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非平衡稠密等离子体中电子离子能量弛豫对理解惯性约束聚变、实验室等离子体和天体物理中的非平衡演化以及宏观热力学和输运性质至关重要. 受密度及温度等环境效应的影响, 等离子体中多种物理效应之间的竞合作用共同主导电子离子能量弛豫过程. 本文从量子Lenard-Balescu动理学方程出发, 建立了考虑电子和离子集体激发及其耦合效应的能量弛豫模型, 并在此基础上采用电子离子解耦、静态极限和长波近似构建了不同的简化模型, 系统研究了静态屏蔽、动态屏蔽、电子和离子等离激元激发及其耦合等效应对电子离子能量弛豫的影响机制. 通过不同模型之间的对比, 发现中等波长和短波区间的屏蔽效应以及电子离子集体激发之间的耦合效应对温热稠密等离子体中电子离子能量弛豫有着显著的影响. 这一结论表明, 准确描述等离子体中的动态响应和屏蔽效应将制约着相关物理体系中非平衡演化建模的精确性和有效性.Accurate knowledge of electron-ion energy relaxation plays a vital role in non-equilibrium dense plasmas with widespread applications such as in inertial confinement fusion, in laboratory plasmas, and in astrophysics. We present a theoretical model for the energy transfer rate of electron-ion energy relaxation in dense plasma, where the electron-ion coupled mode effect is taken into account. Based on the proposed model, other simplified models are also derived in the approximations of decoupling between electrons and ions, static limit, and long-wavelength limit. The influences of dynamic response and screening effects on electron-ion energy relaxation are analyzed in detail. Based on the models developed in the present work, the energy transfer rates are calculated under different plasma conditions and compared with each other. It is found that the behavior of electron screening in the random phase approximation is significantly different from the one in the long-wave approximation. This difference results in an important influence on the electron-ion energy relaxation and temperature equilibration in plasmas with temperature $T_{\rm{e}} < T_{\rm{i}}$. The comparison of different models shows that the effects of dynamic response, such as dynamic shielding and coupled-mode effect, have stronger influence on the electron-ion energy relaxation and temperature equilibration. In the case of strong degeneracy, the influence of dynamic response will result in an order of magnitude difference in the electron-ion energy transfer rate. In conclusion, it is crucial to properly consider the finite-wavelength screening of electrons and the coupling between electron and ion plasmonic excitations in order to determine the energy transfer rate of electron-ion energy relaxation in dense plasma.
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Keywords:
- energy relaxation /
- warm and hot dense matter /
- plasma screening /
- dynamical response of plasmas
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图 1 在密度为$ n_{\rm{e}} = 10^{22} \, {\rm{cm}}^{-3} $, 简并参数为$ \theta_{\rm{e}} = 0.1, 1, 10 $时, 随机相位近似下和长波近似下静态屏蔽效应的行为. 实线为随机相位近似的结果, 点虚线为长波近似下结果
Fig. 1. Electronic static screening in the long-wavelength limit (dot-dashed lines) versus the full static screening in random phase approximation (RPA) (solid lines) for the electron number density $ n_{\rm{e}} = 10^{22} \, {\rm{cm}}^{-3} $ at three different degeneracy parameters $ \theta_{\rm{e}} = 0.1, 1, 10 $.
图 2 密度为$ n_{\rm{e}} = 10^{25} \, {\rm{cm}}^{-3} $, 离子温度为$ T_{\rm{i}} = 10^4 \, {\rm{K}} $的全电离氢等离子体中, 不同离子电子温度比$ \alpha_1 = T_{\rm{i}} / T_{\rm{e}} $下电子和离子集体激发模式的差异$ \mathcal{N}_{\rm{ei}}(\omega) $随约化频率$ \tilde{\omega} = $$ \hbar \omega / (k_{\rm{B}} T_{\rm{i}}) $的变化. 灰色竖线对应该等离子体条件下离子的等离子体频率
Fig. 2. Occupation number difference $ \mathcal{N}_{\rm{ei}}(\omega) $ for reduced frequency $ \tilde{\omega} = \hbar \omega / (k_{\rm{B}} T_{\rm{i}}) $ and different temperature ratio $ \alpha_1 = T_{\rm{i}} / T_{\rm{e}} $ in fully ionized hydrogen plasmas with number density $ n_{\rm{e}} = 10^{25} \, {\rm{cm}}^{-3} $ and ion temperature $ T_{\rm{i}} = $$ 10^4 \, {\rm{K}} $. The gray vertical line marks the reduced ionic plasma frequency.
图 3 密度为$ n_{\rm{e}} = 10^{25} \, {\rm{cm}}^{-3} $, 电子温度为$ T_{\rm{e}} = 10^7 \, {\rm{K}} $的全电离氢等离子体中, 不同离子温度下等离激元多模耦合效应$ \mathcal{C}_{\rm{ei}}(k) = \mathcal{C}_{\rm{ei}}(k, \omega_{\rm{iad}}) $(根据式(11)计算)
Fig. 3. Coupled mode effects determined from the function $ \mathcal{C}_{\rm{ei}}(k) = \mathcal{C}_{\rm{ei}}(k, \omega_{\rm{iad}}) $, i.e. Eq. (11), for two-temperature hydrogen plasmas with density $ n_{\rm{e}} = 10^{25} \, {\rm{cm}}^{-3} $ and electron temperature $ T_{\rm{e}} = 10^7 \, {\rm{K}} $. The red line represents the results for ion temperature $ T_{\rm{i}} = 10^4 \, {\rm{K}} $, while the blue line for the case of ion temperature $ T_{\rm{i}} = 10^6 \, {\rm{K}} $.
图 4 密度为$ n_{\rm{i}} = 10^{25} \, {\rm{cm}}^{-3} $, 离子温度为$ T_{\rm{i}} = 10^4 \, {\rm{K}} $的全电离氢等离子体中, 不同电子温度下的能量转移率. CM (三角符号)和FGR(五角星)的数据引自文献[17]. IAD(蓝色实线)和IPM(红色实线)对应考虑(式(7))和不考虑(式(18))电子离子耦合的能量弛豫率. 绿色点虚线和棕色虚线给出考虑(式(20))和不考虑(式(19))长波近似的静态极限弛豫率. 紫色点线(NCM)给出不考虑等离激元多模耦合(17)的结果
Fig. 4. Numerical results for energy transfer rate in fully ionized hydrogen plasmas for $ n_{\rm{i}} = 10^{25} \, {\rm{cm}}^{-3}, T_{\rm{i}} = 10^5 \, {\rm{K}} $ with different electron temperatures. The CM (orange triangles) and FGR (green stars) results for energy transfer rate are taken from Ref.[17]. The solid blue and red lines represent the results evaluated with Eq.(7) and Eq.(18), respectively. The green dot-dashed line and brown dashed line display the results in static limit with (Eq.(20)) and without (Eq.(19)) long-wavelength approximation, respectively. Predictions marked by NCM (violet dotted curve) give the results calculated from the expression (17).
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