Cylindrical electromagnetic waves in a nonlinear nondispersive medium: Exact solutions of the Maxwell equations

The excitation and propagation of cylindrical electromagnetic waves in a nonlinear nondispersive medium are analyzed. It is assumed that the medium lacks a center of symmetry and that the dependence of the electric displacement on the electric field can be approximated by an exponential function. For this case, a method for integrating the system of the Maxwell equations is proposed. Exact solutions to a set of nonlinear electromagnetic field equations are obtained by this method. It is shown that nonlinear effects described by these solutions can become apparent under experimental conditions.     

柱面非线性麦克斯韦方程组的行波解

柱面电磁波在各种非均匀非线性介质中的传播问题具有非常重要的研究价值.对描述该问题的柱面非线性麦克斯韦方程组进行精确求解,则是最近几年新兴的研究热点.但由于非线性偏微分方程组的极端复杂性,针对任意初边值条件的精确求解在客观上具有极高的难度,已有工作仅解决了柱面电磁波在指数非线性因子的非色散介质中的传播情况.因此,针对更为确定的物理场景,寻求能够精确描述其中更为广泛的物理性质的解,是一种更为有效的处理方法.本文讨论了具有任意非线性因子与幂律非均匀因子的非色散介质中柱面麦克斯韦方程组的行波精确解,理论分析表明这种情况下柱面电磁波的电场分量E已不存在通常形如E=g(r-kt)的平面行波解;继而通过适当的变量替换与求解相应的非线性常微分方程,给出电场分量E=g(lnr-kt)形式的广义行波解,并以例子展示所得到的解中蕴含的类似于自陡效应的物理现象.     

行波管中慢电磁行波与电子注非线性互作用普遍理论

在同时考虑多信号输入和相对论效应的情况下，利用波导激励理论获得了行波管中慢电磁行波与电子注非线性互作用的全三维自洽工作方程组，包括激发方程、运动方程、能量转化方程、相位演化方程等，适合大部分行波管中慢电磁行波与电子注的非线性互作用过程.利用该理论具体分析了一个宽带螺旋线行波管在多信号输入时的交叉调制，并与实验结果进行了比较，验证了理论和计算的正确性.另外，还模拟了一个相对论盘荷波导行波管中的非线性注波互作用过程. 关键词： 行波管 慢电磁行波 非线性注波互作用 交叉调制     

Generalized maxwell equations and quantum mechanics. I. Dirac equation for the free electron

Some preliminary results presented in two previous papers are expanded upon. In the first it was shown that the Maxwell equations are equivalent to a nonlinear Dirac-like spinor equation. In the present paper it is shown that, in that formalism, the Dirac equation for the free electron is susceptible to a puzzling reinterpretation. In fact, it is shown that the Dirac equation is equivalent to the Maxwell equations for an electromagnetic field generated by two currents: one electric in nature and one, magnetic-monopolar. The elaboration of this result brings a nonlinear generalization of Maxwell's equations, as well as a nonlinear Dirac-like equation fully equivalent to them, from which both the electron mass as well as the magnetic monopole mass appear to be fully electromagnetic in nature, and the magnetic monopole to be tachyonic. The corresponding nonlinear Dirac equation reduces, under suitable approximations, to the ordinary Dirac equation for the free electron.     

Nonlinear theory of scattering of linearly polarized electromagnetic waves by unmagnetized electron beam

The nonlinear dynamics of scattering of linearly polarized electromagnetic waves by an unmagnetized beam of nonrelativistic electrons is studied. General nonlinear equations are derived and linear scattering regimes are analyzed. For the case of high-density beams, the general nonlinear equations are reduced to a system containing only cubic nonlinearities. Analytic expressions are provided for the amplitudes of interacting waves and for typical process-development times.     

Propagation properties of TE-mode soliton in rectangular waveguides with nonlinear dielectrics

The problem of rectangular waveguide with nonlinear dielectrics is discussed. The components of electromagnetic fields in the waveguide satisfy nonlinear partial differential equations. Using slowly varying envelope approximation, they can become well known nonlinear Schrodinger equation and soliton solution is got from the equation.     

Application of a model of nonlinear history-dependent magnetic behavior for inductance estimation of a microinductor

This paper presents a method for the numerical inductance calculation of a passive electromagnetic inductive device using cores made of a nonlinear magnetic material. The material model used for this purpose describes the nonlinear magnetic behavior by a set of differential equations. The coupled implicit system of Maxwell equations and material model equations is solved by a simplified algorithm which shall be explained while applied to a new design of a microinductor, the so called I-inductor.     

Localization of intense electromagnetic waves in a relativistically hot plasma

We consider nonlinear interactions between intense short electromagnetic waves (EMWs) and a relativistically hot electron plasma that supports relativistic electron holes (REHs). It is shown that such EMW-REH interactions are governed by a coupled nonlinear system of equations composed of a nonlinear Schro dinger equation describing the dynamics of the EMWs and the Poisson-relativistic Vlasov system describing the dynamics of driven REHs. The present nonlinear system of equations admits both a linearly trapped discrete number of eigenmodes of the EMWs in a quasistationary REH and a modification of the REH by large-amplitude trapped EMWs. Computer simulations of the relativistic Vlasov and Maxwell-Poisson system of equations show complex interactions between REHs loaded with localized EMWs.     

