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惯性约束聚变(ICF)是实现实验室热核聚变点火和燃烧的技术途径之一,对国家能源、国防战略有着举足轻重的作用[1-2]。采用激光间接驱动方式,美国国家点火装置(NIF)上的物理实验产生了约3500亿大气压的高能量密度氘氚等离子体,获得了1016量级的热核聚变氘氚中子[3],实现了聚变放能对点火热斑的进一步加热[2],表明人类已经接近ICF热核聚变点火的门槛[2, 4-6]。
从激光辐照物质开始至热核聚变反应结束,在ICF动作的整个过程中,物质主要处于高能量密度的辐射等离子体状态,电子、离子和光子是其三大组元。在构建描述物质时空演化的物理模型时,假定电子和离子各自处于局域热动平衡状态,也就是认为空间某一点的小体积元内粒子的能量分布满足Maxwell分布,采用电子温度和离子温度的时空演化来刻画电子和离子能量的时空发展;采用流体质量方程和动量方程来刻画物质的质量流动和动量演化;而光子(辐射)的时空演化行为采用多群输运或多群扩散模型[7]。从目前的实验和理论研究看,上述物理模型基本抓住了研究对象的主要物理特点[8],兼顾了物理模型的科学性和可行性[9]。
物理上,假定电子和离子各自处于局域热动平衡状态,就意味着电子平均自由程或离子平均自由程要远远小于特征物理量的空间变化尺度(物理量T的空间变化尺度定义为
${R_{\rm{c}}} = {\left| {\dfrac{1}{T}\dfrac{{\partial T}}{{\partial x}}} \right|^{ - 1}} $ )。但在ICF的动作过程中,这个条件并非总是能够得到满足。例如,激光在等离子体中传播时存在一个临界面,在临界面附近电子能量密度的空间变化剧烈,存在强电子能流;在电子处于局域热动平衡状态假定下,描述电子能流的物理模型为Spitzer-Harm热传导模型。研究已经表明,Spitzer-Harm热传导模型不能够精确描述激光惯性约束聚变中的电子能量传输过程。究其原因,对电子能流起主要贡献是速度接近三倍电子热速度的电子,这些电子的自由程很长,与电子温度的空间变化尺度可比拟[10-11]。再如,激光间接驱动中,采用黑腔将激光转换为软x射线;黑腔中存在腔壁等离子体、靶丸等离子体和充气等离子体三类不同的等离子体,相互间要发生碰撞和对穿。根据现有辐射流体力学数值模拟给出的温度和密度状态,等离子体碰撞与对穿时,局域热动平衡状态假定需要的条件也不能完全满足[12]。理论上,要克服这些问题,需要更深层次的物理建模,需要放弃局域热动平衡假定,需要基于相空间中粒子分布函数来描述粒子动量、能量的时空演化,也就是要采用动理学方法来构建物理模型,包含粒子分布函数的非平衡特征带来的物理效应,这也就是本文讨论的动理学效应的内涵。但是激光惯性约束聚变涉及的问题非常复杂,不仅物理过程多,而且不同物理过程的时间尺度、空间尺度差异大,完全采用动理学方法构建物理模型超出当前计算机的能力,无法实用。兼顾应用的需求和现实的可能,目前的主要做法是采取辐射流体力学和动理学相结合的方法,即基于辐射流体力学方法给出物质的宏观状态,在此基础上采用动理学方法研究粒子分布函数的非平衡特征带来的物理效应,进而修正或改进辐射流体力学物理模型。
ICF物理实验结果和辐射流体力学模拟之间存在的一些差异很可能与动理学效应有关[13-15], 例如黑腔“能量丢失”问题[16],近真空黑腔中的低阶模驱动不对称问题[14, 17-18],模拟给出的面密度 ρR 比实验结果高10%~20%等现象[13]。正是鉴于动理学效应研究的科学意义和应用价值,2016年、2018年美国利弗莫尔国家实验室(LLNL)组织召开了两次ICF中动理学效应的专题讨论会“The Kinetic Physics in ICF Workshop”,重点讨论动理学效应对ICF的影响以及下一步研究计划。我国ICF领域的科研人员也围绕动理学效应研究开展了若干工作,取得了有价值的成果。本文拟对该领域部分进展做简要介绍。
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粒子平均自由程
