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Influence of radiative cooling effect on the plasma filamentations in the interaction of high-power laser with planar targets

Zhao Xin Yang Xiao-Hu Zhang Guo-Bo Ma Yan-Yun Liu Yan-Peng Yu Ming-Yang

Zhao Xin, Yang Xiao-Hu, Zhang Guo-Bo, Ma Yan-Yun, Liu Yan-Peng, Yu Ming-Yang. Influence of radiative cooling effect on the plasma filamentations in the interaction of high-power laser with planar targets. Acta Phys. Sin., 2022, 71(23): 235202. doi: 10.7498/aps.71.20220870
Citation: Zhao Xin, Yang Xiao-Hu, Zhang Guo-Bo, Ma Yan-Yun, Liu Yan-Peng, Yu Ming-Yang. Influence of radiative cooling effect on the plasma filamentations in the interaction of high-power laser with planar targets. Acta Phys. Sin., 2022, 71(23): 235202. doi: 10.7498/aps.71.20220870

Influence of radiative cooling effect on the plasma filamentations in the interaction of high-power laser with planar targets

Zhao Xin, Yang Xiao-Hu, Zhang Guo-Bo, Ma Yan-Yun, Liu Yan-Peng, Yu Ming-Yang
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  • Interaction of high-power laser with planar target is studied by using radiation-hydrodynamics simulation. When the laser interacts with the tungsten planar target, the laser energy deposition is uneven due to thermal filamentation instability and other reasons, and density fluctuations will appear in the front of the plasma, resulting in obvious plasma filamentation in the later stage. The researches of four materials, i.e. aluminum, copper, tungsten and gold, show that in the high-Z material tungsten and gold, due to the strong radiative cooling effect, the filamentation phenomena of the density distribution, electron temperature distribution and pressure distribution obviously occur. The order of magnitude of filamentous plasma density is different from that of the surrounding plasma. The filamentation phenomenon is closely related to the non-uniform energy deposition of the laser and the radiative cooling effect, although the ray beam will cause inhomogeneity of the laser irradiation to a certain extent, this is not the main reason for the filamentation phenomenon observed in this paper. Owing to refraction, reflection and the thermal filamentation instability when the laser is transmitted in the ablation plasma, the laser energy is deposited unevenly, which generates instability seeds in the early stage of plasma formation. The radiative cooling effect then amplifies this instability seeds, creating a radiative cooling instability that eventually results in a filamentous distribution of physical quantities such as plasma density, temperature, and pressure. This filamentation phenomenon destroys the uniformity of the plasma to a certain extent, and lays the seeds for the growth of fluid instability, which will seriously affect fusion-related research. It is shown that radiative cooling is crucial to the filamentation phenomenon, which causes uneven distribution of the plasma pressure during the evolution of the plasma, thereby affecting its transverse motion and enhancing the density fluctuation. After the laser irradiation ends, the density fluctuation gradually develops into filamentations. We also find that the clear filamentation occurs only for high-Z materials like tungsten and gold, but not for the moderate-Z materials like aluminum and copper. This can be attributed to the fact that radiative cooling is stronger for the high-Z materials. Studying the filamentation effect in laser-irradiated planar targets can contribute to understanding the instability in laser plasma, and then suppressing this instability and improving the gain of fusion. The results here can thus be of reference significance to the research of laser fusion, laboratory astrophysics, and other applications of intense-laserdriving.
      PACS:
      52.50.Jm(Plasma production and heating by laser beams (laser-foil, laser-cluster, etc.))
      52.38.Hb(Self-focussing, channeling, and filamentation in plasmas)
      52.65.-y(Plasma simulation)
      Corresponding author: Yang Xiao-Hu, xhyang@nudt.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 12175309, 11775305, 11975308, 12005297), the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDA25050200), the State Key Laboratory of Laser Interaction with Matter, China (Grant No. SKLLIM1908), the Natural Science Foundation of Hunan Province, China (Grant No. CX20190001), and the Financial Support from Fund for NUDT Young Innovator Awards, China (Grant No. 20180104).

    在激光器问世后, 苏联科学家巴索夫[1]和我国科学家王淦昌先生[2]分别独立提出用激光辐照DT靶丸产生热核聚变的设想, Nuckolls等[3]提出利用强激光烧蚀并压缩球形靶丸, 最终在球形内爆中达到劳森判据的条件, 进而实现点火. 高功率激光辐照平面靶可以用来研究激光烧蚀靶丸的情形, 也可以研究中子源的产生[4-6]、烧蚀后等离子体的流体力学行为[7,8]及在等离子体中自生电磁场[9,10]等物理过程. 在激光烧蚀等离子体中由于流体不稳定性的发展, 会出现成丝现象, 但目前对等离子体成丝的产生、发展、演化等的了解还有待加强.

