流体-亚稳态原子传输混合模型模拟空心阴极放电特性

利用流体-亚稳态原子传输混合模型研究了氩气矩形空心阴极放电稳态时的参数. 数值计算得到了压强为10 Torr时的电势、电子、离子和亚稳态氩原子密度以及电子平均能量的分布. 结果表明电子和离子密度峰值为4.7×10¹² cm^-3, 亚稳态原子密度峰值为2.1×10¹³ cm^-3. 本文同时对流体-亚稳态原子传输混合模型和单一流体模型模拟得到的放电参数进行了比较. 结果表明, 分步电离是新电子产生的重要来源, 亚稳态原子对空心阴极放电特性有重要影响. 与单一流体模型相比, 混合模型计算得到的电子密度升高, 阴极鞘层宽度和电子平均能量降低. 关键词： 空心阴极放电 流体-亚稳态原子传输模型 电子密度 分步电离     

高温稠密气态混合物质压强的计算

 基于含温有界相对论自洽场平均原子模型,计算了高温稠密条件下气态混合物的压强。通过求解相对论Dirac方程给出有界原子的电子波函数和轨道能量。电子在各单电子轨道上的平均占据数服从Fermi-Dirac分布。以铝、铝镁混合物、铁和高能炸药HMX（奥克托金）为算例,计算了在一些温度密度点下的压强并给出了分析。     

Transition from gas-kinetic to minimal metal-type conductivity in a supercritical fluid of metal vapor

We have proposed a peculiar model of the plasma of dense metal vapors, containing atoms embedded into the electron jelly, as well as free (thermally ionized) electrons and ions. The main feature of the model is the presence of the electron jelly existing at any density of the atomic component. The number of electrons in the jelly increases under compression. The process of its formation can be called the “cold” ionization, or pressure ionization. The composition of the gas–plasma mixture, including the concentration of atoms and electrons in the jelly, as well as the concentration of free thermally ionized electrons and ions, has been calculated. The conductivity of dense vapors is determined by the sum of the conductivities of thermal electrons (which is calculated using the Frost formula) and jelly electrons (which is calculated by the Regel–Ioffe formula for the minimal metal-type conductivity). The concentration of thermal electrons decreases and the concentration of jelly electrons increases upon compression of the vapor. Accordingly, the conductivity varies from the conductivity of thermal electrons to the conductivity of jelly electrons, continuously passing through the minimum. The calculated values of the conductivity of supercritical metal vapors are in satisfactory agreement with experimental results.     

Statistical description of ionization potentials in dense plasmas

The Thomas-Fermi model is used to investigate the influence of the density on the energies of ions in high-density plasmas (?10²¹?10²⁶ cm^?3). This model can be used to explain the two dominant high-density effects — continuum lowering and pressure ionization — by simple energy considerations. The result shows that only the outermost electrons are affected and that the inner region of the ion is hardly influenced by the density.     

Ionization state and bound level populations in hot,dense plasmas

The ionization state and bound level populations in hot, dense plasmas are studied in the average atom approximation. Bound level energies are fixed self-consistently with the complete set of population numbers, using pre-existent Hartree-Fock calculations. We present a pressure- ionization scheme that gradually merges bound electrons into the continuum. To solve the nonlinear algebraic system of equations of the model, we have derived an efficient iterative algorithm. Results are shown for aluminum and iron.     

Electron and positron impact ionization of atomic hydrogen and helium using CPB approximation with post-collision interaction

Triple differential cross-sections for the electron and positron impact ionization of atomic hydrogen and helium are calculated in a first order model using a product of two Coulomb wavefunctions for the final state continuum electrons supplemented by post-collision interaction effects.     

等离子体电子压强的Hartree-Fock-Slater自洽场计算

在对传统平均原子模型(AAM1)作动态自由电子判据改进的基础上，在中心场近似下使用了带边界条件的正能态波函数，提高电子压强的计算精度，使得电子压强满足常态物理条件.作为算例，计算了Fe，Ni，Pb，Am的电子压强. 关键词： 自治场原子结构 电子压强     

Problems in the use of statistical average atom potentials for estimating average degree of ionization

Consequences of a simple integral definition of electron charge bound to an ion are examined for Thomas-Fermi (TF) and Debye-Huckel-Thomas-Fermi (DHTF) average atom statistical potentials used to describe high temperature high density plasmas. A self-consistent scheme for calculating average degree of ionization within the DHTF approach is described. With the simple integral definition of bound charge the DHTF model, unlike the TF model, exhibits the anomalous behavior that degree of ionization can decrease as temperature increases. It is shown that this results from inclusion in the integration of electron charge density too extended and too near continuum energies to be physically considered as bound.     