${\lambda _{ij}}$ 与特征物理量的空间变化尺度Rc之比称为克努森数${N_{\rm{K}}} \equiv {\lambda _{ij}}/{R_{\rm{c}}}$ ,是丹麦物理学家M.Knudsen在研究冲击波时引入的无量纲参数。当${N_{\rm{K}}} \ll 1$ 时,粒子间的碰撞在演化中起主导作用,系统完全可以由流体描述;随着NK增加,碰撞在系统演化过程中的作用相对减弱,流体描述开始失效,需要用动理学方法处理。假设体系中存在两种离子Zi和Zj,二者有共同的离子温度Ti,那么Zi离子在Zj等离子体中的碰撞平均自由程
${\lambda _{ij}}$ 可以表示为$${\lambda _{ij}} = \frac{{{A_i}}}{{{A_{{\rm{red}}}}Z_i^2Z_j^2\ln {\mathit{\Lambda}} }}{\left( {\frac{{{n_j}}}{{{{10}^{20}}{\rm{c}}{{\rm{m}}^{{\rm{ - 3}}}}}}} \right)^{ - 1}}{\left( {\frac{{{T_i}}}{{1\;{\rm{keV}}}}} \right)^2}$$ (1) 上式表明离子间的碰撞平均自由程和离子温度的平方成正比,和离子密度成反比,和离子电荷数平方成反比。在间接驱动黑腔中,等离子体密度(1019~1025 cm−3)和温度(0.01~10 keV)的跨度大、组分(D,T,Be,Si,Cu,Au等)复杂,离子平均自由程
${\lambda _{ij}}$ 的大小变化范围很宽,在一些特征区域大于或接近该区域的特征尺寸,动理学效应变得重要。图1给出了近点火条件下(NIF-N170601发次),黑腔内不同区域温度、密度的时间演化曲线以及归一化离子碰撞平均自由程
${\lambda _{ii}}{\left\langle Z \right\rangle ^4}$ 等高线[15]。如图1所示,碰撞平均自由程较大的区域出现在腔壁/气体界面的Au,He等离子体区域、腔轴附近的He等离子体区域、DT气体区域和DT热斑区域,有必要研究动理学效应的影响。图 1 NIF170601发次对应模拟的黑腔等离子体不同区域温度、密度演化曲线(实线),及归一化离子碰撞平均自由程等高线(虚线)。(□)峰值激光功率时刻,(○)冲击波回弹时刻,(×)峰值燃烧时刻[15]
Figure 1. Physical regime of density and temperature in the simulation of NIF shot N170601 (solid lines). Contours show normalized ion mean-free-path (dashed lines). Symbols indicate time of (□) peak laser power,(○) shock rebound,and (×) peak burn[15]
在等离子体物理中,动理学这个名词的内涵是指采用粒子的分布函数,也就是基于相空间,来描述或刻画客观系统的演化,本质上是考虑粒子分布函数的非平衡行为的影响,非平衡的强弱可以用分布函数偏离麦克斯韦分布的程度来表征。导致粒子非平衡的物理过程和原因有多种:电离产生的电子,由于时间不够长没有与背景电子充分的碰撞相互作用;被强激光加速的电子,同样由于时间不够长没有与背景电子充分的碰撞相互作用;系统边界处高能粒子的漏失;诸如此类。
迄今为止,已经有若干设计精巧的实验揭示动理学效应的存在和重要性。例如,离子的对撞贯穿和扩散混合[19-22]、离子分层和热退耦[23-26]、界面电磁场效应[27-31]、非平衡超热电子[32-33]、非平衡离子效应[12, 34-35]等。另一方面,相关数值模拟也在不断发展[15],例如混合粒子模型LSP,ePLAS等[36-41],在流体的基础上考虑扩散等输运效应的RIK模型[42], 纯动理学的FPION模型[43]、Fokker-Planck方法[44-47]、PIC方法[12, 48]等。数值模拟和精密实验之间的相互耦合,促进了动理学效应研究的深化。热退耦[23-26]、界面电磁场效应[27-31]、非平衡超热电子[32-33]、非平衡离子效应[12, 34-35]等。另一方面,相关数值模拟也在不断发展[15],例如混合粒子模型LSP,ePLAS等[36-41],在流体的基础上考虑扩散等输运效应的RIK模型[42], 纯动理学的FPION模型[43]、Fokker-Planck方法[44-47]、PIC方法[12, 48]等。数值模拟和精密实验之间的相互耦合,促进了动理学效应研究的深化。
