Landau damping of electrons with bouncing motion in a radio-frequency plasma

One-dimensional particle simulations have been conducted to study the interaction between a radio-frequency electrostatic wave and electrons with bouncing motion. It is shown that bounce resonance heating can occur at the first few harmonics of the bounce frequency (nω_b,n=1,2,3,...). In the parameter regimes in which bounce resonance overlaps with Landau resonance, the higher harmonic bounce resonance may accelerate electrons at the velocity much lower than the wave phase velocity to Landau resonance region, enhancing Landau damping of the wave. Meanwhile, Landau resonance can increase the number of electrons in the lower harmonic bounce resonance region. Thus electrons can be efficiently heated. The result might be applicable for collisionless electron heating in low-temperature plasma discharges.     

Analytic solutions of the ground and excited states of the spin-weighted spheroidal equation in the case of s=2

By using the super-symmetric quantum mechanics (SUSYQM) method, this paper obtains the analytical solutions for the spin-weighted spheroidal wave equation in the case of s = 2. Based on the derived W 0 to W 4 the general form for the n-th-order super-potential is summarized and is proved correct by mathematical induction. Hence the ground eigenvalue problem is completely solved. Particularly, the novel solutions of the excited state are investigated according to the shape-invariance property.     

Ground eigenvalue and eigenfunction of a spin-weighted spheroidal wave equation in low frequencies

Spin-weighted spheroidal wave functions play an important role in the study of the linear stability of rotating Kerr black holes and are studied by the perturbation method in supersymmetric quantum mechanics.Their analytic ground eigenvalues and eigenfunctions are obtained by means of a series in low frequency.The ground eigenvalue and eigenfunction for small complex frequencies are numerically determined.     

Low frequency asymptotics for the spin-weighted spheroidal equation in the case of s=1/2

The spin-weighted spheroidal equation in the case of s=1/2 is thoroughly studied by using the perturbation method from the supersymmetric quantum mechanics.The first-five terms of the superpotential in the series of parameter β are given.The general form for the n-th term of the superpotential is also obtained,which could also be derived from the previous terms W k,k < n.From these results,it is easy to obtain the ground eigenfunction of the equation.Furthermore,the shape-invariance property in the series of parameter β is investigated and is proven to be kept.This nice property guarantees that the excited eigenfunctions in the series form can be obtained from the ground eigenfunction by using the method from the supersymmetric quantum mechanics.We show the perturbation method in supersymmetric quantum mechanics could completely solve the spin-weight spheroidal wave equations in the series form of the small parameter β.     

Gyromonotron with an axial combining periodic magnetic field

On the base of the reference (1), making use of the linear kinetic theory, gyromonotron with an axial combining periodic magnetic field has been analysed in detail. The formulas of electron beam to wave interaction power, frequency shift and starting current, etc. have been derived.     

原子力显微镜探针悬臂几何结构变化对高次谐波信息增强的研究

轻敲模式原子力显微镜高次谐波信号包含待测样品表面纳米力学特性等方面的信息, 但是传统原子力显微镜的高次谐波信号非常微弱. 里兹法证明在探针悬臂的特定位置打孔可以实现探针的内共振从而增强高次谐波信号强度. 本文通过有限元仿真计算获得探针第一共振频、第二共振频及其比值随着孔的尺寸和位置变化的规律. 在实验上通过聚焦离子束在探针悬臂上打孔使其第二共振频约为第一共振频的6倍, 提高了第6次谐波信号的信噪比, 并在实验室研制的高次谐波成像实验装置上获得了6次谐波图像. 关键词： 轻敲模式原子力显微镜 探针悬臂几何结构 高次谐波 聚焦离子束加工     

Theoretical exploration of asymmetric molecular harmonic emission and attosecond pulse generation in the presence of spatially inhomogeneous plasmon-enhanced field

Asymmetric molecular harmonic generation from HeH²⁺ ion in the presence of the spatially inhomogeneous plasmon-enhanced field has been theoretically investigated by solving the two-dimensional non-Born–Oppenheimer time-dependent Schrödinger equation (both the electron and nuclear motions are considered only along the laser polarisation axis). It shows that (1) for the normal homogeneous field, the harmonic cut-off from the asymmetric molecule is beyond the classical harmonic cut-off energy from the atom (I_p + 3.17 U_p). Further analyses show that the multi-channels ionisation–recombination process is responsible for the harmonic extension. (2) For the spatially inhomogeneous plasmon-enhanced field, the harmonic cut-off can be further enhanced, and an optimal 3.0 dB enhanced field with a 482 eV supercontinuum has been obtained. Quantum time-frequency harmonic analyses have been shown to explain the harmonic characteristics and the harmonic extension process. (3) Initial vibrational state and isotopic effects show that intense harmonics can be generated from higher initial vibrational state and the heavier molecule. Finally, by properly superposing the harmonics, a series of sub-30 as attosecond pulses can be obtained.     

Scattering of electromagnetic plane waves by a spheroid uniformly moving in free space

We investigate the scattering process, generated by a plane electromagnetic field that is incident upon a moving perfectly conducting spheroid. An accurate treatment of the electromagnetic waves interaction with scatterers in uniform motion is based on the special relativity principle. In the object's frame the incident wave is assumed to have a wavelength which is much larger than the characteristic dimension of the scatterer and thus the low‐frequency approximation method is applicable to the scattering problem. For the near electromagnetic field we obtain the zeroth‐order low‐frequency coefficients, while in the far field we calculate the leading terms for the scattering amplitude and scattering cross‐section. Finally, using the inverse Lorentz transform, we obtain the same approximations in the observer's frame. Copyright © 2006 John Wiley & Sons, Ltd.     

Error estimates for scattered data interpolation on spheres

We study Sobolev type estimates for the approximation order resulting from using strictly positive definite kernels to do interpolation on the -sphere. The interpolation knots are scattered. Our approach partly follows the general theory of Golomb and Weinberger and related estimates. These error estimates are then based on series expansions of smooth functions in terms of spherical harmonics. The Markov inequality for spherical harmonics is essential to our analysis and is used in order to find lower bounds for certain sampling operators on spaces of spherical harmonics.

     

RECENT PROGRESS ON SPHERICAL HARMONIC APPROXIMATION MADE BY BNU RESEARCH GROUP ——In memory of Professor Sun Yongsheng

As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.