    成丝现象在等离子体物理中比较常见, 研究较多的有激光自聚焦成丝[11-15]、电子束成丝[16]和电磁场成丝[17-19]等. Giulietti等[11]以及Watkins和Kingham[12]利用随机相位板和诱导空间非相干技术对激光进行平滑处理, 结果表明这两种技术通过改善焦斑均匀性降低了成丝水平. 进一步, Afsharrad等[13]研究了磁化热导率对低密度等离子体中激光成丝的影响, 结果表明磁化会导致成丝现象的局部加强. 2003年, 张家泰等[14]研究了部分离化等离子体中的成丝不稳定性, 通过理论计算表明部分电离等离子体中原子成丝不稳定性显著高于相对论成丝不稳定性. 李玉同等[15]采用光学阴影法和散射光成像研究了等离子体中有质动力引起的成丝不稳定性, 结果表明有质动力引起的密度涨落和激光强度的非均匀性成正比, 且成丝不稳定性可能导致密度分布演化成湍流. 电磁场成丝方面, Séguin等[17]利用单能质子成像技术研究了冕区等离子体中丰富的电磁场结构, 结果表明激光与等离子体作用后在冕区出现的电磁场在激光技术后依旧存在, 且可能对驱动效率和流体力学不稳定性产生重大影响. Fox等[18]利用质子成像法研究对撞等离子体中Weibel不稳定性产生的丝状电磁场, 结果表明成像结果与Weibel不稳定性理论和粒子模拟结果相符合. 实验上, 从20世纪开始科学家观测到激光辐照平面靶时等离子体冕区存在丝状射流[20-22], 这种等离子体成丝的行为引起了人们重视, 通过研究, 认为这是激光焦斑强度的不均匀分布造成的[23], 并提出了诱导激光非相干性、光谱色散平滑和随机相位板等匀化激光强度分布的方法来改善激光辐照的均匀性[24,25], 取得了一定效果. 然而, 人们对流体密度成丝现象研究较少, 而物质成丝与聚变中不稳定性密切相关, 故有必要对此现象进行研究.

    本文研究了强度在1014 W/cm2左右纳秒级别长脉冲激光辐照铝、铜、钨和金等4种平面靶的过程, 在分析激光烧蚀后等离子体的物理性质时发现了明显的等离子体成丝现象, 在横向上出现了强烈的密度涨落, 进一步研究发现电子温度、压强等物理量也出现了类似的成丝现象. 研究结果表明, 成丝现象与辐射冷却、靶材料、激光均匀性等因素相关, 激光能量沉积不均匀会导致等离子体中出现密度涨落, 而靶材料原子序数的不同导致辐射冷却效应存在差异, 进一步导致等离子体演化中出现不同程度的成丝现象. 研究等离子体中成丝现象有利于对激光驱动等离子体不稳定性的深入理解, 抑制成丝导致的流体密度涨落则有助于控制不稳定性的发展, 在一定程度上提升聚变点火水平.

    本文基于辐射流体程序FLASH开展研究, FLASH是多物理、高度可扩展的并行有限体积欧拉代码和框架, 其功能包括自适应网格细化、多个流体力学和磁流体力学解算器, 以及使用HYPRE库和激光能量沉积进行扩散的隐式解算器, FLASH使用多温度状态方程和多组分不透明度[26], 多用于高能量密度物理问题的模拟, 尤其是天体物理和核聚变领域.

    模拟使用单流体模型, 不区分电子和离子的运动方程, 只描述统一的运动. 在电子温度Tele、离子温度Tion和辐射温度Trad不相等时, 需要对这三种温度分别计算, 称为三温模型.

