Neutrino radiation in spherically-symmetric gravitational fields. III. Comparison with photon radiation fields

The gravitational properties of spherically-symmetric photon and neutrino radiation fields are compared and found to be identical. A model for the photon radiation field made up of incoherent radiation is first developed, equations for photons being required to satisfy Maxwell's equations.     

Bifurcation and stability of dynamical structures at a current instability

We investigate bifurcation and stability of nonuniform current states at a voltage-controlled current instability. We consider a model which exhibits bulk negative differential conductivity due to Bragg scattering of hot electrons. The system is described by balance equations for momentum and energy densities of the carriers. These transport fields are coupled to Maxwell's equations. The uniform stationary current state is unstable against long-wavelength dielectric relaxation modes at a critical field. We find that the softening of these modes gives rise to a family of periodic travelling waves and to a solitary solution (dipole domain). We show that the periodic travelling waves are unstable, wheras the dipole domain can be stabilized by coupling the sample to a suitable external circuit, if the static impedance of the sample in the domain state is negative. The model describes therefore a discontinuous nonequilibrium transition to a large amplitude domain state.Work Supported by the Swiss National Science Foundation     

Towards a complete coil array

A complete RF coil system, as has been previously defined, is capable of generating any steady-state RF field, at the MR frequency, that is compatible with Maxwell's equations. A coil system is complete if it is capable of generating all basis vector fields in the multipole expansion of the electromagnetic fields. A complete coil system has the potential to reach the ultimate intrinsic signal-to-noise as an MRI receiver coil. It also offers maximum flexibility in tailoring the spatial RF field distribution as an excitation coil. Here, computer simulations have been performed on array coils employing composite coil elements, assuming the current loops are small and can be approximated by magnetic dipoles. We demonstrate that a coil array can be configured to approximate a truncated complete array coil and to generate the basis magnetic vector fields up to certain orders in the multipole expansion of the electromagnetic fields.     

Fields of a radially polarized Gaussian laser beam beyond the paraxial approximation

Analytic expressions for the fields of a tightly focused radially polarized Gaussian laser beam are derived, accurate to epsilon5, where epsilon is the associated diffraction angle. The fields satisfy Maxwell's equations, and the calculated beam power based on them is significantly different from that of the paraxial-approximation fields.     

关于真空中的位移电流、Maxwell方程组、电磁场的源及Jefimenko公式的几点注记

通过分析指出：电磁场是一个不可分割的整体，Maxwell方程组是电磁场的运动方程，电磁场的源是电荷与电流的分布，Jefimenko公式是真空中Maxwell方程组的解。     

柱二维内电磁脉冲的自洽计算方法(Ⅰ)

本文给出柱二维麦克斯韦方程组和速率方程组的差分格式。同时用质点网格(PIC方法)求解(柱二维初级电子数方程组,得到了初级电流。以它作为速率方程组源项又可得到次级电流。这两种电流的代数和是激励电磁脉冲的源。最后求得在核爆炸条件下瞬发γ光子在金属柱腔体中产生的内电磁脉冲。     

Solving the problem of concomitant gradients in ultra-low-field MRI

In ultra-low-field magnetic resonance imaging (ULF MRI), spin precession is detected typically in magnetic fields of the order of 10-100 μT. As in conventional high-field MRI, the spatial origin of the signals can be encoded by superposing gradient fields on a homogeneous main field. However, because the main field is weak, gradient field amplitudes become comparable to it. In this case, the concomitant gradients forced by Maxwell's equations cause the assumption of linearly varying field gradients to fail. Thus, image reconstruction with Fourier transformation would produce severe image artifacts. We propose a direct linear inversion (DLI) method to reconstruct images without limiting assumptions about the gradient fields. We compare the quality of the images obtained using the proposed reconstruction method and the Fourier reconstruction. With simulations, we show how the reconstruction errors of the methods depend on the strengths of the concomitant gradients. The proposed approach produces nearly distortion-free images even when the main field reaches zero.     

