Statistical Model of Dielectronic Recombination of Heavy Ions in Plasmas

Calculation of the total dielectronic recombination (DR) rates was done in the frame of a statistical model of atoms. The model is based on the idea of collective excitations of atomic electrons with the local plasma frequency, which depends on atomic electrons density distribution. The electron density is described in a frame of the Thomas‐Fermi model of atoms. Simple scaling laws for temperature T_e and nuclear charge Z dependences follow from the statistical model of DR. Results of the statistical model were compared with other numerical data following detailed level‐by‐level computations for different multielectron ions. The specific attention is paid to Ni‐like ion sequences of different chemical elements in order to check the Z ‐dependence of DR rates. A comparison with numerical data of Flexible Atomic Code (FAC) is presented for tungsten ions. The reasonable correspondence between the statistical model and the detailed numerical data is demonstrated. The application of the statistical model provides very simple and fast calculations of the DR rates useful in modern plasma modelling. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Au~(34+)离子双电子复合过程的理论研究

复杂结构离子的双电子复合(DR)速率系数在核聚变、极紫外光刻光源等应用研究的等离子体谱模拟中具有重要的价值.利用基于全相对论组态相互作用理论的FAC程序包,详细计算了Au~(34+)离子的双电子复合速率系数.研究分析了激发、辐射通道,组态相互作用,级联退激对DR速率系数的影响.其中,级联退激对DR速率系数的贡献必须予以考虑.对双电子复合、辐射复合以及三体复合速率系数做了比较,在温度大于1 eV范围,双电子复合都大于辐射复合以及三体复合速率系数,相应的DR过程对于等离子体离化态分布和能级布居以及光谱模拟都极为重要.对基态和第一激发态的DR速率系数进行了参数拟合,拟合值与计算值的偏差小于1.73%.研究结果将为复杂结构离子双电子复合过程的进一步研究提供参考.     

Enhancement of electron–ion recombination rates at low energy range in the heavy ion storage ring CSRm

Recombination of Ar¹⁴⁺, Ar¹⁵⁺, Ca¹⁶⁺, and Ni¹⁹⁺ ions with electrons has been investigated at low energy range based on the merged-beam method at the main cooler storage ring CSRm in the Institute of Modern Physics, Lanzhou,China. For each ion, the absolute recombination rate coefficients have been measured with electron–ion collision energies from 0 meV to 1000 meV which include the radiative recombination(RR) and also dielectronic recombination(DR)processes. In order to interpret the measured results, RR cross sections were obtained from a modified version of the semiclassical Bethe and Salpeter formula for hydrogenic ions. DR cross sections were calculated by a relativistic configuration interaction method using the flexible atomic code(FAC) and AUTOSTRUCTURE code in this energy range. The calculated RR + DR rate coefficients show a good agreement with the measured value at the collision energy above 100 meV.However, large discrepancies have been found at low energy range especially below 10 meV, and the experimental results show a strong enhancement relative to the theoretical RR rate coefficients. For the electron–ion collision energy below 1 meV, it was found that the experimentally observed recombination rates are higher than the theoretically predicted and fitted rates by a factor of 1.5 to 3.9. The strong dependence of RR rate coefficient enhancement on the charge state of the ions has been found with the scaling rule of q^3.0, reproducing the low-energy recombination enhancement effects found in other previous experiments.     

基于双激发态对稠密等离子体中双电子复合速率系数的研究

讨论了稠密等离子体中双电子复合速率系数的计算方法,推导出了在双激发态间跃迁过程和关于双激发态的碰撞电离和自电离过程的影响下双电子复合速率系数作为关于电子密度函数的计算公式,并以类氖镍离子为例进行了计算.计算结果展示了双电子复合速率系数随电子密度增大的具体变化趋势.此外,还给出了在不同原子过程影响下双电子复合速率系数的数据,并进行了分析.     

Dielectronic recombination at low energy range with Boron-like Ar13+at the CSRm

In order to extend the dielectronic recombination (DR) experiments from the main cooler storage ring CSRm with intermediate charge state ions to the experimental cooler storage ring CSRe with highly charged ions and even radioactive ions, a test electron-ion recombination experiment of B-like Ar¹³⁺ ions was performed with a section of the new electron beam energy detuning system, which will be installed at the CSRe. We present the measured and also the calculated DR spectra for the ∆n = 0 resonances from 0 to 3 eV. The experimental results agree very well with the previous DR experimental data from CRYRING, and the energy resolution reached 30 meV full width at half maximum. This test experiment demonstrates that the reliability and stability of the newly developed electron beam energy detuning system are satisfactory for the upcoming DR experiments at the CSRe. However, we found large discrepancies between the experimental result and the calculation in both resonance positions and the intensities of the recombination spectrum below 0.7 eV, which indicate that precise calculation of the DR spectrum of multielectron ions is still a challenge.     