    描述辐射流体演化的方程组是:

    ρt+ρv=0, (1)
    ρvt+(ρvv)+Ptot=0. (2)

    考虑三温模型, 分别描述电子、离子和辐射场比内能的变化[27]:

    t(ρeele)+(ρeelev)+Pelev=ρcv,eleτei(TionTele)qele+QabsQemis+Qlas , (3)
    t(ρeion)+(ρeionv)+Pionv=ρcv,eleτei(TeleTion), (4)
    t(ρerad)+(ρeradv)+Pradv=qrad Qabs+Qemis, (5)

    其中, ρ是等离子体质量密度; eele, eion, erad分别是电子、离子、辐射比内能, 即单位质量电子、离子的内能以及单位质量物质辐射场的能量; 总压力Ptot是电子压力、离子压力和辐射压力之和, Pele, Pion, Prad分别是电子、离子、辐射压力; qele , qrad分别是电子热流和辐射热流; v是流体速度; cv,ele是电子比热容; τei是电子-离子碰撞能量交换弛豫时间; Qlas是由于激光加热产生的能量源, Qabs表示由于总辐射吸收而增加的电子内能, Qemis表示由于总辐射发射而减少的电子内能.

    激光能量吸收的主要机制是碰撞吸收, 电子通过逆韧致吸收过程从激光获得能量, 然后电子通过与离子碰撞将能量传递给离子. 高温等离子体的辐射主要是韧致辐射、康普顿散射等过程, 即辐射发生在电子上, 而不是发生在离子上, 故方程中考虑辐射的项只出现在电子能量方程中, 不会出现在离子能量方程中. 利用多群扩散理论描述辐射效应, 通过对能量细致分群可以更精确地计算辐射的输运过程. 本文使用基于托马斯-费米模型的QEOS[28]状态方程参数和平均原子模型的SNOP[29]辐射不透明度参数, 通过使用表格化状态方程和不透明度数据在程序中调用, 从而使上述方程组闭合.

    针对上海光机所的神光II升级装置的激光参数[30], 本文的研究模型主要是纳秒级红外激光与百微米级固体靶相互作用的模型. 该激光基频为1.053 μm, 波形设置为矩形脉冲, 宽度为5 ns, 上升沿与下降沿均为100 ps, 激光能量设定为1500 J, 激光光强在焦斑内为高斯分布, 根据不同的焦斑尺寸调整激光的功率密度. 尽管通过光束匀滑等技术[31-33]可以提升焦斑的辐照均匀性, 但由于激光在等离子体中的折射与反射以及热成丝不稳定性[34]的作用, 等离子中的能量沉积是不均匀的, 从而可能导致流体不稳定性的增长, 最终出现等离子体的成丝现象.

    首先研究激光与钨靶作用, 如图1所示, 其中黄色部分代表固体靶材料, 即钨物质, 激光从靶面正下方垂直辐照到固体靶上, 其中蓝色氦气用以模拟10–3 Pa真空环境, 密度设为10–11 g/cm3, 固体靶厚度为300 μm, 初始时刻固体靶和材料温度均设置为290 K, 采用二维(2D)柱坐标模拟, 对称轴R = 0处采用反射边界条件, 其余设为流出边界条件, 靶半径为1000 μm, 便于统计激光辐照后对物质的烧蚀及等离子体的演化.

    图 1 激光打靶模型. 其中黄色区域为钨靶, 蓝色区域为氦气, 蓝色中间区域为射线束描述的激光功率分布, 激光由下往上入射到钨靶\r\nFig. 1. Schematics of the laser-target interaction. The yellow region is the tungsten target, the blue region is the background helium, and the middle region is the distribution of  laser power. The laser is incident on the tungsten target from bottom to top.
    图 1  激光打靶模型. 其中黄色区域为钨靶, 蓝色区域为氦气, 蓝色中间区域为射线束描述的激光功率分布, 激光由下往上入射到钨靶
    Fig. 1.  Schematics of the laser-target interaction. The yellow region is the tungsten target, the blue region is the background helium, and the middle region is the distribution of laser power. The laser is incident on the tungsten target from bottom to top.

    模拟中激光光束由大量射线组成, 利用射线追踪方法计算激光能量沉积, 射线传输路径根据网格局部折射率进行追踪, 激光射线沉积在网格中的功率根据逆韧致吸收功率进行计算, 取决于局域电子数密度和电子温度. 虽然使用2D柱坐标系模拟激光辐照平面靶的过程, 但是激光能量沉积在三维(3D)笛卡尔坐标系中模拟. 在3D下激光焦斑为半径300 μm的圆形, 模拟中由小的正方形网格去填充圆形焦斑, 根据特定算法调整正方形网格大小使圆形内正方形数目最接近射线束4096, 正方形网格即为射线形状, 在本文算例中正方形射线边长约为8 μm. 模拟中采用4阶自适应网格, 网格大小分别为1.5625, 3.125, 6.25和10 μm, 射线宽度与网格大小可比拟. 射线束会在一定程度引起激光辐照的不均匀性, 但从下面的研究结果可以看出, 这种不均匀性不是本文观察到的成丝现象的主要原因. 模拟中时间步长根据流体计算的稳定性条件, 从初始时刻的1016 s增加到最大1012 s, 典型的时间步长在1013 s左右, 远远小于模拟时间10 ns.