Vectorial coupled—mode solitons in one—dimensional photonic crystals

We study the dynamics of vectorial coupled-mode solitons in one-dimensional photonic crystals with quadratic and cubic nonlinearities. Starting from Maxwell's equations, the vectorial coupled-mode equations for the envelopes of two fundamental-frequency optical mode and one low-frequency mode components due to optical rectification are derived by means of the method of multiple scales. A set of coupled soliton solutions of the vectorial coupled-mode equations is provided. The results show that a modulation of the fundamental-frequency optical modes occurs due to the optical rectification field resulting from the quadratic nonlinearity. The optical rectification field disappears when the frequency of the fundamental-frequency optical fields approaches the edge of the photonic bands.     

Hydrodynamic modes,soft modes and fluctuation spectra near the threshold of a current instability

We give a full threedimensional treatment of the stability and the fluctuations of the uniform stationary current state in a voltage-controlled current instability. We consider a model which exhibits bulk negative differential conductivity due to Bragg scattering of hot electrons. The model consists of Langevin equations for the mean momentum and the mean energy of the charged carriers, coupled to Maxwell's equations. We investigate the normal modes and the fluctuation spectra of this system, in particular the occurrence of soft modes and of critical fluctuations at the stability limit of the uniform current state. It is shown that the nature of the normal modes is strongly determined by the electromagnetic interactions between the carriers, giving rise to hydrodynamic flux modes and to dielectric relaxation modes. As the threshold field is approached, the dielectric relaxation modes soften and couple strongly to the flux modes. It is shown that as a consequence of this coupling the exponential decay of the correlation functions due to ordinary dielectric relaxation is followed at very long times by a power law decay due to the hydrodynamic modes.Work supported by the Swiss National Science Foundation     

An Investigation of Coupled D. C.-Induction Arc Discharges

The object of this study is to analytically determine the properties of an arc discharge generated by a combination of induction and d. c. electromagnetic fields. Induction power is supplied to the discharge by a solenoidal coil whose axis of symmetry is aligned with the applied d. c. electric field. A numerical technique is used to simultaneously solve a set of linear differential equations which include Maxwell's field equations, the single fluid energy equation, the momentum balance equation, Ohm's law, and the radiation diffusion equation. It is necessary to make a number of reasonable assumptions to obtain the final set of equations for programming. These assumptions restrict the calculations to azimuthally symmetric plasmas with axial gradients only in static pressure. In addition, the radiant energy flux is assumed to be isotropic within the plasma.     

线圈炮电枢电磁-热耦合仿真分析

 从麦克斯韦方程组和导热微分方程出发,导出了3维多级感应线圈炮电磁场、温度场分布的基本方程,并以电磁场和温度场有限元分析为基础,建立了3维有限元分析模型,忽略级间的相互影响,多级线圈炮中电枢温升可以等效为多个单级电枢的温升,运用通用有限元分析软件ANSYS的耦合计算流程,对单级感应线圈炮中电枢电磁场和温度场进行仿真。计算中考虑了材料物理参数随温度变化对温度场的影响。仿真结果表明：电枢内的温升主要分布在电枢的外表面和尾部;电枢的温度随着电容器组电压和电容增加而升高,这是因为总能量增大,电枢中涡流也增大,从而电枢的温度升高;电枢的触发位置和速度匹配关系,也会对电枢温升造成很大的影响;电枢的温度随着级数的增加逐渐升高,说明电枢在一定级数后达到了材料的熔点而被破坏。     

Current algebra and Wess-Zumino model in two dimensions

We investigate quantum field theory in two dimensions invariant with respect to conformal (Virasoro) and non-abelian current (Kac-Moody) algebras. The Wess-Zumino model is related to the special case of the representations of these algebras, the conformal generators being quadratically expressed in terms of currents. The anomalous dimensions of the Wess-Zumino fields are found exactly, and the multipoint correlation functions are shown to satisfy linear differential equations. In particular, Witten's non-abelean bosonisation rules are proven.     

Discontinuous Galerkin methods for dispersive and lossy Maxwell's equations and PML boundary conditions

In this paper, we will present a unified formulation of discontinuous Galerkin method (DGM) for Maxwell's equations in linear dispersive and lossy materials of Debye type and in the artificial perfectly matched layer (PML) regions. An auxiliary differential equation (ADE) method is used to handle the frequency-dependent constitutive relations with the help of auxiliary polarization currents in the computational and PML regions. The numerical flux for the dispersive lossy Maxwell's equations with the auxiliary polarization current variables is derived. Various numerical results are provided to validate the proposed formulation.     

