Study of a compact external magnetic field radial split-cavity oscillator

With the experiment result analyses of a coaxial virtual cathode oscillator (CVCO), a new kind of compact radial split cavity oscillator (RSCO) is presented in this paper. On the oscillator, a low resistance tube is formed by using the diode structure of a CVCO, and a radial split-cavity structure is formed by several meshes that cause the electronic beam to transmit. Calculating all kinds of parameter, at the input parameter 350 kV, 27 kA, the numerical simulation results show that the average output microwave power is about 4.0 GW, the microwave frequency is 1.37 GHz, and the electronic efficiency is 42.3%.     

同调谐振子的变形

实现了在保持本征值谱结构不变情况下同调谐振子的几种变形.这些变形包括三维各向同性谐振子径向方程、开普勒径向方程、Morse势s态等问题.每一个变形体系对应着同调参量g的确定取值.同调谐振子有一定的普遍适应性,具有丰富的内容. 关键词： 同调谐振子 同调参量 产生算符 湮没算符     

径向三腔渡越时间振荡器数值模拟

 基于渡越辐射机理结合径向结构的低阻抗特性,提出了一种新型的低阻抗高功率微波器件——径向三腔渡越时间振荡器,它由3个等间距的边耦合同轴腔组成,径向运动电子束与谐振腔中的角向均匀模式场相互作用。采用PIC粒子模拟程序进行了模拟研究。在电子束能量450 keV、束流60 kA且无外加引导磁场的条件下,当结构参数网长为4.8 cm,腔间距为1.4 cm,电子发射面为0.8 cm,内径为8 cm时,获得了平均功率7.4 GW,频率4.1 GHz的微波输出,效率达27.4%,阻抗7.5 Ω。通过粒子模拟给出了束波互作用效率随电子束电压、电流以及谐振腔间距的变化曲线,电子束电压对输出微波频率的影响曲线以及不同谐振频率与最佳谐振腔间距的对应曲线,这些曲线表明该器件具有渡越时间效应的基本特征,属于渡越辐射器件,且具有对电子束质量要求不高的特点。     

Radial coherent states—From the harmonic oscillator to the hydrogen atom

We construct spectrum generating algebras of SO(2, 1) ～ SU(1, 1) in arbitrary dimension for the isotropic harmonic oscillator and the Sturm-Coulomb problem in radial coordinates. Using these algebras, we construct the associated radial Barut-Girardello coherent states for the isotropic harmonic oscillator (in arbitrary dimension). We map these states into the Sturm-Coulomb radial coherent states and show that they evolve in a fictitious time parameter without dispersing.     

Shell structure in nuclei

A review of shell structure for spherical and a variety of deformed nuclei is presented. The microscopic-macroscopic method of Strutinsky is used to calculate potential energy surfaces with the pure harmonic oscillator and the modified harmonic oscillator. New sets of “magic numbers” for a variety of different prolate, oblate and axially asymmetric shapes are generated. Experimental evidence for the special stability caused by these shell effects is presented with special emphasis on the lightest and heaviest nuclei where the effects are most pronounced. The radial diffuseness parameter is treated as a Strutinsky variable and its significance in extrapolating into the superheavy region considered. The calculation of shell effects for high spin states is also reviewed.     

Analytic radial dependence of diatomic electronic structure constants in terms of the vibration-rotation spectroscopic data

A direct procedure is proposed for investigating the internuclear distance dependence of diatomic structure constants (fine structure, spin rotation, etc.) from the vibration-rotation spectroscopic data. Starting from previous results concerning an elaborate solution of the anharmonic oscillator model wave equation, analytic relations are obtained allowing the determination of the radial form of any electronic parameter in terms of the measured values of its associated vibrational and first centrifugal distortion constants or, alternatively, of its vibrational constants alone. These relations are valid for any electronic state. Several applications are considered and discussed.     

一种新型径向三腔同轴虚阴极振荡器全三维粒子模拟研究

提出了一种新型径向三腔同轴虚阴极振荡器,并进行了数值模拟研究. 研究表明: 这种径向三腔结构在束波转换面进行电场调制,能够大幅提高束波转换效率;同时,由阳极栅网和径向三腔结构构成的谐振装置能有效地抑制模式竞争;另外,由于采用了同轴引出结构,在提高能量引出的同时还能有效吸收漂移管中被利用过的电子,因此这种新型虚阴极振荡器能够获得较高的输出功率. 模拟的电子束电压为400 kV,电流为50 kA,主频为4.5 GHz,峰值功率达到6 GW,平均输出功率为3.1 GW,束波转换效率达到15%. 关键词： 高功率微波 同轴虚阴极振荡器 粒子模拟 束波转换效率     