    当激光作用于靶时, 能量主要沉积在临界密度面附近, 图2(a)(d)中黑线给出临界密度面的位置, 针对本文激光波长1.053 μm, 临界密度nc=9.921×1020 g/cm3. 图2(a)图2(b)显示激光能量沉积最多到达临界密度面, 且能量沉积是不均匀的, 这造成了临界面附近最初始的密度涨落. 图2(c)图2(d)给出7和8 ns时对数密度分布图, 图中显示出明显的密度成丝现象, 即密度在横向上出现明暗相间的条纹, 二维密度结果给出在激光结束后等离子体向外运动过程中水平方向出现了明显的密度涨落, 图2(e)图2(f)进一步给出了7和8 ns时Z值为500 μm处水平方向的密度线分布, 密度线分布显示等离子体密度在103101g/cm3之间, 且横向出现了严重的密度涨落, 同一水平线上密度相差约2个数量级, 这体现了二维结果中密度成丝的现象.

    图 2 L2激光辐照钨靶的能量沉积及密度分布 t = 4 ns (a), t = 5 ns (b) 时密度背景上的能量沉积, 红色表示射线束的能量沉积; (c) t = 7 ns, (d) t = 8 ns时二维密度分布; (e) t = 7 ns , (f) t = 8 ns时Z = 500 μm处密度线分布\r\nFig. 2. Energy deposition and density distributions of L2 laser irradiating the tungsten target: Energy deposition on the density background at t = 4 ns (a) and 5 ns (b), the red color for the energy deposition of the ray beam; 2D density distribution at t = 7 ns (c) and 8 ns (d); the profile of density at Z = 500  μm along R direction at t = 7 ns (e) and 8 ns (f).
    图 2  L2激光辐照钨靶的能量沉积及密度分布 t = 4 ns (a), t = 5 ns (b) 时密度背景上的能量沉积, 红色表示射线束的能量沉积; (c) t = 7 ns, (d) t = 8 ns时二维密度分布; (e) t = 7 ns , (f) t = 8 ns时Z = 500 μm处密度线分布
    Fig. 2.  Energy deposition and density distributions of L2 laser irradiating the tungsten target: Energy deposition on the density background at t = 4 ns (a) and 5 ns (b), the red color for the energy deposition of the ray beam; 2D density distribution at t = 7 ns (c) and 8 ns (d); the profile of density at Z = 500 μm along R direction at t = 7 ns (e) and 8 ns (f).

    在早期研究激光打靶的实验中, 激光焦斑在空间上的均匀性较差, 导致打靶时出现“射流”状结构[23], 后来提出了光束匀滑技术来改进激光焦斑均匀性, 对抑制丝状射流出现有一定效果. 本文中, 直径600 μm的圆形焦斑用4096束射线来模拟, 在激光辐照靶面的初始阶段, 由于激光在等离子体中的反射和折射以及热成丝不稳定性等作用, 导致激光能量沉积不均匀, 从而同一水平线位置的等离子体出现密度涨落, 这种不可避免的密度涨落在激光作用时期保持着有限的水平, 而激光作用结束后, 随着辐射流体动力学的演化, 密度涨落越来越大, 进而形成了密度的丝状分布.

    为了分析成丝的具体原因, 下面给出模拟中电子的温度分布. 在激光作用期间, 烧蚀等离子体温度在2—3 keV左右, 在5 ns激光辐照结束后, 等离子体温度快速下降, 在百eV的量级. 如图3所示, 在激光辐照钨靶的模拟中, 观察到了明显的电子温度成丝的现象. 图3(a)图3(b)给出了7和8 ns时的二维电子温度分布, 电子温度最高达到60 eV左右, 在二维图中出现电子温度丝状分布. 进一步, 图3(c)图3(d)给出7和8 ns时Z = 500 μm处电子温度的线分布, 在丝状分布附近电子温度高于周围. 模拟中电子温度是依附于物质而存在的物理量, 故电子温度成丝的位置和密度成丝的位置相同, 在密度涨落附近, 电子温度表现出成丝的特性. 电子在聚变中是重要的传递能量的物质, 在激光辐照平面靶中电子温度出现成丝现象, 显示了成丝区域电子温度较高的特征, 这可能会影响等离子体中能量传输的过程.

