Group Velocity Vg Research Articles

Nonlinear propagation of electromagnetic waves in a plasma by means of electromagnetically induced transparency

Magnetized plasma can be made transparent at the cyclotron frequency by addition of a helical undulator. The purpose of the undulator is to couple the transverse (propagating) and longitudinal (non-propagating) electromagnetic waves in the plasma. The coupling is particularly strong when the electron cyclotron and plasma frequencies are equal. It is demonstrated that this coupling gives rise to ultra-slow electromagnetic waves with group velocity vg ≪ c (where c is the speed of light in vacuum), resulting in the extreme energy compression in the plasma. A linear propagation equation for the electromagnetic wave envelope is derived, and its group velocity and group velocity dispersion are calculated. Relativistic corrections to the plasma electron motion are included to derive the nonlinear propagation equation. It is shown that, in comparison with unmagnetized plasma, an enhancement of non-linearities of order 1/v 2 g is expected. Implications for relativistic self-focusing in the plasma are discussed.

Nonlinear propagation of electromagnetic waves in a plasma by means of electromagnetically induced transparency

Abstract Magnetized plasma can be made transparent at the cyclotron frequency by addition of a helical undulator. The purpose of the undulator is to couple the transverse (propagating) and longitudinal (non-propagating) electromagnetic waves in the plasma. The coupling is particularly strong when the electron cyclotron and plasma frequencies are equal. It is demonstrated that this coupling gives rise to ultra-slow electromagnetic waves with group velocity vg ≪ c (where c is the speed of light in vacuum), resulting in the extreme energy compression in the plasma. A linear propagation equation for the electromagnetic wave envelope is derived, and its group velocity and group velocity dispersion are calculated. Relativistic corrections to the plasma electron motion are included to derive the nonlinear propagation equation. It is shown that, in comparison with unmagnetized plasma, an enhancement of non-linearities of order 1/v 2 g is expected. Implications for relativistic self-focusing in the plasma are discussed.

Negative group velocity of a light pulse in cesium vapour

Electromagnetically induced absorption in cesium vapour causes an extremely strong anomalous dispersion, leading to the propagation of radiation at a low negative group velocity Vg. As a result, a resonance light pulse appears from the medium before than a nonresonance pulse. The advance time measured in the experiment corresponds to the group velocity Vg ≈ -c/3600, which is an order of magnitude lower than that reported by Wang L.J., et al. Nature, 406, 277 (2000).

Theory and group velocity of ultrashort, tightly focused laser pulses

The wave equation describing an ultrashort, tightly focused laser pulse in vacuum is solved analytically. Plasma dispersive effects are also included. Based on exact short-pulse solutions, analytical expressions are obtained for the pulse-length evolution, the pulse centroid motion, and the group velocity. Approximate short-pulse solutions are obtained to arbitrary order in the parameter λ/2πL < 1, where λ is the pulse wavelength and L is the length of the pulse envelope. Comparisons are made to the solutions of the paraxial wave equation and to numerical solutions of the full wave equation. The exact analytical expression for the pulse group velocity vg, which is correctly determined from the motion of the pulse centroid, is in excellent agreement with the numerical solution. In vacuum, 1 − vg/c ≅ (λ/2πr0)2, where r0 is the laser spot size at focus. Estimates for the quantity 1 − vg/c, based on the paraxial wave equation, are found to be in error by a factor of 2.

Lamb Wave and its Application to a Digitizer

An anti-symmetric mode Lamb wave with different phase velocity Vp and group velocity Vg has been studied. An algorithm for accurate measurement of the distance between two points is established using Lamb wave of low frequency and measuring both phase delay time Tp and group delay time Tg.

Anisotropic cyclotron radiation from stellar atmospheres

We present the radiation formula which describes the power received at a far field per unit solid angle centred around the group velocity Vg due to a mildly relativistic current moving in a magnetised plasma. This formula differs from the usual one by two factors: (i) the group Doppler factor; (ii) energy centred around Vg can be associated with K vectors in directions quite different from Vg. Some numerical examples are given.

Group Doppler effect in anisotropic plasmas

In anisotropic plasmas, the radiative power emitted and the power observed per unit solid angle should be calculated along the direction of the group velocityv g . The two power functions referred differ by a product of two factors: one is the group Doppler factor and the other is the ‘squeezing effect’ of the radiative energy due to the dependence ofv g on direction. In this paper, the group Doppler factor is derived using two different methods, and the relevant physical concepts are analyzed in details. A number of numerical examples pertaining to astrophysical situations are presented, to illustrate the significance of the group Doppler effect with respect to the ‘wave Doppler effect’ which is valid in isotropic media.

The brownian theory of light

Probabilistic origin of the laws of Mechanics and Relativity: In a diffusion with exclusion principle, the brownian bridges propagate pressure wavelets which interfere and make wave packets of which the group velocity Vg tends to equal the expansion velocity v of the Huygens sphere envelope of these wavelets. This convergence Vg > v due to the strong large numbers law involves the Galilean and Lorentz groups, the limit Vg =v is reached on monochromatic waves and stationary states. The fundamental structure involved, open or closed, is to be found also in the central nervous system of Man, emerging through Evolution.