X-ray spectra simulation of Li-like nickel L-shell Ions

The X-ray emission spectra of nickel plasma were simulated under the collisional radiative model (CRM) by using the flexible atomic code (FAC). The dynamical processes including collisional excitation (CE), radiative recombination (RR), dielectronic recombination (DR), collisional ionization (CI) and resonance excitation were considered in the model, and the rate coefficients of DR, RR as well as CI were consistent with previous results within 15%. It was found that the contributions to spectra from cascades and indirect processes could not be ignored. The intensities of spectral lines for lithium-like nickel L-shell ions are sensitive to the electron temperature. The good agreement between present spectral peaks and earlier observed results can be taken as a measure of the accuracy of the present work.     

DIELECTRONIC RECOMBINATION RATE COEFFICIENTS FOR NEONLIKE IONS

ＤＩＥＬＥＣＴＲＯＮＩＣＲＥＣＯＭＢＩＮＡＴＩＯＮＲＡＴＥＣＯＥＦＦＩＣＩＥＮＴＳＦＯＲＮＥＯＮＬＩＫＥＩＯＮＳＤＩＥＬＥＣＴＲＯＮＩＣＲＥＣＯＭＢＩＮＡＴＩＯＮＲＡＴＥＣＯＥＦＦＩＣＩＥＮＴＳＦＯＲＮＥＯＮＬＩＫＥＩＯＮＳ￥ＺｈａｏＬｉｂｏ；ＬｉＳ...     

类He的Y离子双电子复合计算

采用准相对论的多组态Hartree-Fock(HFR)方法计算了类Li的Y离子(Z=39)的能级和振子强度,并且通过采用扭曲波方法计算自由电子的波函数,我们得到了由类He的基态到类Li的双激发态的自电离几率和双电子复合系数。在计算中,相对论质量—速度和Darwin修正都包含在哈密顿中。为了便于等离子体细致能级占据数密度的动力学计算,我们用一个解析表达式来表示作为自由电子温度函数的双电子复合速率系数,这个表达式精确地描写了从类He的基态到类Li的单激发态的双电子复合。     

高Z等离子体中的双电子复合与电子碰撞激发

 采用准相对论性Hartree-Fock-Relativistic方法与不可分辨跃迁组模型相结合,对Au和Ta元素的类Ni离子的双电子复合速率,以及Au元素类Cu离子的电子碰撞激发速率进行了计算。计算结果表明,对于Au类Ni离子的3d¹⁰-3d⁹4l5f-3d¹⁰4l双电子复合过程以及类Cu离子的3d¹⁰4l-3d⁹4l5f电子碰撞激发过程,当电子温度高于1.0 keV时,电子离子碰撞激发速率随电子温度增加而增加,双电子复合速率随电子温度增加而减小,并且电子碰撞激发对谱线辐射的贡献要比双电子复合大得多。     

类Li氧等离子体光谱模拟

 在FAC程序包中碰撞辐射模型的基础上,模拟出了L壳层的类Li氧等离子体的X射线辐射光谱,其中包括了单、双和三离子模型。经过分析得出,除了碰撞激发以外,级联效应和其它的动力学过程(如：碰撞电离、双电子复合、辐射复合以及共振激发等)对光谱的贡献都是不能被忽略的。并分析了类Li氧等离子体各动力学过程与温度和光谱相对强度之间的关系,分析结果表明X射线光谱的强度能及时响应等离子体温度的变化。     

Ionization equilibrium and radiative energy loss rates for C,N, and O ions in low-density plasmas

The results of calculations of the ionization equilibrium and radiative energy loss rates for C, N and O ions in low-density plasmas are presented for electron temperatures in the range 10⁴–10⁷ °K (～1–10³ eV). The ionization structure is determined using the steady-state corona model, in which electron impact ionization from the ground states is balanced by direct radiative and dielectronic recombination. Using an improved theory, detailed calculations are carried out for the dielectronic recombination rates in which account is taken of all radiative and autoionization processes involving a single-electron electricdipole transition of the recombining ion. The radiative energy loss processes considered are electron-impact excitation of resonance line emission, direct radiative recombination, dielectronic recombination, and electron-ion bremsstrahlung. For all three elements, resonance line emission resulting from 2s?2p transitions produces a broad maximum in the energy loss rate near 10⁵°K(～ 10 eV).     

