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高能粒子在等离子体中的能量沉积及其导致的电子离子能量分配对理解惯性约束聚变的点火和燃烧过程至关重要. 基于量子动理学的T矩阵扩展模型, 本文研究了宽广温度密度区间的能量沉积和电子能量分配因子. 相较于基于小角度散射的阻止本领模型, T矩阵扩展模型能考虑由大角度库仑散射及其累积过程带来的横向偏转效应. 本文首先研究了横向偏转效应对电子能量分配因子的影响, 然后计算了宽温度密度区间的电子能量分配因子, 基于这些数据的分析发展了适用于惯性约束聚变模拟的电子能量分配因子拟合表达式. 研究发现, 考虑横向偏转效应会对电子能量分配因子带来约27.5%的差异. 这一结论表明, 准确描述高能粒子能量沉积过程中的大角度库仑散射及其累积效应带来的横向偏转会影响惯性约束聚变点火和燃烧的模拟的精确性.Energy deposition of high-energy ions and the resulting electron-ion energy partition in dense plasmas are of essential importance in understanding the hot-spot ignition and burning of inertial confinement fusion. In this work, the energy deposition and electron-ion energy partition of high-energy ions are studied in a wide range of temperatures and densities based on the improved T-matrix model. Compared with the stopping power model based on the assumption of small -angle scattering, the improved T-matrix model can consistently take into account the large-angle Coulomb scattering and the resulting transversal deflection of the high-energy ions. We investigate the influence of the effect of transversal deflection on the electron-ion energy partition and propose a fitting formula for the electron energy partition factor. This formula is applicable to inertial confinement fusion simulations. It is found that when the effect of transversal deflection is considered, the relative energy deposited into electrons in plasma is reduced by about 27.5% at most. This conclusion suggests that the transversal deflection of energetic ions, induced by the large-angle Coulomb scattering and its cumulative effect, ought to be considered in accurately simulating the hot-spot ignition and burning of the fuel in inertial confinement fusion.
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Keywords:
- energy deposition /
- electron-ion energy partition /
- nonideal plasmas /
- inertial confinement fusion
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图 1 左图: 温度为$ 200 \; \mathrm{keV} $和电子密度为$ 10^{25} \; \mathrm{cm^{-3}} $的DT等离子体中, 不同类型的等离子体粒子对能量为$ E_0 = $$ 3.54 \; \mathrm{Mev} $的α粒子CSD阻止本领的贡献. 右图: 电子密度为$ 10^{25} \; \mathrm{cm^{-3}} $的DT等离子体中, 不同阻止本领为0时α粒子的速度, 红色虚线对应能量为$ E_\mathrm{min} = 3 k_\mathrm{B} T / 2 $时α粒子的速度
Fig. 1. Left: partial and total CSD stopping power of α particle with $ E_0 = 3.54 \; \mathrm{Mev} $ in a DT plasma with $ T = $$ 200 \; \mathrm{keV} $ and $ n_\mathrm{e} = 10^{25} \; \mathrm{cm^{-3}} $. Right: the characteristic velocity of α particle for the case of partial and total stopping power equal to $ 0 $ in DT plasmas with $ n_\mathrm{e} = $$ 10^{25} \; \mathrm{cm^{-3}} $. The red dash line represents the velocity of α particle when $ E_\alpha = E_\mathrm{min} = 3 k_\mathrm{B} T / 2 $.
图 2 电子密度为$ 10^{26} \; \mathrm{cm^{-3}} $的DT与$ \mathrm{p}^{11}\mathrm{B} $等离子体中的电子能量分配因子. 方形和三角形符号分别对应$ \mathrm{p}^{11}\mathrm{B} $等离子体中CSD和BPS模型计算的结果, 而圆形和五边形分别对应DT等离子体中CSD和BPS模型计算的结果
Fig. 2. Energy partition of electrons in DT and $ \mathrm{p}^{11}\mathrm{B} $ plasmas at a fixed electron density $ 10^{26} \; \mathrm{cm^{-3}} $. The square and triangle symbols displays the predictions from CSD and BPS stopping power for $ \mathrm{p}^{11}\mathrm{B} $ plasmas, while the circles and pentagons correspond to CSD and BPS results for DT plasmas.
