温稠密钛电导率计算

温稠密物质是惯性约束核聚变、重离子聚变、Z箍缩动作过程中物质发展和存在的重要阶段. 其热力学性质和辐射输运参数在聚变实验和内爆驱动力学模拟过程中有至关重要的作用. 本文通过建立非理想Saha方程, 结合线性混合规则的理论方法模拟了温稠密钛从10^-5-10 g·cm^-3, 10⁴ K到3×10⁴ K区间的粒子组分分布和电导率随温度密度的变化, 其中粒子组分分布由非理想Saha方程求解得到. 线性混合规则模型计算温稠密钛的电导率时考虑了包括电子、原子和离子之间的多种相互作用. 钛的电导率的计算结果与已有的爆炸丝实验数据相符. 通过电导率随温度密度变化趋势判断, 钛在整个温度区间, 密度0.56 g·cm^-3时发生非金属相到金属相相变. 对于简并系数和耦合系数的计算分析, 钛等离子体在整个温度和密度区间逐渐从弱耦合、非简并状态过渡到强耦合部分简并态.

A simple and effective simulation for electrical conductivity of warm dense titanium

A linear mixture rule has been used to calculate the electrical conductivity of warm dense titanium plasmas in the density and temperature ranges of 10^-5–10 g·cm^-3 and 10⁴–3×10⁴ K, in which the interactions among electrons, atoms, and ions are considered systemically. In the first place, the coupling and degeneracy parameters of titanium plasma are shown as a function of density and temperature in the warm dense range. The warm dense titanium plasmas span from weakly coupled, nondegenerate region to strongly coupled, degenerate domain in the whole density and temperature regime. The titanium plasma becomes strongly coupled plasma at higher than 0.22 g·cm^-3 and almost in the whole temperature range where the coupling parameter Γ_ii > 1. In particular, the Coulomb interactions become stronger at higher than 0.56 g·cm^-3 where 10 < Γ_ii < 216. At the same time, the titanium plasma is in the degenerate regime at higher than 0.35 g·cm^-3 where the degeneracy parameter Θ< 1, and is in the nondegenerate or partial degenerate regime at lower than 0.35 g·cm^-3 where Θ≥ 1. The influence of temperature on the coupling and degeneracy parameters is less than that of the density, and the plasma composition is calculated by the nonideal Saha equation felicitously. Thus the ionization degree decreases with increasing density at lower density, which is due to the thermal ionization in that regime where the free electrons have sufficiently high thermal energy. Meanwhile, the ionization degree increases with the increase of density at higher than 0.1 g·cm^-3, in which the pressure ionization takes place in the region where the electrons have sufficiently high density and the collisions increase rapidly. There is a minimum for the ionization degree at about 0.1 g·cm^-3, while the maximum ionization degree reaches 4 at 10 g·cm^-3. In the whole temperature regime, the titanium plasma is mostly in the partial plasma domain at lower than 1 g·cm^-3, and becomes completely ionized at higher than 1 g·cm^-3. The calculated conductivity is in reasonable agreement with the experimental data. At a fixed temperature, there is a minimum in each of the ionization curves at lower than 3×10⁴ K. And the position of the minimum is shifted towards decreasing density with increasing temperature. The conductivity monotonously increases as the density increases at a temprature of 3×10⁴ K. At a constant density, the conductivity increases with increasing temperature for lower than 0.56 g·cm^-3, while it decreases with increasing temperature for higher than 0.56 g·cm^-3. This behavior is connected with the nonmetal to metal transition in a dense plasma regime. So the nonmetal to metal transition in dense titanium plasma occurs at about 0.56 g·cm^-3 and its corresponding electrical conductivity is 1.5×10⁵ Ω^-1·m^-1. Finally, the contour of electrical conductivity of titanium plasma is shown as a function of density and temperature in the whole range. Its electrical conductivity spans a range from 10³ to 10⁶ Ω^-1·m^-1. It can be seen that the titanium plasma gradually approaches the semiconducting regime as temperature increases. When the order of magnitude of the electrical conductivity reaches 10⁵ Ω^-1·m^-1, the plasma almost becomes conducting fluid in the higher density range. This also demonstrates that a nonmetal-metal transition has taken place in the warm dense titanium plasma.