霍尔推力器磁场位形及其优化的数值研究

基于麦克斯韦方程,在轴对称假设下建立了霍尔推力器磁场的数学模型.用有限差分方法对模型进行了离散.给出了数值求解模型的迭代法.通过对模型的数值求解,得到了相应的数值结果.通过对所得数值结果的分析,研究了磁场线圈电流变化对霍尔推力器磁场位形的影响.通过调整磁场线圈电流的大小找到了理想磁场位形.研究表明,对于理想磁场位形,内通道的磁镜比在3—3.5之间,外通道的磁镜比在0.4—0.9之间;增加磁场线圈的电流,出口的磁场强度随着增加,但不能增加磁镜比.通道内部的磁场强度几乎不随着磁场线圈电流的变化而变化. 关键词： 霍尔推力器 磁场位形 磁场线圈电流 磁镜比     

Mode competition in the orotron

A nonlinear, self-consistent and multimode analysis of the orotron is presented. The field in the cavity is expanded into the Hermite-Gaussian modes with time-dependent amplitudes, for which a set of ordinary differential equations is obtained from Maxwell's equations. The equations for the amplitudes are coupled to the equations of motion for the electrons. To yield a self-consistent solution, this set of coupled equations is solved simultaneously. The calculations yield transient and steady state behaviour, saturated efficiency, mode competition and multi-frequency behaviour.     

Derivation of quantum Maxwell equations from relativistic particle Hamiltonian

Given the Hamiltonian forN relativistic particles with charges and intrinsic magnetic moments interacting via pair potentials and self-interactions, we derive not only the particle equations, but also the full set of Maxwell's equations, thereby testing the consistency of particle equations, currents, and field equations in the Heisenberg picture.     

一维光子晶体缺陷模激光器的放大特性

光子晶体中引入缺陷后将形成缺陷模,这些缺陷模在增益介质中将被放大形成激光。基于麦克斯韦方程和速率方程相结合的模型,用时域有限差分法(FDTD)计算和分析了一维单缺陷光子晶体激光器中缺陷模的空间分布和频谱特性,以及这些缺陷模的放大特性,主要研究了缺陷层的厚度、晶体层数对缺陷模放大特性的影响。模拟结果显示,类似于传统激光腔的腔模,这些缺陷模能够被放大,形成激光。调整缺陷层的厚度、晶体层数等结构参量,将改变缺陷模的谐振,激射频率以及空间分布,这将直接影响激射阈值和饱和特性。增加晶体的层数,激光器的阈值将降低,饱和值将增加,但晶体层数增加到一定限度时,这种增减趋势变弱。模拟结果证明了有效层数的存在。     

双间隙谐振腔的高频分析

 从麦克斯韦方程组出发,运用电磁场的匹配条件,导出了双间隙谐振腔等效周期结构横磁模的色散关系及场分布表达式。然后通过数值计算,求出了双间隙谐振腔的谐振频率和场分布,并分析了谐振腔的结构尺寸对频率的影响,为C波段双间隙输出腔的设计提供了理论依据。     

微波谐振腔中电子与微波作用的非稳态过程研究

 在微波腔中微波场影响电子的运动，同时电子束作为电流源也产生辐射，影响微波场，这种相互作用包含线性和非线性过程。根据Maxwell理论，微波腔中的实际微波场可以按微波腔的模式展开，而且不同模式与电子束之间的相互作用不同。将电子束作为激励源，根据Maxwell方程和电子受到的洛伦兹力，建立不同模式在电子束作用下的激励方程和电子束电子在不同模式作用下的运动方程（即微波谐振腔中电子束与微波场相互作用的自洽方程组），并由此进一步分析一维情况下单间隙微波腔中微波建场、辐射场呈指数增长和饱和等非稳态作用过程，该过程涉及到电子束与微波作用的线性和非线性过程。