. Moreover, the reduced sensitivity of the physical quantities to variations in irradiation time for multilayer targets, compared to conventional designs, implies a more gradual performance degradation in the presence of timing errors. In this regard, multilayer fuel targets demonstrate enhanced robustness against variations in beam irradiation time, potentially simplifying parameter optimization procedures. The ability to maintain a reasonable performance level even with less stringent irradiation time control, coupled with the potential for shorter irradiation times, presents a compelling advantage for practical applications. Furthermore, based on the results presented in Fig. 5, we evaluated the variation in key implosion parameters as a function of the beam irradiation time using the coefficient of variation (CV). The CV is a statistical measure that quantifies the relative dispersion of data points around the mean value within a data series. It is calculated as the ratio of the standard deviation (σ) to the mean value (μ) as follows:
| (1) |
A lower CV value indicates greater stability and less variability in the data. The calculated CV values for each physical quantity, obtained from simulations conducted with varying beam irradiation times, are presented in Table 1.
| CV | Al pusher | Pb pusher | Without Foam |
|---|---|---|---|
| Compression ratio | 0.274 | 0.245 | 0.626 |
| Areal density | 0.304 | 0.207 | 0.376 |
| Ion temperature | 0.0551 | 0.0497 | 0.338 |
| Implosion velocity | 0.0544 | 0.0207 | 0.0647 |
A comparative analysis of the calculated CV values across different target configurations revealed consistent trends regarding the stability of key implosion parameters against variations in the beam irradiation time. Notably, a consistent trend emerged across all physical quantities: the Pb pusher configuration consistently exhibited the lowest CV values, whereas the configuration without a foam layer consistently showed the highest CV values. Furthermore, the disparities in CV values among the target configurations were more pronounced for the compression ratio and areal density when compared to the ion temperature and maximum implosion velocity.
Specifically, the configuration employing a Pb pusher consistently demonstrated superior stability across all investigated parameters, including the compression ratio, areal density, ion temperature, and maximum implosion velocity. This enhanced stability is attributed to the inherent material properties of Pb, particularly its high density and atomic number. These properties significantly influence both the radiation transport and hydrodynamic behavior, thereby reducing the system’s sensitivity to variations in beam timing. In particular, the high opacity of Pb, in all likelihood, contributes to maintaining the uniformity of the radiation field incident on the inner layers, thereby promoting a more stable implosion.
Conversely, the configuration lacking a foam layer exhibited markedly elevated CV values across all parameters, indicating a pronounced sensitivity to fluctuations in the beam irradiation time. This observation strongly suggests that the foam layer plays a crucial role in modulating energy and momentum transport processes, potentially mitigating the adverse effects stemming from variations in beam timing.
Interestingly, the Al pusher configuration displayed intermediate levels of stability, positioned between the Pb pusher and foam-layer-free configurations. Although not attaining the same level of stability as the Pb pusher, it offered improved stability when compared to the configuration without a foam layer. Notably, the CV values associated with the Al pusher, while intermediate, tended to be closer to those obtained for the Pb pusher. This suggests a potential correlation between the pusher material in multilayer fuel targets and a characteristic stability profile. Further investigation is warranted to fully elucidate this aspect.
In this study, we discussed the implosion process of multilayered fuel targets using HIBs based on 1-D hydrodynamic simulations. The primary objective was to elucidate the effects of the HIB pulse waveform and irradiation time on the implosion performance and stability, particularly in comparison with conventional target design.
Our investigations revealed significant differences in the response of implosion parameters to variations in HIB irradiation conditions between multilayer and conventional targets. Conventional targets exhibited a sensitive, pulse-like dependence of the compression ratio and areal density on irradiation time, demanding stringent timing control for peak performance, and multilayer targets showed a more gradual, monotonic decline in performance with increasing irradiation time. This characteristic of multilayer targets suggests that comparatively high performance levels can be achieved even with shorter irradiation durations, thus implying a more forgiving response to timing errors.
Quantitatively, the analysis using the CV clearly demonstrated the enhanced robustness of multilayer fuel targets against beam irradiation time fluctuations. Specifically, the configuration employing a Pb pusher exhibited the lowest CV values for all assessed parameters, highlighting its superior stability. This enhanced stability is attributed to the material properties of Pb such as high density and atomic number, which favorably influence radiation transport and hydrodynamic stability. Furthermore, the presence of the foam layer appears to be crucial in modulating energy and momentum transport, thereby mitigating the adverse effects of timing variations observed in targets without a foam layer.
In conclusion, multilayer fuel targets offer a compelling pathway towards more robust and reliable implosion in HIF. Their reduced sensitivity to beam timing variations, particularly when utilizing a high-Z pusher material such as Pb, represents a significant advantage over conventional designs, potentially simplifying beam delivery requirements and enhancing the feasibility of achieving stable, high-gain implosions in practical HIF systems. Further optimization of multilayer target design and irradiation schemes is warranted to fully exploit their potential.