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传统高充气黑腔(约1 mg·cm−3氦气)存在LPI严重、激光能量耦合效率低的问题,随着高密度HDC靶丸技术的突破,人们可以采用中低充气密度的黑腔,配合短脉宽的驱动激光,可以实现较高的能量耦合,但人们发现对于低充气黑腔,实验和模拟给出的靶丸压缩低阶模非对称性不一致[14, 31-18]。人们认为这些异常现象和腔壁/充气/靶丸烧蚀等离子体界面处的动理学效应有关。研究发现该区域存在大尺度的混合效应、界面电磁场效应、非平衡离子等效应,相关的数值模拟也在不断发展。
MIT的Li等人利用D3He内爆质子照相观察到腔壁Au等离子体膨胀引起的自生电场[27-29, 49],图2给出了典型质子照相的结果。在真空条件下,激光弹着点的Au泡之间会挤出高速Au等离子体射流,由于射流区域和周围等离子体之间存在较强的压力梯度
$\nabla {p_{\rm{e}}}$ ,这会引起108 V/m量级的自生电场,而准单能D3He内爆质子是诊断电磁场的绝佳手段。对于充气黑腔,质子照相发现在Au-气体界面,电场效应会加速离子混合,同时由于轻的离化气体等离子体推动重的Au等离子体,界面处还会产生经典的RT不稳定性。理论分析表明该电场效应主要来自气压扩散机制[23, 31]。该电场效应的发现有助于人们更好地认识间接驱动黑腔内部的激光等离子体相互作用和内爆压缩等物理。LLNL的S. Le. Pape等人在OMEGA激光器上研究了真空条件和充气条件下等离子体(金和碳)的对撞混合过程[19]。图3给出了汤姆逊散射的实验结果。真空条件下,金等离子体和碳等离子体在很大尺度内(约500 μm)存在混合,同时混合区域离子温升达到数十keV。在充气条件下(0.15 mg·cm−3氦气)二者的混合效应显著减弱(小于50 μm),同时离子温升只有几keV,主要是因为氦气抑制了在真空前沿Au等离子体的高速膨胀(约1700 km/s),导致离子碰撞平均自由程下降了一个量级。填充气体使整个体系从动理学对穿过程向流体描述过渡。
中物院激光聚变研究中心与北京应用物理与计算数学研究所合作,结合辐射流体程序和粒子模拟程序,在真空黑腔中发现非平衡超热离子现象,并提出了基于静电冲击波的物理机制[12, 34-35]。强激光与Au腔壁相互作用,Au等离子体高速向外膨胀,与被辐射烧蚀而反向高速膨胀的靶丸烧蚀等离子相遇,由于微观双流不稳定性的非线性增长,驱动产生静电冲击波。静电冲击波传播方向与Au膨胀速度方向一致,并且能反射波前的低Z离子(H,C等)达到几十keV。图4给出了相关粒子模拟结果和核表征的实验结果。实验采用DD反应[D+D→He3+n(2.45 MeV)]产生的中子来表征非平衡离子信息。并进一步结合质子照相的结果验证了静电冲击波的物理机制。非平衡离子的发现为解释近真空黑腔靶丸压缩低阶模对称性方面的模拟和实验不一致问题提供了新的思路[17-18]。
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在间接驱动物理实验中,人们发现了一些与流体不一致的结果。例如,NIF实验发现测量的DT中子下散射比值(该值与燃料面密度成正比)比预测值低10%~20%,而由DT中子谱宽度给出的Brysk温度比预测值高20%~40%[50]。在DT低温分层实验中,DD中子与DT中子产额比高于预期[51]。Clark等尝试将DT燃料中的热传导系数人为降低一倍后,实验和模拟结果就会更加接近,具体原因尚不明确,可能与热斑区域的微观动理学效应有关[13]。热斑区域动理学效应的研究直接关系到点火热斑的形成和演化以及点火判据的标准,近期实验和模型都有较多的发展,下面介绍一些典型结果。
