Analysis of the fractal intrinsic quality in the ionization of Rydberg helium and lithium atoms

We study the fractal rhythm in the ionization of Rydberg helium and lithium atoms in an electric field by using the semiclassical method. The fractal structures present a nested relationship layer by layer in the initial launch angles of the ionized electrons versus the escape time, which is defined as the rhythm attractor, and exhibit similar rhythm endings. The gradually enhanced chaotic regions of the escape time plots tend to broaden as the scaled energy increases. In addition,the fractal rhythm changes synchronously with the oscillations of the kinetic energy spectrum. We note that the intrinsic quality of the fractal rhythm is closely related to the kinetic energy distribution, that is, the inherent dynamic properties of the Hamiltonian equations have an impact on the fractal regularities. In addition, different ionizing closed trajectories exhibit iterate properties and the inherent beauty of symmetry. Our results and analysis can not only reveal new laws in the ionization of Rydberg atoms, but also promote the establishment of the dynamic mechanism of fractals.     

平行电磁场中里德堡氢原子的自相似结构研究

利用半经典方法研究了平行电磁场中里德堡氢原子的分形自相似现象. 通过研究平行电磁场中里德堡氢原子的逃逸时间和初始出射角间的关系, 发现了逃逸时间图的自相似结构, 并通过研究与图中冰柱对应的逃逸轨道, 得到了自相似结构和逃逸轨道之间的关系, 发现了该类自相似逃逸轨道满足的规律. 进一步研究了标度能量和标度磁场对体系动力学的影响, 表明标度能量和标度磁场均控制体系的分形自相似结构. 当标度能量或标度磁场比较小时, 没有自相似现象, 随着标度能量或标度磁场的增大, 自相似出现, 体系变复杂.     

Semiclassical calculation of ionisation rate for Rydberg helium atoms in an electric field

The ionisation of Rydberg helium atoms in an electric field above the classical ionisation threshold has been examined using the semiclassical method, with particular emphasis on discussing the influence of the core scattering on the escape dynamics of electrons. The results show that the Rydberg helium atoms ionise by emitting a train of electron pulses. Unlike the case of the ionisation of Rydberg hydrogen atom in parallel electric and magnetic fields, where the pulses of the electron are caused by the external magnetic field, the pulse trains for Rydberg helium atoms are created through core scattering. Each peak in the ionisation rate corresponds to the contribution of one core-scattered combination trajectory. This fact further illustrates that the ionic core scattering leads to the chaotic property of the Rydberg helium atom in external fields. Our studies provide a simple explanation for the escape dynamics in the ionisation of nonhydrogenic atoms in external fields.     

The fractal structure in the ionization dynamics of Rydberg lithium atoms in a static electric field

The ionization rate of Rydberg lithium atoms in a static electric field is examined within semiclassical theory which involves scattering effects off the core. By semiclassical analysis, this ionization process can be considered as the promoted valence electrons escaping through the Stark saddle point into the ionization channels. The resulting escape spectrum of the ejected electrons demonstrates a remarkable irregular electron pulse train in time-dependence and a complicated nesting structure with respect to the initial launching angles. Based on the Poincaré} map and homoclinic tangle approach, the chaotic behaviour along with its corresponding fractal self-similar structure of the ionization spectra are analysed in detail. Our work is significant for understanding the quantum-classical correspondence.     

Semiclassical calculation of ionization rate for Rydberg hydrogen atoms near a metal surface

The ionization of Rydberg hydrogen atoms near a metal surface at different scaled energies above the classical saddle point energy has been discussed by using the semiclassical method. The results show that the atoms ionize by emitting a train of electron pulses. In order to reveal the chaotic and escape dynamical properties of this system in detail, the sensitive dependence of the ionization rate upon the scaled energy is discussed. As the scaled energy is close to the saddle point energy, the ionization process of the hydrogen atom is nearly the same as the case of hydrogen atom in an electric field. There is only a single pulse of electrons, with an exponentially decaying tail. With the increase of the scaled energy, the ionization rates are similar to the case of the hydrogen atom in parallel electric and magnetic field, a series of electron pulses appear in the ionization process. This is caused by classical chaos, which occurs for the metal surface. Our studies also suggest that the metal surface can play the role of both the electric and the magnetic fields. Our theoretical analysis will be useful for guiding experimental studies of the ionization of atoms near the metal surface.     

The chaotic property in the autoionization of Rydberg lithium atom

This paper presents theoretical computations of the ionization rate of Rydberg lithium atom above the classical ionization threshold using semiclassical approximation. The yielded random pulse trains of the escape electrons are recorded as a function of emission time such that they can be related to the terms of the recurrence periods of the photoabsorption. This fact illustrates that it is ionic core scattering processes which give rise to chaos in autoionization dynamics and this is verified by comparison of our results with the hydrogen atom situation. In order to reveal the chaotic properties in detail, the sensitive dependence of the ionization rate upon the scaled energy is discussed for different scaled energies. This approach provides a simple explanation for the chaotic character in autoionization decay of Rydberg alkali-metal atoms.     