    图 3 L2激光辐照钨靶的电子温度分布 t = 7 ns (a)和t = 8 ns (b) 时二维电子温度分布; t = 7 ns (c) 和t = 8 ns (d) 时 Z = 500 μm处电子温度线分布\r\nFig. 3. Electron temperature distribution for L2 laser irradiating the tungsten target: 2D electron temperature distribution at t = 7 ns (a) and 8 ns (b); (c), (d) profile of electron temperature at Z = 500 μm along the R direction at t = 7 ns (c) and 8 ns (d).
    图 3  L2激光辐照钨靶的电子温度分布 t = 7 ns (a)和t = 8 ns (b) 时二维电子温度分布; t = 7 ns (c) 和t = 8 ns (d) 时 Z = 500 μm处电子温度线分布
    Fig. 3.  Electron temperature distribution for L2 laser irradiating the tungsten target: 2D electron temperature distribution at t = 7 ns (a) and 8 ns (b); (c), (d) profile of electron temperature at Z = 500 μm along the R direction at t = 7 ns (c) and 8 ns (d).

    接下来给出压强分布, 进一步分析成丝的过程. 模拟中激光辐照靶面时长5 ns, 图4给出压强分布情况. 由图4(a)图4(b)可知烧蚀前沿压强达到几十Mbar (1 Mbar = 106 Pa)的量级, 压强从激光烧蚀位置到两边逐渐递减, 压强分布较为平滑, 而图4(d)显示激光结束后压强在同一水平线上会产生剧烈波动, 大小相差1.5个数量级左右, 这表明激光作用有助于使压强保持均匀, 而激光结束后同一水平位置上的压强分布倾向于不均匀, 这是由不均匀的辐射引起的. 图4(e)显示在激光结束后的流体演化中压强明显出现丝状分布, 这种压强的不均匀性发展在图4(f)一维线图中表现得更直观. 在7 ns时同一水平线上的压强相差1.5个数量级左右, 压强的不均匀性必然导致物质被压缩聚集到压强较小的位置, 进而出现成丝现象.

    图 4 L2激光辐照钨靶的压强分布 5 ns (a), 7 ns (c)和8 ns (e)时二维压强分布; 5 ns (b), 7 ns (d)和8 ns (f) 时Z = 500 μm处的压强线分布\r\nFig. 4. Pressure distribution of L2 laser irradiating the tungsten target: 2D pressure distribution at t = 5 ns (a), t = 7 ns (c) and t = 8 ns (e); the profile of pressure at Z = 500 μm along R direction at t = 5 ns (b), t = 7 ns (d) and t = 8 ns (f)
    图 4  L2激光辐照钨靶的压强分布 5 ns (a), 7 ns (c)和8 ns (e)时二维压强分布; 5 ns (b), 7 ns (d)和8 ns (f) 时Z = 500 μm处的压强线分布
    Fig. 4.  Pressure distribution of L2 laser irradiating the tungsten target: 2D pressure distribution at t = 5 ns (a), t = 7 ns (c) and t = 8 ns (e); the profile of pressure at Z = 500 μm along R direction at t = 5 ns (b), t = 7 ns (d) and t = 8 ns (f)

    为了分析辐射对成丝现象的影响, 在模拟中保持其他参数不变, 关闭辐射模块后发现成丝现象会消失, 这表明辐射对成丝现象有至关重要的影响. 在激光等离子体作用中, “辐射冷却”效应[35-37]对流体动力学演化有重要影响, 高温等离子体通过向外辐射能量使自身温度降低, 进而压强降低, 如果辐射不均匀, 则压强不均匀会改变等离子体形态分布. 辐射冷却主要被用于解释天体物理中出现的射流现象, 在相似性原理下实验室可以通过控制参数产生等离子体射流[38], 对这些现象的研究发现了辐射冷却对等离子体行为的影响.

