Integrability and pseudointegrability in billiards illustrated by the harmonic wedge

We discuss Liouville's theorem for nonsmooth integrable systems of the billiard type and give a scheme of calculation of angle-action variables for the flow. We also deal with the problem of pseudointegrability. We discuss the relationship between the continuous-time (flow) and the discrete-time (map) approaches. We treat all these aspects through a specific billiard—a wedge embedded in a two-dimensional isotropic harmonic potential. Varying the parameters provides two integrable and two pseudointegrable cases. It turns out that the dynamics of one of the latter is indeed integrable in a certain sense. We also address the problem of applying perturbation theory.     

强磁场中氢分子离子H2^＋能级的绝热及绝热变分计算

采用绝热近拟和绝热变分近似两种方法,计算了均匀强磁场（１０≤β≤１０００）中Ｈ２＾＋的σｇ,πｕ,δｇ,Φｕ,γｇ,ηｕ态的能有有原子核间的平衡距离,并与前人的结果进行了比较。     

磁场中等离子体鞘层的结构

采用流体力学理论，研究了斜磁场作用下的等离子体鞘层结构.在不同大小及方向的磁场作用下，对鞘层的离子，电子密度分布，离子流速度分布，电势分布和Bohm判据进行了讨 论.结果显示磁场对鞘层的结构有明显的影响.在静电力和洛仑兹力的作用下，离子流作螺旋进动，离子密度分布产生振荡. 关键词： 磁鞘 等离子体 磁场     

An effective potential method for the calculation of hydrogen molecule ion energy in a strong magnetic field

Using the adiabatic approximation and adiabatic variational approximation with an effective potential, the total energies and the equilibrium internuclear separations of H₂⁺ ion in states σ_g, π_u, δ_g, φ_u, γ_g, η_u in strong magnetic fields have been calculated. Our results reproduced those obtained by Vincke and Baye (Vincke M and Baye D 1985 J. Phys. B: At. Mol. Phys. 18 167), which are considered the most reliable. We found a basic function with better convergence than the Landau functions.     

Recurrence of particles in static and time varying oval billiards

Dynamical properties are studied for escaping particles, injected through a hole in an oval billiard. The dynamics is considered for both static and periodically moving boundaries. For the static boundary, two different decays for the recurrence time distribution were observed after exponential decay for short times: A changeover to: (i) power law or; (ii) stretched exponential. Both slower decays are due to sticky orbits trapped near KAM islands, with the stretched exponential apparently associated with a single group of large islands. For time dependent case, survival probability leads to the conclusion that sticky orbits are less evident compared with the static case.     

导体对磁场的屏蔽作用分析

分析了导体球壳对静磁场和对交变磁场的屏蔽作用,讨论了影响导体球壳对静磁场和对交变磁场的屏蔽作用的因素.     

磁场微重力效应的研究

将导电的液体置于磁场中,使导电液体中浮力驱动的自然对流减弱甚至消失,在导电液体中制造出了二级微重力效应,将这种情况称为磁场微重力效应.通过研究导电液体自然对流驱动力的无量纲Grashof数的变化,发现微重力效应的水平可以用公式g_m＝（β₀/β_m）（ν₀ /ν_m）²g₀ 计算,如果略去一次项,则可用g_m＝（ν₀ /ν_m）²g₀来估算.测量研究了不同磁场条件下硅熔体的磁黏度,估算不同磁场强度对应的磁场微重力水平后,发现估算结果与实验结果基本符合. 关键词： 磁场 二级微重力效应 Grashof数 微重力水平     

定轴转动带电体的远区磁场分布

类比定轴转动刚体转动惯量以及电偶极子电场的计算方法，得出定轴转动带电体的磁矩及其远区磁场分布。     

磁多极场场参数的理论计算与分析

根据磁多极场的对称性，首先导出了磁多极场磁场分量的泰勒级数展开式，定义了磁多极场的场参数，然后根据毕奥-萨伐尔定律，导出了马鞍型磁多极场线圈的场参数理论计算公式.对各个场参数数量级的大小进行了分析，找出了场参数的递推规律，给出了场参数高阶导数的计算方法，从而能够准确计算整个空间的磁场值.还从简单单根导线计算结果过渡到多根导线或具有某种连续分布的情况. 这对于磁二极场、磁四极场、磁六极场等的应用提供了可靠的理论依据. 关键词： 磁多极场 场参数 马鞍型线圈     

改进型Helmholtz线圈及其磁场均匀性的分析

提出将Helmholtz线圈改为3个同半径的串联线圈,以得到改进型的Helmholtz线圈,经计算得到了改进型Helmholtz线圈磁场的简单公式,对公式的分析表明：改进型Helmholtz线圈的均匀磁场区比一般Helmholtz线圈大得多。     

Inverse beta decay of arbitrarily polarized neutrons in a magnetic field

We calculate the cross-section of the inverse beta decay process,v _e+n → p+e, in a background magnetic field which is much smaller than m _p ^2/e . Using exact solutions of the Dirac equation in a constant magnetic field, we find the cross-section for arbitrary polarization of the initial neutrons. The cross-section depends on the direction of the incident neutrino even when the initial neutron is assumed to be at rest and has no net polarization. Possible implications of the result are discussed.     