图 3 α粒子在电子密度$ 10^{26} \; \mathrm{cm^{-3}} $, 温度为1 keV的DT等离子体中的CSD$ ({\rm{d}}E/{\rm{d}}s) $和LET$ ({\rm{d}}E/{\rm{d}}x) $阻止本领
Fig. 3. CSD and LET stopping power for α particle in a DT plasma with $ n_\mathrm{e} = 10^{26} \; \mathrm{cm^{-3}} $ and $ T_\mathrm{e} = 1 \; \mathrm{keV} $.
图 4 左轴: 电子密度为$ 10^{26} \; \mathrm{cm^{-3}} $的DT等离子体中, 电子能量分配因子$ F_\mathrm{e} $随温度的变化. 方形和圆形分别对应Li-Petrasso模型[14]和BPS模型[10]的结果, 而五角星和三角符号表示不考虑和考虑入射粒子反冲效应的结果[16]. BPS$ (E_0) $和BPS$ (E_\mathrm{dep}) $分别表示$ E_\mathrm{min} = 0, \; 3 k_\mathrm{B} T / 2 $对应的结果. CSD (蓝色点虚线)和LET (红色实线)之间的差异表征偏转效应的贡献. 黑色虚线对应方程(2)中取$ T_0 = 25 $的结果. 右轴: LET和CSD阻止本领对应的电子能量分配因子之间的比值
Fig. 4. Left axis: energy partition of electron $ F_\mathrm{e} $ in DT plasmas with $ n_\mathrm{e} = 10^{26} \; \mathrm{cm^{-3}} $ at different temperatures. Square and circle symbols denotes the results of Li-Petrasso[14] and BPS[10] models, while pentagram and triangle symbols represent the results without and with projectile recoil based on dielectric formalism of stopping power[16]. BPS$ (E_0) $ and BPS$ (E_\mathrm{dep}) $ are predictions with $ E_\mathrm{min} = 0, \; 3 k_\mathrm{B} T / 2 $, respectively. The difference between LET (red solid line) and CSD (blue dotted-dash line) describes the influence of deflection effect. The black dash line displays the results calculated with $ T_0 = 25 $ in Eq.(2). Right axis: the ratio of energy partition $ F_\mathrm{e} $ from LET and CSD stopping power.
图 5 左图: 电子密度为$ 10^{26} \; \mathrm{cm^{-3}} $的DT等离子体中, 基于CSD阻止本领计算的电子能量分配因子$ F_\mathrm{e} $及其拟合. 右图: CSD模型中, 电子能量分配因子$ F_\mathrm{e} $拟合参数$ a_i $随密度的变化及其拟合
Fig. 5. Left: fitting for energy partition of electron $ F_\mathrm{e} $ based on the CSD stopping power in a DT plasma with $ n_\mathrm{e} = 10^{26} \; \mathrm{cm^{-3}} $. Right: the corresponding fitting parameters $ a_i $ for the CSD $ F_\mathrm{e} $.
表 1 基于CSD和BPS阻止本领的电子能量分配因子$ F_\mathrm{e} $的拟合参数, 见方程(18)和方程(19). 其中符号$ x(y) $表示$ x\cdot 10^y $
Table 1. Fitting parameters in Eq.(18) and (19) for $ F_\mathrm{e} $ based on CSD and BPS stopping power. The symbol $ x(y) $ means $ x\cdot 10^y $.
模型 CSD BPS $ b_i^0 $ $ b_i^1 $ $ b_i^2 $ $ b_i^0 $ $ b_i^1 $ $ b_i^2 $ $ a_1 $ $ -4.3914(1) $ $ 9.9935(0) $ $ -2.7411(-1) $ $ 1.4686(1) $ $ 5.0738(0) $ $ -1.6737(-1) $ $ a_2 $ $ -2.0193(-1) $ $ 1.0276(-1) $ $ -2.2237(-3) $ $ 3.2581(-1) $ $ 5.9071(-2) $ $ -1.3240(-3) $ $ a_3 $ $ 3.6309(-3) $ $ -2.9969(-4) $ $ 7.5755(-6) $ $ 8.6989(-4) $ $ -5.5310(-5) $ $ 2.1109(-6) $ $ a_4 $ $ 1.5664(0) $ $ 2.5995(-2) $ $ -5.9935(-4) $ $ 1.6985(0) $ $ 1.3887(-2) $ $ -3.4874(-4) $ $ a_5 $ $ 5.7808(-1) $ $ 5.6886(-2) $ $ -1.3692(-3) $ $ 1.0067(0) $ $ 1.9037(-2) $ $ -5.4891(-4) $ 
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