    有无辐射时等离子体展示了完全不一样的演化行为, 图5给出了无辐射时的模拟结果. 图5(a)给出不考虑辐射时的能量沉积结果, 图5(b)显示二维密度分布中没有出现成丝现象, 图5(c)显示水平方向没有出现明显的密度涨落. 对比考虑辐射效应时(图2)的结果, 发现成丝现象出现在考虑辐射的模拟中, 辐射效应对成丝现象有决定性作用. 首先, 由于激光在等离子体中的反射和折射以及热成丝不稳定性等作用, 在模拟中会出现激光能量沉积不均匀, 而能量沉积不均匀会导致出现初始密度涨落: 在等离子体产生后激光首先会穿越等离子体, 在其中发生折射、反射损失一部分能量, 而后才到达靶面, 且由于热成丝不稳定性, 引起激光能量沉积不均匀, 导致出现初始密度涨落, 这在图2(a)图2(b)中有直观的体现.

    图 5 无辐射下L2激光辐照钨靶的模拟 (a) 4 ns时的密度分布和能量沉积, 红色表示射线束的能量沉积; (b) 7 ns时二维密度分布; (c) 7 ns时Z = 500 μm处密度线分布\r\nFig. 5. Simulation of L2 laser irradiating the tungsten target without radiation: (a) Energy deposition at 4 ns, the red for the energy deposition of the ray beam; (b) 2D density distribution at 7 ns; (c) the  density profile along the R direction at Z = 500 μm and t = 7 ns.
    图 5  无辐射下L2激光辐照钨靶的模拟 (a) 4 ns时的密度分布和能量沉积, 红色表示射线束的能量沉积; (b) 7 ns时二维密度分布; (c) 7 ns时Z = 500 μm处密度线分布
    Fig. 5.  Simulation of L2 laser irradiating the tungsten target without radiation: (a) Energy deposition at 4 ns, the red for the energy deposition of the ray beam; (b) 2D density distribution at 7 ns; (c) the density profile along the R direction at Z = 500 μm and t = 7 ns.

    其次, 辐射不均匀可放大初始的密度涨落. 图6给出考虑辐射时激光辐照钨靶的辐射温度分布, 图6(a)图6(b)显示二维辐射温度最高达到120 eV左右, 从激光辐照位置向两侧逐渐减小, 图6(c)图6(d)显示Z = 700 μm处辐射温度水平分布不均匀. 辐射效应和等离子体温度和密度相关, (6) 式给出韧致辐射比功率与温度和密度的关系[39],

    图 6 L2激光辐照钨靶的辐射温度分布 4 ns (a)和5 ns (b)时二维辐射温度分布; 4 ns (c)和5 ns (d)时 Z = 700 μm处辐射温度线分布\r\nFig. 6. Radiation temperature distribution of L2 laser irradiating the tungsten target: 2D radiation temperature distribution at t = 4 ns (a) and t = 5 ns (b); the profile of radiation temperature at Z = 700 μm along R direction at t = 4 ns (c) and 5 ns (d).
    图 6  L2激光辐照钨靶的辐射温度分布 4 ns (a)和5 ns (b)时二维辐射温度分布; 4 ns (c)和5 ns (d)时 Z = 700 μm处辐射温度线分布
    Fig. 6.  Radiation temperature distribution of L2 laser irradiating the tungsten target: 2D radiation temperature distribution at t = 4 ns (a) and t = 5 ns (b); the profile of radiation temperature at Z = 700 μm along R direction at t = 4 ns (c) and 5 ns (d).
    Pbr(W/g)=1.76×1017Te(keV)Z3iρ(g/cm3)/A2. (6)

    其中Pbr是韧致辐射比功率, Te是电子温度, Zi是电离度, ρ是物质密度, A是元素质量数. 从(6)式可以看出, 密度越高、温度越高则辐射效应越明显, 而辐射冷却会导致局部温度变低, 进而压强减小(图4显示了压强的不均匀分布), 压强减小则导致等离子体对流(图7显示了等离子体流速方向改变), 等离子体流向压强低的区域, 使该处密度进一步增加, 由此可产生辐射冷却不稳定性[40], 导致密度涨落逐渐增加, 最后演化为明显的成丝现象.

    图 7 t = 3 ns有无辐射时L2激光辐照钨靶的等离子体速度分布\r\nFig. 7. Plasma velocity distribution at t = 3 ns of L2 laser irradiating the tungsten target with and without radiation.
    图 7  t = 3 ns有无辐射时L2激光辐照钨靶的等离子体速度分布
    Fig. 7.  Plasma velocity distribution at t = 3 ns of L2 laser irradiating the tungsten target with and without radiation.

    辐射效应导致压强不均匀, 会引起等离子体流速特征改变, 图7给出了有无辐射时的速度矢量分布图. 红色和蓝色箭头分别表示考虑和不考虑辐射效应时的速度矢量, 图中红圈位置可以看到有辐射时速度向内, 而无辐射时速度均为向外. 向内的速度说明辐射冷却不稳定性导致压强不均匀, 进而引起了等离子体的对流, 放大了初始的密度涨落, 最终出现成丝的宏观物理现象.