Semiclassical Calculations of Autoionization Rate for Lithium Atoms in Parallel Electric and Magnetic Fields

By using a semiclassical method, we present theoretical computations of the ionization rate of Rydberg lithium atoms in parallel electric and magnetic fields with different scaled energies above the classical saddle point. The yielded irregular pulse trains of the escape electrons are recorded as a function of emission time, which allows for relating themselves to the terms of the recurrence periods of the photoabsorption. This fact turns to illustrate the dynamic mechanism how the electron pulses are stochastically generated. Comparing our computations with previous investigation results, we can deduce that the complicated chaos under consideration here consists of two kinds of seff-similar fractal structures which correspond to the contributions of the applied magnetic feld and the core scattering events. Furthermore, the effect of the magnetic field plays a major role in the profile of the autoionization rate curves, while the contribution of the core scattering is critical for specifying the positions of the pulse peaks.     

Photoionization microscopy of hydrogen atom near a metal surface

We have studied the ionization of Rydberg hydrogen atom near a metal surface with a semiclassical analysis of photoionization microscopy. Interference patterns of the electron radial distribution are calculated at different scaled energies above the classical saddle point and at various atom-surface distances. We find that different types of trajectories contribute predominantly to different manifolds in a certain interference pattern. As the scaled energy increases, the structure of the interference pattern evolves smoothly and more types of trajectories emerge. As the atom approaches the metal surface closer, there are more types of trajectories contributing to the interference pattern as well. When the Rydberg atom comes very close to the metal surface or the scaled energy approaches the zero field ionization energy, the potential induced by the metal surface will make atomic system chaotic. The results also show that atoms near a metal surface exhibit similar properties like the atoms in the parallel electric and magnetic fields.     

氦气空心阴极放电动力学过程的模拟研究

利用流体模型模拟研究了氦气空心阴极放电的时空动力学过程,计算得到了不同放电时刻电子和亚稳态氦原子密度、电势、电场、基态电离速率和分步电离速率等的时空分布特性。特别是讨论了亚稳态原子和分步电离对于放电的影响。结果表明,随着电流的增长,放电处于五个不同的放电模式:第一阶段电流上升非常缓慢,为汤生放电模式,带电粒子密度、亚稳态原子密度和径向电场均很弱;第二阶段电流迅速上升,放电模式由汤生放电向空心阴极放电过渡,带电粒子密度、亚稳态原子密度和径向电场迅速增强;第三阶段达到准稳态阶段,放电电流增长速度变缓,形成了明显的阴极鞘层结构;第四阶段为空心阴极效应形成阶段,向稳态阶段过渡;第五阶段为稳态放电阶段。研究结果同时表明,亚稳态氦原子和分步电离在放电的初始阶段对于放电的发展作用较弱,在前三阶段中,电子的产生以基态电离为主。随着放电的发展,由亚稳态原子引起的分步电离对新的电子产生的作用逐渐接近并超过基态电离,对总电离的贡献率越来越高。     

铯47D精细能级超冷里德堡原子自由演化的动力学研究

用连续窄线宽激光器将超冷铯里德堡原子分别激发到47D_3/2, 47D_5/2精细态, 观察了处于里德堡精细态的铯原子向超冷铯等离子体自由演化的过程, 详细对比了不同精细态的铯里德堡原子预电离时间、电离速率以及等离子体的转化效率. 将里德堡原子快速转化为等离子体的过程解释为局域势阱内由预电离产生的电子与里德堡原子的快速碰撞导致的雪崩电离.     

Chaos-induced pulse trains in the ionization of hydrogen

We predict that a hydrogen atom in parallel electric and magnetic fields, excited by a short laser pulse to an energy above the classical saddle, ionizes via a train of electron pulses. These pulses are a consequence of classical chaos induced by the magnetic field. We connect the structure of this pulse train (e.g., pulse size and spacing) to fractal structure in the classical dynamics. This structure displays a weak self-similarity, which we call "epistrophic self-similarity." We demonstrate how this self-similarity is reflected in the pulse train.     

Magnetic field-aligned plasma expansion in critical ionizationvelocity space experiments

The temporal evolution of a plasma cloud released in an ambient plasma is studied. Time-dependent Vlasov equations for both electrons and ions, as well as the self-consistent electric field parallel to the ambient magnetic field, are solved. The initial cloud is considered to consist of cold, warm, and hot electrons with temperatures of approximately 0.2 eV, 2 eV, and 10 eV, respectively. It is found that the minor hot electrons escape the cloud; their velocity distribution function shows the typical time-of-flight dispersion feature, i.e. the average drift velocity of the escaping electrons is proportional to the distance from the cloud. The major warm electrons expand along the magnetic field lines with the corresponding ion-acoustic speed. The combined effect of the escaping hot electrons and the expanding warm ones sets up an electric potential structure that accelerates the ambient electrons into the cloud. Thus, the energy loss due to the electron escape is partly replenished. The electric field distribution in the potential structure depends on the stage of the evolution; before the rarefaction waves propagating from the edges of the cloud reach its center, the electric fields point into the cloud. After this stage the cloud divides into two subclouds, each having its own bipolar electric field. The effects of collisions on the evolution of plasma clouds are also discussed. The relevance of the results seen from the calculations are discussed in the context of space experiments on critical ionization velocity     