Rosenberg等人在OMEGA[20]和NIF[52]上利用不同D3He(等原子比)充气压力的爆推靶实验来研究动理学效应。实验发现随着充气压力的降低,模拟聚变产额和实验聚变产额的比值偏差越来越大(见图5(b)),充气密度为3.1 mg/cm3时该比值约为2,充气密度为0.14 mg/cm3时该比值约为100。随着充气压力的减低,离子碰撞平均自由程从40 μm增加到800 μm,克努森数NK从0.3变到9,这说明体系从碰撞主导变成动理学主导。人们认为有限热斑区域高能离子的逃逸以及热斑边界离子扩散效应是实验偏离模拟的主要原因[20, 46]。
实验结果进一步发现,不同离子的扩散程度也不同,这导致不同离子会出现空间脱离、温度脱离的分层退耦现象[23-24, 53-56]。Casey等人在OMEGA上开展了直接驱动DT充气内爆实验[55],以DT中子作为比较的基准,实验发现DD质子相对产额YDD/YDT明显低于预期,而TT中子相对产额YTT/YDT显著高于预期(见图6)。分析认为压力扩散导致不同离子的扩散速度不同,更轻的离子会更远离热斑的中心区域,从而引起了DT分离现象。克努森数NK越大,离子分层效应就越强[57]。在直接驱动的冷冻靶实验中,人们发现相对产额比YDD/YDT与预期结果比较一致[58],这是因为即使在冲击阶段存在DT分层效应,那么在压缩阶段由于DT内壳层物质再次进入热斑区域,进而使得压缩段的产额受离子分层的影响变小。
此外,人们也在发展一些新的技术来表征和研究动理学效应。例如,在热斑区域掺杂Ar元素,利用特征元素的谱数据来研究离子分层效应[59-61];利用X射线、核反应时间历程信息来研究离子扩散、分层动理学效应等[26, 62-64]。
以上研究主要关注热斑区域离子向外的扩散效应,还有一类是研究壳层材料混入热斑区域的物理机制,非流体的动理学混合是人们关注的热点问题。Rinderknecht等人利用直接驱动爆推靶聚变产额信息表征了动理学混合效应[21],实验发现:基于同样的CD壳层,充D3He(1∶1)混合气体与只充相同压力的3He气对应的聚变质子产额非常接近(见图7),这一结果很难用流体不稳定性单一因素来解释,内壳层区域离子与充气区的动理学扩散混合可能是主要的原因。除了利用聚变核产物信息,人们还利用聚变反应的伽玛信号来研究壳层和热斑区域的混合问题[65-66]。
燃料内壳和芯部气体界面区域是动理学非常关注的区域。强冲击波穿过该界面引起的界面电磁场效应往往就是导致动理学效应的原因,因此对强冲击波动理学效应、界面电场的研究也是动理学研究的热点[24, 30, 57, 67-68]。图8(a)是给出了OMEGA装置上的内爆压缩聚芯过程的质子照相结果[65],在0.8 ns时刻质子在中心聚集,而在1.6 ns时刻中心质子被排空,这是由于电子压力梯度引起的电场
$E \approx - \nabla {p_{\rm{e}}}/e{n_{\rm{e}}}$ 方向翻转造成的。0.8 ns时刻冲击波尚未聚芯,芯部压力相对小,电场方向指向中心,而在1.6 ns时刻后,冲击波已经聚芯,芯部压力高于四周,电场方向从中心指向四周。图8(b)是利用OMEGA-EP产生靶后鞘场质子对平面靶构型下的冲击波从CH材料传输进入气体区域的拍照结果。可以看到两个环形质子聚集区域,一个是烧蚀层与气体的密度陡变界面散射质子引起的,一个是电子压力梯度陡变界面的电场偏转引起的[69]。最后需要指出,关于黑腔注入口附近的激光等离子体相互作用(LPI)和超热电子产生也是一大类重要的动理学现象[1, 32-33, 70-74],本文并不细致讨论。双等离子体衰变、受激拉曼散射、受激布里渊散射等LPI过程以及非平衡超热电子会改变激光传输、引起靶丸预热、影响驱动和靶丸压缩对称性。理论上人们使用非局部热平衡模型、束间能量转移模型来研究这些效应的影响,但由于LPI对局域等离子体温度、密度等状态参数非常敏感,二者之间是非线性反馈的关系,所以精准预测黑腔LPI演化仍然极具挑战性,需要深入的实验和模拟研究。