实验室光致电离等离子体中激发过程的研究

光致电离等离子体在宇宙中广泛存在于强辐射场附近. 近年来随着高能量密度实验装置的发展, 在实验室内也能构造出光致电离等离子体. RCF是一个基于The Flexible Atomic Code 数据的针对光致电离等离子体的辐射碰撞模型, 该模型模拟了两个光致电离实验, 其 理论结果中电离态分布和光谱与测量值符合得很好. 在理论模拟中发现, 光致电离等离子体中光致激发和碰撞激发过程对离子态布居和发射光谱都有非常重要的影响. 光致激发过程可以通过将离子激发到双激发态从而间接电离离子; 碰撞激发过程会因为电子将基态离子激发到电离截面小的单激发态而抑制光子对等离子体的电离. 光致激发过程可以加强类锂离子的类氦离子的卫线, 而碰撞激发过程会影响类氦离子谱线的线强之比.     

W44+ 离子双电子复合速率系数的理论研究

利用全相对论组态相互作用方法,详细研究了W44+ 离子从基组态3s23p63d104s2俘获一个电子形成双激发态(3s23p63d104s2)nln′l′(n = 4 ~ 6,n′= 4 ~7) 的双电子复合(DR) 过程。通过比较不同壳层电子激发的DR 速率系数,得知4s 电子激发和3d 电子激发的DR 速率系数分别在低温和中高温度时给出了主要贡献,得到了主要的电子激发DR通道。在1 eV~50 keV 温度范围内,计算了n = 4~18 的DR速率系数,并外推到了n= 100,得到总DR 速率系数。比较总DR 速率系数、三体复合(TBR) 以及辐射复合(RR) 速率系数,结果表明DR 速率系数在研究的温度范围内远大于TBR 和RR 速率系数,其将明显地影响ITER 等离子体的电离平衡和离化态布居。Based on the fully relativistic configuration interaction method, theoretical calculations are carried out to research the dielectronic recombination (DR) processes, in which W44+ ions in the ground state 3s23p63d104s2 trap an electron to form doubly excited states (3s23p63d104s2)nln’l’(n =4~6,n′= 4~7). The comparison of the DR rate coefficients of different shells shows that DR approach is as follow: the 4s subshell excitation dominates to DR at low temperature, but 3d subshell excitation attributes to DR at high temperature. Total DR rate coefficients from n=4~18 are evaluated directly, and the results are extrapolated up to n = 100 in the temperature range from 1 to 5×104 eV, and thus get the total DR rate coefficients. Compared total DR rate coefficients to three-body recombination (TBR) rate coefficients and radiative recombination (RR) rate coefficients, it showed that the total DR rate coefficients obviously significantly greater than other two recombination rate coefficients, and thus it obviously influence ionization equilibrium and ionization state population of ITER plasma.     

Recent dielectronic recombination experiments

New recombination experiments with merged cold beams of electrons and atomic ions have been carried out at the storage ring facilities TSR in Heidelberg, ESR in Darmstadt, and CRYRING in Stockholm. A brief overview is given on the recent activities in which the Giessen group was engaged. Topics of this research were dielectronic recombination (DR) of astrophysically relevant ions, recombination of highly charged ions with respect to cooling losses in storage rings, field effects on DR, search for interference effects in photorecombination of ions, correlation effects in DR of low-Z ions, spectroscopy of high-Z ions by DR, and lifetimes of metastable states deduced from DR experiments. This revised version was published online in July 2006 with corrections to the Cover Date.     

高离化金和铅离子双电子复合速率研究

 基于多组态准相对论自洽场方法和扭曲波方法,理论研究了类铍金和 铅离子三类双电子复合过程,计算了这些离子在电子温度0.6～10.0keV范围内的双电子复合速率系数,并讨论了它们随电子温度、复合类型及原子序数的变化。     

The KLL dielectronic recombination processes for highly charged krypton, iodine and barium ions

The KLL dielectronic recombination (DR) processes of ions from highly charged helium-like to oxygen-like krypton, iodine and barium ions are studied systematically in the relativistic distorted-wave approximation with configuration interaction. The KLL DR resonant energies, the corresponding resonant strengths and the theoretical spectra for each highly charged ion species are obtained. The results accord well with other available values. The behaviour of KLL resonant strengths for He-like ions with atomic number Z is analysed.     