    模拟中, 5 ns激光辐照结束后逐渐发生成丝现象(t = 7, 8 ns), 之后成丝现象会逐渐消失(t = 9, 10 ns), 消失的原因是等离子体中的不均匀性会被扩散、热传导等效应逐渐抹平. 在丝状出现后, 流体的典型运动速度是5×106cm/s, 即50 μm, 而等离子体丝之间的距离在100 μm左右, 由此可知扩散约需要2 ns来匀滑密度不均匀性.

    为了更深入理解成丝现象的成因, 本文研究了激光辐照铝、铜、钨、金等4种靶材料的结果. 激光辐照不同材料时, 在高Z物质钨、金中成丝现象较为明显, 在激光辐照结束后水平方向会出现有数量级差距的密度涨落, 而铜靶结果中有较弱的成丝现象, 铝材料中的密度成丝现象几乎观察不到, 这说明成丝现象与靶材料有关. 图8用模拟结果中7 ns时Z = 400 μm水平上取常用对数后密度的最大值log10ρ1与最小值log10ρ2之差log10ρgap来表征成丝现象的强弱, 给出铝、铜、钨和金4种元素中成丝现象强弱的定性关系:

    图 8 在不同物质中由对数密度表示成丝现象的强弱\r\nFig. 8. Logarithmic density versus atomic number, showing the strength of filamentation for different materials.
    图 8  在不同物质中由对数密度表示成丝现象的强弱
    Fig. 8.  Logarithmic density versus atomic number, showing the strength of filamentation for different materials.
    log10ρgap=log10ρ1log10ρ2. (7)

    总体上, 成丝现象与原子序数正相关, 在铝和铜中, 横向密度差在1个数量级左右; 而钨和金中, 密度差最大相差近3个数量级. 成丝现象表现出对高Z材料的依赖性, 由(6)式看出高Z物质的辐射效应更强, 故辐射冷却不稳定性更强, 导致成丝效应更明显.

    另一方面, 研究了激光强度不同对成丝现象的影响, 表1给出三种模拟中用到的激光参数, 激光波形为方波, 总能量为1500 J, 脉冲时间为5 ns, 焦斑半径为200, 300和400 μm的激光分别命名为L1, L2和L3. 在相同的功率下, 焦斑大小不同导致激光强度不同, 最高强度为2.387×1014 W / cm2. 这三种激光参数作用下, 强度越大的激光参数下成丝现象表现越明显, 因为激光强度越强导致电子温度越高, 由(6)式可知辐射冷却效应会越强, 最终导致更强的密度差. 在2.387×1014 W / cm2激光强度下, 钨的对数密度差达到2.69, 图2中有直观的显示.

    表 1  激光参数
    Table 1.  Laser parameters.
    L1L2L3
    E/kJ1.51.51.5
    t/ns[0,0.1,5,5.1][0,0.1,5,5.1][0,0.1,5,5.1]
    P/GW[0,300,300,0][0,300,300,0][0,300,300,0]
    r/μm200300400
    I/(Wcm2)2.387×10141.061×10145.968×1013
    λ/μm1.0531.0531.053
    下载: 导出CSV 
    | 显示表格

    本文基于辐射流体力学模拟研究了高功率激光辐照平面靶中的成丝行为, 结果显示, 在高Z材料钨和金中存在明显的密度分布、电子温度分布和压强分布的成丝现象, 丝状等离子体密度与周围等离子体有着数量级的差距. 成丝现象与激光的能量沉积不均匀和辐射冷却效应密切相关, 射线束会在一定程度引起激光辐照的不均匀性, 但这不是本文观察到的成丝现象的主要原因. 由于激光在烧蚀等离子体中传输时的折射和反射及热成丝不稳定性的发展, 导致激光能量沉积不均匀, 进而在等离子体形成初期产生不稳定的种子, 随后辐射冷却效应会放大这种不稳定性, 产生辐射冷却不稳定性, 最终形成等离子体密度、温度和压强等物理量的丝状分布. 这种成丝现象一定程度上破坏了等离子体的均匀性, 为流体不稳定性的增长埋下了种子, 将会严重影响聚变相关研究. 研究激光辐照平面靶中的成丝效应有助于了解激光等离子体中的不稳定性, 进而抑制这种不稳定性, 提高聚变的增益.