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近年来,ICF领域有关“动理学效应”的研究受到较多关注,这方面的研究有助于理解很多用流体模拟难以解释的实验现象。本文主要回顾了腔壁/充气/靶丸界面区域和靶丸芯部区域的典型动理学现象,包括界面电磁场效应、等离子体对穿混合、非平衡离子效应、热斑区域离子的扩散和分层效应、强冲击波界面效应等。在激光聚变领域,这类研究还处于发展阶段,无论是从高能量密度物理前沿研究的角度,还是从实现惯性约束热核聚变点火和自持燃烧的角度,都有必要更系统、更深入地开展动理学效应研究。
Research progress of kinetic effects in laser inertial confinement fusion
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摘要: 动理学效应的研究是近年来激光惯性约束聚变领域的研究热点,有助于理解实验结果和传统流体模拟之间的偏差。间接驱动黑腔中等离子体的温度、密度跨越多个量级且靶丸组分复杂,在局域的高温低密度区域,粒子的非平衡效应开始变得显著,可能会间接影响内爆性能。对ICF领域动理学效应的概念和部分进展做了简要综述。Abstract: In recent years, the study of kinetic effects is a hot issue in the field of laser inertial confinement fusion, which helps to understand the deviation between experimental results and traditional fluid simulation. The temperature and density of the plasma in indirect-drive hohlraum span multiple orders of magnitude, and the composition of capsule is complex. In the local high temperature and low density region, the thermal non-equilibrium effect of particles becomes significant, which may indirectly affect the implosion performance. In this paper, the concept and some progress of kinetic effects in the ICF field are briefly reviewed.
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Key words:
- laser fusion /
- kinetic effect /
- thermal non-equilibrium
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图 1 NIF170601发次对应模拟的黑腔等离子体不同区域温度、密度演化曲线(实线),及归一化离子碰撞平均自由程等高线(虚线)。(□)峰值激光功率时刻,(○)冲击波回弹时刻,(×)峰值燃烧时刻[15]
Figure 1. Physical regime of density and temperature in the simulation of NIF shot N170601 (solid lines). Contours show normalized ion mean-free-path (dashed lines). Symbols indicate time of (□) peak laser power,(○) shock rebound,and (×) peak burn[15]
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