极板电压与间距对大气压射频氩等离子体放电参数的影响

 基于1维流体力学模型,对大气压射频裸露金属电极氩气放电过程进行了研究。模型中考虑了氩等离子体放电过程中主要发生的激发和电离等7个反应过程,对等离子体反应产生的主要粒子,包括电子、氩原子离子Ar⁺、氩分子离子Ar2⁺和氩激发态Ar^*等,建立连续性方程、动量方程和电流平衡方程。分析了极板电压、极板间距对上述粒子数密度分布的影响。给出了电子,Ar⁺,Ar^*和Ar₂⁺密度随极板电压及间距变化的时空演化过程。得出极板电压或极板间距的改变会使放电空间的电场发生改变,对应一定的极板间距,极板电压有一个最佳值,极板电压和间距的变化会使对应的极板间有一个最佳电场值,而对应最佳电场有一个等离子体气体间最佳反应系数,从而使放电空间粒子数密度发生改变。     

Self-Consistent Solutions for the Scattering State with Two Free Electrons

Wave functions for the scattering states with two free electrons in the field of an ion core are explicitly calculated by the self-consistent, continuum Hartree–Fock (CHF) theory. Typically, such states are associated with the three-body recombination, collisional ionization and photo-double ionization, but have never been directly studied previously. The calculated continuum orbitals are found to be predominantly of the plane-wave forms, as though the system is translation invariant, in the context of many-body HF theory. The symmetry is mildly broken by the presence of the core ion, at about fifteen-percents level, indicating that the orbitals are largely delocalized and the effect of the core potential is an important but minor perturbation. The properties of channel orthogonality and completeness are preserved by the nearly plane wave forms. To test the validity of this finding and the CHF, the continuum orbitals are used to evaluate the amplitudes for the electron impact ionization, and the amputation procedure, that is crucial in the theory, is also critically re-examined.     

Average Atom Model in Hot Plasmas

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Ionization cross sections for electron scattering from metastable rare-gas atoms （Ne~＊ and Ar~＊）

The optical-model approach has been used to investigate the electron-impact ionization of metastable rare-gas atoms. A complex equivalent-local polarization potential is obtained to describe the ionization continuum channels. We have calculated the cross sections for collisional ionization of the metastable atoms Ne* and Ar* by electrons in the energy range from threshold to 200 eV. The present results are in agreement with the available experimental measurements and other theoretical calculations.     

Pauli blocking in degenerate plasmas and the separable potential approach

The Mott effect describes the dissolution of bound states in a dense partially ionized plasma. It occurs when the ionization potential depression, owing to effects of correlation and degeneracy, compensates the binding energy of the bound state. At high densities and moderate temperatures, the Pauli blocking becomes important and influences significantly the degree of ionization in the region of degenerate plasmas. A quantum statistical approach is used where the total density is decomposed in an uncorrelated, “free” part and correlations, as a consequence of the cluster decomposition of the self‐energy. The contribution of correlations to the total density is given by bound states and continuum correlations. Exact solutions for a separable potential are compared to perturbation theory and numerical solutions of the in‐medium Schrödinger equation. The in‐medium scattering phase shifts are evaluated, and the role of continuum correlations is discussed. The Pauli blocking of bound states and the density of states are considered for warm dense matter conditions.     

温稠密铝等离子体物态方程及其电离平衡研究

温稠密物质的物性参数在惯性约束聚变能源、Z箍缩等高能量密度物理领域的实验结果分析和物理过程数值模拟等方面有着重要的应用价值.本文应用部分电离等离子体模型,在理想自由能的基础上考虑了库仑相互作用、排斥体积作用和极化作用等非理想特性,开展了温稠密等离子体物态方程和电离平衡的研究.计算了温稠密铝等离子体的压强等物态方程数据和在密度为1.0×10^-4-3.0 g/cm^3,温度为1.0×10^4-3.0×10^4 K范围内的粒子组分.计算结果显示,铝等离子体的平均电离度在临界密度区域内随着密度的增加而突然增大.根据非理想Saha方程中有效电离能这一关键参数,分析了铝等离子体平均电离度在临界密度区域内随密度迅速增大的现象.     