    感谢国防科技大学崔野、郑鹏飞、曾博同学的有益讨论和帮助.

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  • 图 1  激光打靶模型. 其中黄色区域为钨靶, 蓝色区域为氦气, 蓝色中间区域为射线束描述的激光功率分布, 激光由下往上入射到钨靶

    Figure 1.  Schematics of the laser-target interaction. The yellow region is the tungsten target, the blue region is the background helium, and the middle region is the distribution of laser power. The laser is incident on the tungsten target from bottom to top.

    图 2  L2激光辐照钨靶的能量沉积及密度分布 t = 4 ns (a), t = 5 ns (b) 时密度背景上的能量沉积, 红色表示射线束的能量沉积; (c) t = 7 ns, (d) t = 8 ns时二维密度分布; (e) t = 7 ns , (f) t = 8 ns时Z = 500 μm处密度线分布

    Figure 2.  Energy deposition and density distributions of L2 laser irradiating the tungsten target: Energy deposition on the density background at t = 4 ns (a) and 5 ns (b), the red color for the energy deposition of the ray beam; 2D density distribution at t = 7 ns (c) and 8 ns (d); the profile of density at Z = 500 μm along R direction at t = 7 ns (e) and 8 ns (f).

    图 3  L2激光辐照钨靶的电子温度分布 t = 7 ns (a)和t = 8 ns (b) 时二维电子温度分布; t = 7 ns (c) 和t = 8 ns (d) 时 Z = 500 μm处电子温度线分布

    Figure 3.  Electron temperature distribution for L2 laser irradiating the tungsten target: 2D electron temperature distribution at t = 7 ns (a) and 8 ns (b); (c), (d) profile of electron temperature at Z = 500 μm along the R direction at t = 7 ns (c) and 8 ns (d).

    图 4  L2激光辐照钨靶的压强分布 5 ns (a), 7 ns (c)和8 ns (e)时二维压强分布; 5 ns (b), 7 ns (d)和8 ns (f) 时Z = 500 μm处的压强线分布

    Figure 4.  Pressure distribution of L2 laser irradiating the tungsten target: 2D pressure distribution at t = 5 ns (a), t = 7 ns (c) and t = 8 ns (e); the profile of pressure at Z = 500 μm along R direction at t = 5 ns (b), t = 7 ns (d) and t = 8 ns (f)

    图 5  无辐射下L2激光辐照钨靶的模拟 (a) 4 ns时的密度分布和能量沉积, 红色表示射线束的能量沉积; (b) 7 ns时二维密度分布; (c) 7 ns时Z = 500 μm处密度线分布

    Figure 5.  Simulation of L2 laser irradiating the tungsten target without radiation: (a) Energy deposition at 4 ns, the red for the energy deposition of the ray beam; (b) 2D density distribution at 7 ns; (c) the density profile along the R direction at Z = 500 μm and t = 7 ns.

    图 6  L2激光辐照钨靶的辐射温度分布 4 ns (a)和5 ns (b)时二维辐射温度分布; 4 ns (c)和5 ns (d)时 Z = 700 μm处辐射温度线分布

    Figure 6.  Radiation temperature distribution of L2 laser irradiating the tungsten target: 2D radiation temperature distribution at t = 4 ns (a) and t = 5 ns (b); the profile of radiation temperature at Z = 700 μm along R direction at t = 4 ns (c) and 5 ns (d).

    图 7  t = 3 ns有无辐射时L2激光辐照钨靶的等离子体速度分布

    Figure 7.  Plasma velocity distribution at t = 3 ns of L2 laser irradiating the tungsten target with and without radiation.

    图 8  在不同物质中由对数密度表示成丝现象的强弱

    Figure 8.  Logarithmic density versus atomic number, showing the strength of filamentation for different materials.

    表 1  激光参数

    Table 1.  Laser parameters.

    L1L2L3
    E/kJ1.51.51.5
    t/ns[0,0.1,5,5.1][0,0.1,5,5.1][0,0.1,5,5.1]
    P/GW[0,300,300,0][0,300,300,0][0,300,300,0]
    r/μm200300400
    I/(Wcm2)2.387×10141.061×10145.968×1013
    λ/μm1.0531.0531.053
    DownLoad: CSV
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Publishing process
  • Received Date:  04 May 2022
  • Accepted Date:  28 July 2022
  • Available Online:  22 November 2022
  • Published Online:  05 December 2022

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