Microwave spectroscopy of the Zeeman effect in Rydberg atoms of sodium

Experimental results of studying the spectrum of the microwave 37P-37S transition of Rydberg sodium atoms in a weak magnetic field (≤7 G) are reported. The populations of the Rydberg states were measured using the method of selective ionization with a pulsed electric field. When the magnetic field was parallel to the ionizing electric field, a good agreement between the calculated and experimental spectral shapes was observed, making it possible to determine the unknown polarization of the microwave radiation. In the case of the orthogonal configuration of the fields, the resonance structure was suppressed in the field ionization signals due to the strong influence of the magnetic field on the electron trajectories in the detection system.     

Transition state theory without time-reversal symmetry: chaotic ionization of the hydrogen atom

We present the first application of transition state theory to a system that evolves from an initial to a final state without time-reversal symmetry. The problem studied is the chaotic ionization of a hydrogen atom in crossed electric and magnetic fields. The stable manifolds of the transition state reveal a fractal tiling which connects the geometrical properties of the tiling to the ionization rate, leading to a theoretical explanation for the computational and experimental observation of "prompt" and "delayed" electrons in this problem.     

Recombination during expansion of ultracold plasma

Signals of ultracold plasma are observed by two-photon ionization of laser-cooled caesium atoms in a magneto-optical trap. Recombination of ions and electrons into Rydberg atoms during the expansion of ultracold plasma is investigated by using state-selective field ionization spectroscopy. The dependences of recombination on initial electron temperature (1--70 K) and initial ion density ($ \sim $10$^{10}$ cm$^{ - 3})$ are investigated. The measured dependence on initial ion density is $N^{1.547\pm 0.004}$ at a delay time of 5 $\mu $s. The recombination rate rapidly declines as initial electron temperature increases when delay time is increased. The distributions of Rydberg atoms on different values of principal quantum number $n$, i.e. $n=30$--60, at an initial electron temperature of 3.3 K are also investigated. The main experimental results are approximately explained by the three-body recombination theory.     

Ionization of fast rydberg atoms in longitudinal and transverse electric fields

The main properties of longitudinal and transverse electric field ionizers for fast Rydberg atoms n=21–40 have been investigated. The dispersion and the background due to collisional processes between fast atoms and residual gas molecules have been measured and calculated. The kinetic energy spread of ions formed by field ionization of Rydberg atoms and their trajectories have been calculated. The potassium beam energy was 3.9 keV.     

Inelastic electron collisions with Rydberg atoms

The standard classical method of computer simulation is used for evaluation of the inelastic cross section in electron collisions with a highly excited (Rydberg) atom. In the course of collision, the incident and bound electrons move along classical trajectories in the Coulomb field of the nucleus, and the scattering parameters are averaged over many initial conditions. The reduced ionization cross section of a Rydberg atom by electron impact approximately corresponds to that of atoms in the ground states with valence s-electrons and coincides with the results of the previous Monte Carlo calculations. The cross section of an atom transition between Rydberg atom states as a result of electron impact is used for finding the stepwise ionization rate constant of atoms in collisions with electrons or the rate constant of three-body electron-ion recombination in a dense ionized gas because these processes are determined by kinetics of highly excited atom states. Surprisingly, the low-temperature limit of electron temperatures is realized when the electron thermal energy is lower than the atom ionization potential by about three orders of magnitude, as follows from the kinetics of excited atom states. The article is published in the original.     

二维Hénon-Heiles势及其变形势体系逃逸率与分形维数的研究

采用Chin和Chen的动力学算法追踪粒子在体系中的运动情况, 首次研究并对比了粒子在Hénon-Heiles体系与变形Hénon-Heiles六边形体系中的混沌逃逸规律, 在Hénon-Heiles体系中, 对于不同能量范围, 分形维数与逃逸率随能量而改变, 但在变形Hénon-Heiles六边形体系中, 仅在低能区分形维数与逃逸率随能量的改变而变化, 而高能区逃逸率和分形维数趋于稳定值. 并且得到普遍规律, 即不同混沌体系中粒子的混沌逃逸率和粒子逃逸的分形维数呈现较强的线性相关性. 因而分形维数可以作为工具研究混沌体系中粒子的逃逸规律, 在介观器件设计中可以通过研究混沌电子器件的分形维数来表征粒子在器件中的传输行为.     

Ba Rydberg原子M = 0电场常数标度能谱

选择激光偏振方向，同步改变激发激光的波长(即原子的激发能量E）和外加电场强度 F，使标度能ε=E/F保持为常数，得到了原子束中Ba Rydberg原子在标度 能ε=-300时M=0激发的常数标度能谱.由实验标度能谱的Fourier变换得到的回 归谱与氢的均匀化近似后的闭合轨道理论计算相比较，发现实验回归谱的峰值位置与理论计 算符合较好，而峰值强度则与理论相差较大，分析认为是由于受到核散射和双电子微扰态的 影响所致. 关键词： 标度能谱 闭合轨道理论