Calculations of total ionization cross sections of Ne,Ar, Kr,and Xe atoms in the born approximation allowing for electron perturbations in the continuous spectrum

Electron impact ionization cross sections of Ne, Ar, Kr, and Xe atoms are numerically calculated. The electron perturbation in the continuous spectrum in the target field is taken into account. The matrix elements are calculated in many-electron, nonrelativistic approximation with allowance for the superposition of configurations and relaxation effect. The radial part of the electron wave function in the continuum is calculated by solving the single-configuration Hartree-Fock equation. The wave functions of electrons in the continuum are orthogonalized with respect to the core orbital functions. The calculated cross sections are compared to the experimental data and calculations made using the plane-wave Born approximation and that involving generalized oscillator strengths.     

Excitation and emission of metal electrons in atom-surface collisions

Electron-hole pair excitation and ionization probabilities are calculated for atomic collisions with metal surfaces at high incident energies. The method adopted is based on a Sudden Collision Approximation, and a realistic model is employed for the bound and continuum electronic states involved. The parameters used in the calculations are for Ar, He, H atoms impinging on a Li surface at 300 eV. The main results are: (1) Only single electron-hole pair excitations are important; multiple pair contributions are small. (2) The transitions are dominated by the behavior of the electronic wavefunctions in the tunneling region and may serve as a probe of this regime. (3) The excitation efficiency is in the order H ? Ar ? He, the effectiveness of hydrogen being due to its stronger, longer-range coupling. (4) The maximum excitation probabilities are for electrons ejected with relatively low excess energies. (5) Total transition probabilities are about 0.5 per collision for H, and about 0.1 for Ar, indicating that these are important, easily detectable processes. Experiments in this field should provide important information on electronic wavefunctions at the metal-gas interface, and on gas-metal interactions at high energies.     

Modeling of electronegative radio-frequency discharges

A continuum model is presented for low-pressure, radio-frequency electronegative discharges commonly encountered in reactive ion etching and plasma-deposition applications. The model is based on the moments of the Boltzmann transport equations. Local and convective acceleration terms are retained in the momentum equations for the electrons and ions as it allows nonlocal transport in weakly collisional regions. A stable numerical scheme to solve these equations is also presented. A chlorine discharge at 13.56 MHz is simulated as a case study. The simulation results reproduce features observed experimentally in Cl₂ discharges under similar conditions. Of particular importance is the simulated excitation and ionization waveforms. In the bulk, the waveforms peak twice per cycle, which is essentially due to the modulation of electron temperature; in the sheath regions, the waveforms peak only during the anodic part of the cycle when the electrons are accelerated toward the electrode     

Mechanism for the streamer propagation toward the anode and cathode due to background electron multiplication

A simple mechanism for the propagation of an ionization wave in a dense gas due to the multiplication of background electrons in a nonuniform electric field is proposed. The mechanism does not depend on the sign of the field projection onto the streamer propagation direction. The streamer propagation is caused by the enhancement of the electric field at the streamer head. It is shown that, in a prebreakdown field, the intense multiplication of electrons takes place in both electropositive and electronegative gases. The prebreakdown multiplication can provide a fairly high density of background electrons; this allows one to treat the background as a continuous medium when considering streamer propagation as a multiplication wave. The initial ionization is enabled by the natural background of ionizing radiation and cosmic rays. An analytical expression for the velocity of the ionization front is obtained based on a simple equation for the multiplication of background electrons. This expression is in good agreement with numerical simulations performed within both a simple model of background electron multiplication and a more comprehensive drift-diffusion model. In particular, the drift-diffusion model predicts the propagation of the ionization front from a small-radius anode to the cathode due to the multiplication of background electrons. The velocity of the ionization wave front is calculated as a function of the electric field at the streamer head for helium, xenon, nitrogen, and sulfur hexafluoride. It is shown that some features of streamer propagation (e.g., its jerky motion) can be related to the recently found nonmonotonic dependence of ionization frequency on the electric field.