新型高功率虚阴极径向反射速调管振荡器

 提出了一种新型的高功率虚阴极径向反射速调管振荡器,它结合了虚阴极振荡器容易起振和速调管微波产生效率较高的特点。利用虚阴极反射电子束对调制腔的正反馈,可以减小起振电流和起振时间,而且提高了微波产生效率。它是一种结构简单、紧凑的器件。用2.5维PIC程序对这种器件进行了数值模拟研究。得到的数值模拟结果表明,输入电压620 kV,电流25 kA,输出微波周期平均功率为2.5 GW。虚阴极振荡频率被锁定,频率为1.25 GHz。     

On the eigenvalues of the rotating harmonic oscillator

The eigenvalues of the radial Schrödinger equation of a rotating harmonic oscillator depending on a parameter α > 0 are shown to be independent of α and equal to integers.     

高效强流径向分离腔振荡器研究

根据同轴虚阴极的结构特点,提出了一种紧凑型径向分离腔振荡器,该径向分离腔的特点是输入电子束的电流可以很大,从而可以得到较高的微波输出功率. 综合考虑影响微波输出的各种因素,在电子束为410kV,电流为35kA的条件下,模拟得到的平均功率大于50GW,频率为146GHz,电子束功率效率达到348%. 关键词： 径向分离腔 高功率微波 同轴虚阴极 电子束分布     

新型径向三腔同轴虚阴极振荡器的模拟研究

 提出了一种新型的径向三腔同轴虚阴极振荡器，并对其进行了理论分析和数值模拟。这种虚阴极振荡器采用径向三腔结构，通过改变束-波互作用区的电场分布来提高电子束与TM₀₁模式的耦合效率，并通过采用准谐振腔的结构来进一步抑制模式竞争以获得较高的输出微波增益。同时采用能量同轴提取的方式进一步提高器件的功率和效率。粒子模拟结果表明，在二极管电压400 kV，束流50 kA的条件下，径向三腔同轴虚阴极振荡器在4.14 GHz处获得了平均功率约2.45 GW的微波输出，功率转换效率达到12％。输出微波模式纯度较高，频谱非常窄。     

Barut-Girardello Coherent States for Nonlinear Oscillator with Position-Dependent Mass

Using ladder operators for the non-linear oscillator with position-dependent effective mass, realization of the dynamic group SU(1,1) is presented. Keeping in view the algebraic structure of the non-linear oscillator, coherent states are constructed using Barut-Girardello formalism and their basic properties are discussed. Furthermore, the statistical properties of these states are investigated by means of Mandel parameter and second order correlation function. Moreover, it is shown that in the harmonic limit, all the results obtained for the non-linear oscillator with spatially varying mass reduce to corresponding results of the linear oscillator with constant mass.     

Quantum entanglement and squeezing in coupled harmonic and anharmonic oscillator systems

We investigate the fundamental connection between quadrature squeezing and continuous variable entanglement within a general class of two-coupled oscillator systems. We determine the quantitative relationship between them through the squeezing parameter and the entanglement entropy of the lowest energy eigenstate of the coupled oscillator systems numerically. Unlike the relation between entanglement and uncertainty product, we found that this relationship is, by no means, the same for the whole class of coupled oscillator systems: to a large extent it depends on the order and strength of the anharmonic potential, which implies that knowledge of the anharmonic potential of the coupled oscillator system is required before one can characterize the degree of entanglement through the squeezing parameter. Our results reveal that a more effective approach to enhance squeezing is to adjust the anharmonicity of the system potential, instead of increasing the quantum correlations between the oscillators. In addition, by probing into a quantum catastrophe model, we uncover transitions in the entanglement entropy and squeezing relation as the potential changes from a single well to a triple well, and then a double-well structure. The transitions appear through distinct entropy–squeezing relation, with a multi-well structure displaying a larger change in the antisqueezing behavior of the position quadrature than the single-well structure, for the same change in the entanglement entropy.     

氦原子自旋-其它轨道相互作用精细结构参数的理论计算

以多电子原子精细结构哈密顿的球张量形式和氦原子非相对论性能级结构理论为基础,借助不可约张量理论,建立了计算氦原子自旋-其它轨道相互作用精细结构参数的一种解析理论形式.完成了所有的角向积分和自旋求和计算,自旋-其它轨道相互作用精细结构参数最终用若干个径向积分来表示.以氦原子(1s2p)3P态为例,借用类氢形式的径向函数对这些径向积分进行了近似计算.计算结果表明:在氦原子的精细结构中,自旋-其它轨道相互作用与纯自旋-轨道相互作用的作用效果相反;在总自旋-轨道相互作用精细结构参数中,自旋-其它轨道相互作用起决定性作用,它决定着精细结构分裂的顺序.     

