The effect of the shell mass on the hot spot pressure is investigated numerically for the Inertial Confinement Fusion (ICF) implosion. By using a simplified one-dimensional spherical model, it is found that there exists a critical shell mass that determines whether the hot spot can reach the maximum pressure. When the shell mass is larger than the critical mass, the hot spot pressure reaches the maximum value determined by the conventional scaling law $P_{hs}^{\text{max}}\propto \mathit{Mac}{h}^{3.2}$ (Mach is the Mach number of the imploding shell) and is independent of the shell mass. When the shell mass is smaller than the critical mass, the hot spot pressure decreases with decreasing shell mass. The dependence of the hot spot pressure on the shell mass can be uniformly described by an analytic formula. A similar effect of the shell mass on the hot spot pressure is also found in realistic ICF implosion for both direct drive and indirect drive. The conventional ICF implosions belong to the situation that the shell mass is smaller than the critical mass. The analytic formula can also be used to quantify the shell mass effect on the hot spot pressure for realistic ICF implosion when the effective shell mass is correctly taken into account.

中文翻译：

---

惯性约束聚变内爆中壳质量对热点压力的影响

对于惯性约束聚变（ICF）内爆，通过数值研究了壳质量对热点压力的影响。通过使用简化的一维球形模型，发现存在确定临界点是否可以达到最大压力的临界壳质量。当外壳质量大于临界质量时，热点压力达到常规缩放定律确定的最大值$P_{Hs}^{\text{最大限度}}\propto \mathit{苹果}{H}^{3.2}$（马赫数是内爆壳的马赫数），与壳质量无关。当壳质量小于临界质量时，热点压力会随着壳质量的降低而降低。热点压力对壳质量的依赖性可以通过解析公式统一描述。在直接驱动和间接驱动的实际ICF爆破中，也发现了壳质量对热点压力的类似影响。常规的ICF内爆属于壳体质量小于临界质量的情况。当正确考虑有效壳质量时，该解析公式还可用于量化壳质量对热点压力的影响，以实现实际的ICF内爆。