Dispersion Relation For Electromagnetic Waves Research Articles

Beyond Clausius-Mossotti - Wave propagation on a polarizable point lattice and the discrete dipole approximation

We derive the dispersion relation for electromagnetic waves propagating on a lattice of polarizable points. From this dispersion relation we obtain a prescription for choosing dipole polarizabilities so that an infinite lattice with finite lattice spacing will mimic a continuum with dielectric constant e(ω). The Discrete Dipole Approximation is used to calculate scattering and absorption by a finite target by replacing the target with an array of point dipoles. We compare different prescriptions for determining the dipole polarizabilities. We show that the most accurate results are obtained when the lattice dispersion relation is used to set the polarizabilities

Measurement of photonic band structure in a two-dimensional periodic dielectric array.

The photonic band structure in a two-dimensional dielectric array is investigated using the coherent microwave transient spectroscopy (COMITS) technique. The array consists of alumina-ceramic rods arranged in a regular square lattice. The dispersion relation for electromagnetic waves in this photonic crystal is determined directly using the phase sensitivity of COMITS. The experimental results are compared to theoretical predictions obtained using the plane-wave expansion technique. Configurations with the electric field parallel and perpendicular to the axis of the rods are investigated.

The effects of weak self-fields on electron orbits for a free electron laser

A set of coupled equations for electron motion and the dispersion relation of electromagnetic wave (wiggler) in electron beam are studied. The instability of steady-state electron orbits is reduced to the problem of the fourth-order and fifth-order linear ordinary differential equations. It is found that the presence of self-fields plays an important role in determining the behaviour of stable electron orbits.

Dispersion of electromagnetic waves in the presence of magnetic monopoles of electron mass in a uniform magnetic field

The dispersion relation of electromagnetic waves in the presence of magnetic monopoles of electron mass in a uniform magnetic field is obtained. The waves of the frequencyω in the range ωϱi<Ωi<ω<Ω e <ωϱa are analysed. It is shown that the monopole charges lead to observable effects. Finally, the results are applied to a typical pulsar.

Gap solitons in nonlinear periodic structures.

In a medium with a dielectric constant periodic in one spatial direction, there are gaps in the dispersion relation of electromagnetic waves which propagate in the structure. If the index of refraction also contains a term proportional to the local-field intensity, we show that for frequencies within the gap, there exist soliton solutions to the nonlinear wave equation of the medium. This is demonstrated by analytic methods; the results agree with conclusions reached earlier, in numerical studies of power-dependent transmission through a finite superlattice, with a nonlinear element in each unit cell.

Application of Davidenko's Method to the Solution of Dispersion Relations in Lossy Waveguiding Systems

Davidenko's method is a reduction of Newton's method for the numerical solution of n-coupled nonlinear algebraic equations into n-coupled first-order differential equations in a dummy variable. This algorithm is useful for the solution of dispersion relations of electromagnetic waves propagating in lossy waveguiding structures, particularly layered geometries containing one or more gyrotropic layers. In this class of problems, Newton-based numerical techniques are not always satisfactory and Davidenko offers an altenative which is efficient and reliable and which relaxes the extent of the restriction placed on the initial guess to be sufficiently close to the solution. Presented are Davidenko's method, its application to lossy-waveguide dispersion relations, and an example where the algorithm was applied successfully.

ON ELECTROMAGNETIC INSTABILITIES OF PLASMA (II)

In paper [1], a strict and general instability criterion is obtained by analysing the geometric properties of the dispersion relation of electromagnetic waves in plasma with anisotropic velocity distribution, but the wave propagates only along one specific direction. In this paper, the propagation of electromagnetic waves along an arbitrary direction is discussed. The rigorous instability criterion is obtained.

Propagation and Absorption of Electromagnetic Waves in a Coaxial Plasma-Waveguide-System (m=1)

Abstract The dispersion relation of electromagnetic waves propagating in a coaxial plasma-waveguide-system is solved for a cold plasma. The influence of losses, discharge tube, and radial gradients of electron density are discussed in detail. Strong absorption is found near the dipole resonance of the plasma column.