Dielectronic recombination and related resonance processes

We review recent progress in understanding of the atomic process known as dielectronic recombination (DR). Currently applied schemes for the calculation of DR cross sections and rate coefficients are described in detail. Methods of dealing with such problems as cascade correction, configuration interaction, and angular momentum coupling are considered. Both two-electron and multi-electron systems are treated. Results obtained by these methods are presented for ions of the He, Li, B, F, Na, Mg, and K isoelectronic sequences. Other results are referenced. Semiempirical formulas for DR rate coefficients are discussed. The recently discovered electric field effect in DR is described. The connection to DR of other resonance processes such as photo-Auger ionization, resonance transfer excitation, and resonance excitation is explained.     

Re30+离子双电子复合速率系数的理论研究

复杂结构离子的双电子复合速率系数在极紫外光刻光源、核聚变等应用研究的等离子体光谱模拟和诊断中具有重要的应用价值。利用全相对论组态相互作用方法,详细计算了基组态为4p64d9的Re30+离子经双激发态（4p64d9）-1nln'l'（n=4~6,n'=4~23）的双电子复合（DR）过程。研究分析了激发、辐射通道,组态相互作用,级联退激对DR速率系数的影响。其中内壳层4p电子激发的DR速率系数是总DR速率系数的28.2%~44.9%,所以内壳层4p电子激发的贡献不可以忽略。级联退激对DR速率系数的最大贡献为12.9%,也必须要予以考虑。通过对双电子复合、辐射复合、以及三体复合速率系数的比较,辐射复合速率系数的最大值为DR速率系数的22.6%,三体复合速率系数的最大值仅为DR速率系数的0.3%。因此,DR速率系数远远大于辐射复合和三体复合速率系数。该结果表明DR过程对于等离子体离化态分布、能级布居以及光谱模拟都极为重要。为了方便应用,对基态和第一激发态的总DR速率系数进行了参数拟合。该研究结果将为Re激光等离子体的光谱模拟及复杂结构离子DR过程的进一步研究提供参考。Dielectronic recombination (DR) rate coefficients of complex ions are very important in some application research, such as extreme ultraviolet lithography and nuclear fusion. Based on the fully relativistic configuration interaction method, theoretical calculations are carried out to research the DR processes, in which Re30+ ions in the ground state 4p64d9 to (4p64d9)-1nln'l'(n=4~6, n'=4~23). Influence of excitation and radiation channels, configuration interaction, the effect of decays to autoionizing levels possibly followed by radiative cascades (DAC) are analyzed. The contributions through 4p subshell excitations to the total rate coefficient are 28.2%~44.9% in the whole temperature region. Hence the contributions from inner-shell electron excitation are very important. The contributions from the DAC transitions increase smoothly with the increasing temperature and are about 12.9% at 50 000 eV. The contributions of DAC can not be neglected. By means of compared total DR rate coefficients to radiative recombination rate coefficients and three-body recombination rate coefficients, it shows that the maximum value of the radiation recombination rate coefficient is 22.6% of the DR rate coefficient and the maximum value of the three-body recombination rate coefficient is only 0.3% of the DR rate coefficient. The total DR rate coefficient is greater than either the radiative recombination or three-body recombination coefficients in the whole temperature range. The corresponding DR process is very important for plasma ionization distribution, population level and spectrum simulation. In addition to facilitate the application, the total DR rate coefficients for the ground state and the first excited state are fitted to an empirical formula. These results will provide the reference for the further analyses of rhenium laser plasma spectrum simulation and the complex structures ions DR process.     

Dielectronic Recombination of Sn^10＋ Ions and Related Satellite Spectra

Based on the multi-configuration Dirac-Fock method, theoretical calculations are carried out for the dielectronic recombination （DR） rate coefficients and the collision excitation rate coefficients of Sn^10＋ ions. It is found that the total DR rate coefficient has its maximum value between 10eV and 100eV and is greater than either the radiative recombination or three-body recombination rate coefficients （the number of free electrons per unit is 10^21 cm^3） for the ease of Te 〉 1 eV. Therefore, DR can strongly influence the ionization balance of laser produced multi-charged tin ions. The related dieleetronie satellite cannot be ignored at low temperature Te 〈 5 eV.