A three-dimensional time-dependent theory for helix traveling wave tubes in beam-wave interaction

This paper presents a three-dimensional time-dependent nonlinear theory of helix traveling wave tubes for beamwave interaction.The radio frequency electromagnetic fields are represented as the superposition of azimuthally symmetric waves in a vacuum sheath helix.Coupling impedance is introduced to the electromagnetic field equations’ stimulating sources,which makes the theory easier and more flexible to realize.The space charge fields are calculated by electron beam space-charge waves expressed as the superposition solutions of Helmholtz equations.The focusing forces due to either a solenoidal field or a periodic permanent magnetic field is also included.The dynamical equations of electrons are Lorentz equations associating with electromagnetic fields,focusing fields and space-charge fields.The numerically simulated results of a tube are presented.     

Nonlinear TM modes in cylindrical liquid crystal waveguide

We consider a nonlinear cylindrical fiber with a nematic liquid crystal (LC) core having initially the escaped configuration and subject to the action of a normal mode propagating electromagnetic field of arbitrary intensity. We derive a set of coupled equations governing the nonlinear dynamics of the electromagnetic field and the confined LC. We solve numerically these coupled equations and find simultaneously the distorted textures of the nematic inside the cylinder and the Transverse Magnetic modes in the guide. We analyze the dependence of these solutions on the electromagnetic field intensity by assuming consistently soft boundary conditions. We have found a dramatic correlation in the spatial distribution of the nematic's configuration and the Transverse Magnetic modes. Thus, the director adopts configurations completely guided by the specific mode involved. We show that the cut-off frequencies and dispersion relations can be tuned by varying the intensity of the electromagnetic propagating field.     

Interacting electromagnetic waves in general relativity

The problem is considered of finding exact solutions of the Einstein-Maxwell equations which describe the physical situation of two colliding and subsequently interacting electromagnetic waves. The general theory of relativity predicts a nonlinear interaction between electromagnetic waves. The situation is described using an approximate geometrical method, and a new exact solution describing two interacting electromagnetic waves is given. This describes waves emitted from two sources mutually focusing each other on the opposite source.     

A new variant of nonlinear electrodynamics. II

The electrostatic solution of nonlinear electrodynamic equations is studied, the characteristic peculiarity of these equations being their consideration of the effect of electromagnetic spin on the space-time continuum. The energy of the nonlinear electromagnetic field proves to be finite for a quite wide spectrum of seed masses. Three-dimensional soliton solutions are constructed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 46–53, October, 1978.We express our deep indebtedness to N. N. Kolesnikov, V. R. Khalilov, and participants in the theoretical physics seminar led by Professor D. D. Ivanenko for evaluating the results of the study.     

A relativistic field theory of the electron

A set of nonlinear partial differential equations covariant in a non-Euclidean space is reduced to the Dirac equation for the electron and the Maxwell-Lorentz equations of electromagnetic fields under certain assumptions. In the course of reduction, we have opportunities for understanding the relationship between the Dirac equation and the Maxwell-Lorentz equations, and also for visualizing conditions which limit feasible applications of those known equations in physics.     

Propagation of electromagnetic waves in a medium with nonlinear magnetic susceptibility

The interaction of electromagnetic waves in a medium with nonlinear magnetic susceptibility is investigated. On the basis of Tinkham's measurements an antiferromagnet showing a resonance in the submillimeter region is considered as a nonlinear medium. The solution of both the Landau-Lifshitz and Maxwell equations leads to the RHS wave equation. Its solution with boundary conditions shows that the amplitude of the reflected wave from the nonlinear medium on a combined frequency can be non-zero.     

3.3MeV直线感应加速器的电子束传输研究

采用SLAC-226程序,模拟了电子束在3.3MeV加速器中的加速与传输过程,并与从电子束传输的层流近似出发所推导的边包络方程解进行了比较。程序和包络方程都考虑了束流的自生电磁场及外加电磁场。     

Nonstatic charged fluid spheres in general relativity

Faulkes has shown that shear-free solutions of the Einstein-Maxwell field equations can be found by solving a single second-order nonlinear differential equation containing two arbitrary functions of the radial coordinate. In this work a very general method is proposed to solve this nonlinear equation which, in effect, extends an earlier work of Wyman to its electromagnetic analog.     

Coherence and saturation properties of second-harmonic generation with a nonlinear crystal inside the laser cavity

The basic equations for second-harmonic generation including noise are derived for the case that the nonlinear crystal is put inside the laser cavity. A realistic model of a (detuned) laser with two-level atoms in single-mode operation is taken using the nonlinear theory of laser noise which describes the laser saturation effects, the phase diffusion and the intensity fluctuations. The reaction of the second-harmonic field on the fundamental field is taken into account as well as the reaction of the fundamental field on the laser. The nonlinear crystal is described by microscopic anharmonic oscillator equations (without introducing nonlinear susceptibilities by perturbation theory). The saturation of the polarization of the nonlinear medium is taken into account exactly with the only assumption that the influence of third and higher harmonics should be small. The electromagnetic field is described semiclassically by stochastic equations. In all equations, the damping is introduced simultaneously with Markoffian fluctuating forces by coupling to heatbaths. The equations are solved exactly in the stationary state without noise (the time dependent solution including noise will be presented in a subsequent paper). The most important saturation effect is a frequency shift which depends on the laser intensity.