Electromagnetic instabilities in an anisotropic loss-cone plasma

A form of general dispersion relation for electromagnetic waves in a fully ionized anisotropic plasma with loss-cone that explicates the contribution of the loss-cone to the dispersion relation is developed. By initially ignoring effects due to anisotropy, it is shown by means of Nyquist diagram technique that an isotropic loss-cone distribution can be unstable to EM waves corresponding to the whistler mode (0<ω<Ω e ). The growth rate is then determined analytically for this distribution, assuming cyclotron resonance between the waves in the whistler mode and particles in the high energy tail of the velocity distribution. By including the effects of anisotropy, a general growth rate is obtained which is found to depend on the anisotropy, the size of the loss-cone, the softness of the energy spectrum, and the fraction of the particles which are resonant with the wave. For particular distributions the relative contributions of the anisotropy and of the loss-cone to the growth rate have been determined. It is seen that loss-cone effects, which depend on the size of the loss-cone as well as the softness of the energy spectrum, can be a significant factor in the determination of the growth rate. For the Lorentzian distribution, the half-width of unstable waves is considerably broadened and the growth rates are somewhat more severe as compared to a two-temperature Maxwellian. The threshold frequency is $$\omega _r \simeq \tfrac{8}{9}\Omega _e $$ which confirms the presence of unstable EM waves in the magnetospheric plasma leading to turbulence.

Electromagnetic effects on the modified two-stream instability

The linear dispersion relation for electromagnetic waves in a Vlasov plasma with unmagnetized ions and magnetized electrons undergoing an E × B drift is derived and studied. Results show that electromagnetic effects reduce the growth rate of the modified two-stream instability while they spread the region of instability in wave vector space. The possible contribution of this instability to two bow shock parameters, the ratio of electric to magnetic field wave energy densities and the shock width, is discussed.

A theory of auroral hiss and implications on the origin of auroral electrons

A theory for auroral hiss is developed based on the existence of a beam of energetic particles that is also believed responsible for the visual aurora. A dispersion relation for electromagnetic waves in a plasma consisting of an electron beam and a background plasma is derived. The Hermitian part of the dispersion relation is assumed to be governed by the denser cold background plasma, whereas the anti-Hermitian part is governed by the electron beam. It is shown that the electron beam can excite an electron whistler mode instability near the resonance cone by the Landau interaction because near the resonance cone the phase velocity of the wave can be made arbitrarily small. The instability can be excited at all frequencies between the lower hybrid resonance and the electron plasma frequencies. The wave normal angles along the resonance curve vary between 0° and 90° with respect to the magnetic field. Waves whose wave normal angles are small have the largest growth rates and are most likely to grow to observable amplitudes. Only waves generated within a few degrees of the vertical can reach the ground. The results of the calculations are applied to auroral hiss observations. From the fact that auroral hiss is observed on the ground at frequencies less than 10 kHz it is concluded that at least some of the auroral hiss is generated at altitudes where the ambient electron density is of the order of 1 cm−3. This suggests that auroral electrons are energized in regions where the ambient density is of the order of 1 cm−3 or less.

Stability of Waves in Relativistic Plasma

AbstractThe dispersion relation of electromagnetic waves propagating perpendicular to an applied uniform magnetic field B0 in relativistic plasma is derived. Waves propagating perpendicular to the uniform applied magnetic field can be separated into two modes ‐ one is the linearly polarized transverse wave and the other is a hybrid mode. In the present analysis, dispersion relation of the first mode i. e., for a pure transverse wave is analysed under the assumption that the wavelength is much longer than the cyclotron radii of the electrons. A stability criterion which limits the thermal energy of the electrons along B0 is obtained.

Phase and damping constant of helicons in intrinsic InSb with a tilted magnetic field

Helicons in InSb were investigated experimentally and compared with the theoretical dispersion relation of electromagnetic waves in a temperate plasma. A very good agreement was found.

The Nature of Helicon-Wave Instabilities

The generalized dispersion relation for electromagnetic waves in a medium with drifting carriers is calculated in the hydrodynamic description of plasmas. The basic configurations of k, B0 and E0, involving the velocity-driven instabilities in semiconductor plasmas are discussed briefly. As a special case, helicon-wave instabilities when k// B0// E0 are studied in detail by a “resistive hole approximation.” It is shown that the left-polarized-helicon instability is convective (amplifying) for (n0h/n0e)(ωceτe)(ωchτh)<1, and non-convective (absolute) for (n0h/n0e)(ωceτe)(ωchτh)≧1.

ON ELECTROMAGNETIC INSTABILITIES OF PLASMA

摘要 本文阐述了由分析色散关系几何性质的方法,导出速度分布各向异性的等离子体中的电磁波不稳定性的严格和普适的判据,具体讨论了温度不均匀性和粒子束流对不稳定性的影响。最后导出了Weibel的电磁波增长系数的相对论修正公式。 Abstract In this paper, a strict and general instability criterion is obtained by analysing the geometric properties of the dispersion relation of electromagnetic waves in plasma with anisotropic velocity distribution. The criterion is applied to the cases of anisotropic temperature and current-carrying plasma. Finally, the relativistic correction of Weibel's formula is obtained. 作者及机构信息 陆全康 1. 复旦大学物理系 Authors and contacts LOH CHYUAN-KONG 1. 复旦大学物理系 参考文献 [1] 施引文献