Localization: The effect of a weak magnetic field

The effect of a weak magnetic field on the diffusion of noninteracting electrons in a disordered system is studied in a nonlinear-model context. The effective Lagrangian describing the soft modes of the system in the weak field limit is derived. The result does not have the simple form that has been suggested by several authors. Therefore the crossover of the system under a weak perturbing magnetic field is not analogous to that found in spin systems.     

光磁共振实验中抵消地磁场垂直分量的方法

介绍了光磁共振实验装置的各磁场线圈,分析了光磁共振实验中抵消地磁场垂直分量传统方法的缺陷,利用垂直磁场对磁共振信号的影响,提出了一种重复性较好的抵消地磁场垂直分量的方法,减小了传统实验方法产生的误差.这种方法也可用于测量地磁场垂直分量的大小.     

Statistic properties of Fermi gas in a strong magnetic field

Based on the thermodynamic potential function of Fermi gas in a strong magnetic field, using the thermodynamics method, the integrated analytical expressions of thermodynamic quantities of the system at low temperatures are derived, and the effects of the magnetic field on the statistic properties of the system are analysed. It is shown that, as long as the temperature is not zero, the effects of the magnetic field on the thermodynamic quantities of the system contain both oscillatory and non-oscillatory parts. For the non-oscillatory part, compared with the situation of Fermi gas in a weak magnetic field, the influence of the magnetic field on the thermodynamic quantities is not exactly the same. For the oscillatory part, the period and amplitude of the oscillation are all related to the magnetic field. Due to the oscillation, the chemical potential may be greater than Ferim energy of the system, but the oscillation does not affect the thermodynamic stability of the system.     

带电粒子在地磁场中的运动

用计算机模拟的方法研究了地磁场中带电粒子的运动特性,绘制了粒子轨迹曲线,对粒子运动进行了分析,解释了地磁场的磁瓶效应和辐射带.     

Exact solution of a triangular ising model in a nonzero magnetic field

A closed-form expression is obtained for the free energy per site of the Ising model on the triangular lattice in a nonzero magnetic field and with two- and three-site interactions. The solution is valid along a trajectory in the parameter space, and is derived using a method of exact decimation. A criterion determining the validity of the decimation method is also established.     

Bohlin transformation for a two-dimensional singular oscillator in a constant magnetic field

Bohlin transformation for a circular singular oscillator in a constant magnetic field is considered. It is shown that this transformation leads to a two-dimensional Kepler problem with an additional centrifugal potential from the constant magnetic field whose strength decreases inversely proportional to the distance from the center of attraction of the system. The energy spectrum of the considered system is obtained.     

强磁场中Fermi气体的稳定性及顺磁性

运用理论解析和数值模拟的方法,研究强磁场中Fermi气体在低温下的稳定性及顺磁性, 分析温度、磁场对稳定性及磁化率的影响.研究结果显示,强磁场引起系统稳定性的改变, 这种改变与温度有关,而温度对稳定性改变及磁化率的影响又与自由气体的化学势即粒子数密度有关. 当自由系统的化学势为偶数时,磁场弱化系统的稳定性,温度升高可降低系统的磁化率; 当自由系统的化学势为奇数时,磁场强化系统的稳定性,温度升高可增大系统的磁化率. 升高温度,可以弱化磁场对系统稳定性的影响;加强磁场,可以使得系统稳定性的改变发生振荡, 使系统磁化率的振荡中心下移.     

直线感应加速器中聚束磁场的数值计算方法

为了准确模拟出直线感应加速器中聚束磁场的值,首先利用单积分法计算出理想情况下的聚束磁场的值,再进一步用磁路分析的方法考虑直线感应加速器的加速腔中匀场环对聚束磁场的影响,然后推导出一组偏离角度与磁场分量相关的公式。将最终得到的聚束磁场分量与直线感应加速器模型结合起来,采用粒子模拟的方法来模拟电子束在加速段中的输运过程,并对结果加以分析。