一类非谐振模型势径向平均值的解析表达式及其递推关系

获得了一类非谐振模型势，即环形非球谐振子、非球谐振子和环形振子径向平均值的两个递推关系.给出了这些非谐振模型势的部分径向幂次平均值的解析表达式. 关键词： 环形非球谐振子 非球谐振子 环形振子 径向平均值 解析表达式 递推关系     

The 2D Kramers–Dirac oscillator

The Dirac oscillator was initially introduced as a Dirac operator which is linear in momentum and coordinate variables. In contrast to the usual 2D Dirac oscillator, the 2D Kramers–Dirac oscillator admits the time-reversal symmetry, which is a reason for the present nomenclature. It is shown that there exists a family of eigenstates associated with an eigenvalue linear in the control parameter, and the eigenvalue in question goes down from positive values to negative values as the parameter varies in the positive direction. The other eigenvalues are broken up into two bands, positive and negative. The 2D Dirac and the 2D Kramers–Dirac oscillators are compared in their physical grounds and in their spectral structure from the viewpoint of the time-reversal symmetry.     

Blind parameter estimation of pseudo-random binary code-linear frequency modulation signal based on Duffing oscillator at low SNR

Conventional parameter estimation methods for pseudo-random binary code-linear frequency modulation(PRBCLFM) signals require prior knowledge, are computationally complex, and exhibit poor performance at low signal-to-noise ratios(SNRs). To overcome these problems, a blind parameter estimation method based on a Duffing oscillator array is proposed. A new relationship formula among the state of the Duffing oscillator, the pseudo-random sequence of the PRBC-LFM signal, and the frequency difference between the PRBC-LFM signal and the periodic driving force signal of the Duffing oscillator is derived, providing the theoretical basis for blind parameter estimation. Methods based on amplitude method, short-time Fourier transform method, and power spectrum entropy method are used to binarize the output of the Duffing oscillator array, and their performance is compared. The pseudo-random sequence is estimated using Duffing oscillator array synchronization, and the carrier frequency parameters are obtained by the relational expressions and characteristics of the difference frequency. Simulation results show that this blind estimation method overcomes limitations in prior knowledge and maintains good parameter estimation performance up to an SNR of-35 d B.     

Spectroscopy of a driven solid-state qubit coupled to a structured environment

We study the asymptotic dynamics of a driven spin-boson system where the environment is formed by a broadened localized mode. Upon exploiting an exact mapping, an equivalent formulation of the problem in terms of a quantum two-state system (qubit) coupled to a harmonic oscillator which is itself Ohmically damped, is found. We calculate the asymptotic population difference of the two states in two complementary parameter regimes. For weak damping and low temperature, a perturbative Floquet-Born-Markovian master equation for the qubit-oscillator system can be solved. We find multi-photon resonances corresponding to transitions in the coupled quantum system and calculate their line-shape analytically. In the complementary parameter regime of strong damping and/or high temperatures, non-perturbative real-time path integral techniques yield analytic results for the resonance line shape. In both regimes, we find very good agreement with exact results obtained from a numerical real-time path-integral approach. Finally, we show for the case of strong detuning between qubit and oscillator that the width of the n-photon resonance scales with the nth Bessel function of the driving strength in the weak-damping regime.     

Studies on the 3D confined potentials using generalized pseudospectral approach

In presence of the spherically confined three-dimensional potentials with impenetrable boundaries, the generalized pseudospectral method is shown to provide accurate eigenvalues, eigenfunctions, and radial expectation values for (a) the isotropic harmonic oscillator, (b) the H atom and (c) the Davidson oscillator. Several novel degeneracy conditions are obtained for (a) when the radius of confinement is suitably chosen at the radial nodes corresponding to the free states.     

Exact solutions of the Klein—Gordon equation with ring-shaped oscillator potential by using the Laplace integral transform

We present exact solutions for the Klein-Gordon equation with a ring-shaped oscillator potential. The energy eigenvalues and the normalized wave functions are obtained for a particle in the presence of non-central oscillator potential. The angular functions are expressed in terms of the hypergeometric functions. The radial eigenfunctions have been obtained by using the Laplace integral transform. By means of the Laplace transform method, which is efficient and simple, the radial Klein-Gordon equation is reduced to a first-order differential equation.