Formation of Wave Packets in the Ion Acoustic Turbulence

Formation of wave packets is observed in a current-driven ion acoustic turbulence by the microwave scattering method. The wave packets propagate along the direction of the electron drift with a group velocity vg approximately equal to the value obtained from the dispersion curve for the turbulent ion acoustic waves.

Ultrasonic attenuation and velocity in two-phase microstructures

The scattering attenuation and velocity of elastic waves propagating in two-phase microstructures are computed by an extension of multiple scattering analysis. The computation is based on a model of an array of isotropic spherical scatterers embedded in an isotropic matrix. Attenuation α is predicted to increase with volume fraction and number density of scatterers and to approach a plateau with frequency. Group velocity vg is predicted to decrease with volume fraction and frequency. Ultrasonic measurements of α and vg are made on model microstructures consisting of Cu spheres embedded in a polymethylmethacrylate matrix. The measured values agree qualitatively with the predicted ones, and physical reasons are proposed to account for the agreement. The inability of the theory to provide accurate quantitative predictions of these quantities is discussed. Subject Classification: 35.26; 20.30, 20.35.

Ray tracing in an anisotropic absorbing medium

With the generalized group velocity vg = Re (∂ω/∂k) for media with moderate absorption, derived in a previous paper, the Hamilton equations for group propagation in non-absorbing media are generalized to include moderate absorption. They contain directional derivatives not only in the direction of v but also in the direction of Im (∂ω/∂k). Two iterative computational methods are presented for ray tracing with the generalized Hamilton equations.

Effect of Dispersion and Scattering on the Startup of Brass Instrument Tones

A clean attack is favored if the round-trip time Tr for the initial sound from the lips sent down the bore and back is an integral multiple of the playing frequency period Pn. Consider a Bessel horn of length L, radius r, with r(y)=B/yα. For a pulse with spectral center ωn, the group velocity vg=c[1−(c/ωn)2α(α+1)]12, whence Tr=(2/c) [L2−ln2]12, where ln2=(c/ωn)2α(α+1). The oscillation period of the nth mode of this horn is approximately Pn=(4/c) (L−ln)/(2n−1) implying that a Bessel horn does not give a clean attack. A mouthpiece, mouthpipe, cylindrical tube, and Bessel bell can be designed to give good attack plus correct tuning. Short constrictions in a bore give early partial reflections which also damage tone onset. A 10% diam reduction 2 cm long (as in some horn valves) gives a 7% reflected amplitude at 330 Hz. Valves in combination can give considerably larger reflections. Missed notes and burbles are less common in instruments with slight constrictions.

Design of the Deflector for the rf Beam Separator at the Brookhaven AGS

The design of the iris-loaded deflector for the Panofsky type rf beam separator now under construction at the Brookhaven AGS is presented. General expressions for the transverse momentum acquired by an ultrarelativistic particle traversing the deflector are derived from the field equations. Useful figures of merit (shunt impedance R, series impedance Z, quality factor Q, R/Q, etc.) are defined. Computational results for the aperture radius a, the guide radius b, Q, R/Q, and R as functions of group velocity vg, the number of irises per wavelength N, and iris thickness d/w are presented for structures with the phase velocity vp=c. They are compared with experimental results reported from deflection tests. The design procedure of a deflector is developed for the realistic case that the shunt impedance varies with group velocity. Optimization of operating frequency fπ/2, deflector length l, vg, d/w, and N is carried out. Higher order modes in iris-loaded waveguides are investigated and methods for the suppression of mode degeneracies are outlined. The effect of the mechanical tolerances on the phase shift per cell Φ is considered. The chosen deflector structure has λ0=10.495 cm, N=4, Φ=½π, d/w=0.8, 2a=48.13 mm, 2b=116.71 mm, l=3.07 m, rounded iris edges, and lateral rods as mode stabilizers. ``Cold'' measurements on cavities and waveguides are described, and a precise R/Q perturbation method is detailed. Pertinent results are fπ/2=2856.35 Mc, Q=8700, phase error per cell ΔΦ=2.7° rms, R/Q=1.41 kΩ/m, vg/c=−0.0204, αl≈0.5. It is concluded that a klystron pulse of ≥14 MW is sufficient to give a 1 mrad peak deflection of 18 GeV/c particles.

Particle Properties of Radiant Energy in Wave Guides

The mean energy per excitation wavelength of e.m. radiation propagated along a lossless uniform wave guide is found to be w = Qμ, Q being independent of frequency for a given amplitude of the longitudinal field intensity, mode of the field, and structure of the guide. The frequency μ and the group velocity vg of the radiant energy are related by the equation μ/μc = [1 − (vg/c)2]−12 where μc = c/λc denotes the frequency at cutoff, and λc the excitation wavelength at cutoff. This equation permits one to put hμ = hμc+hμc{[1 − (vg/c)2]−12 − 1}. The amplitudes of the field intensities are chosen such that Q equals Planck's constant h. Applying the mass-energy relation, the term hμc = hc/λc = m0c2 may be interpreted as the “potential” (= rest) energy of the quantum hμ and m0 as the rest mass. The momentum p associated with hμ is found to be p = h/λg, λg being the wavelength along the guide. When radiant energy passes from one guide into another one of different cross-sectional structure via a tapered piece of wave guide, a partial conversion of “potential” to “kinetic” energy, and vice versa, occurs along the tapered section. In the case of TEM waves, which, however, can only be supported in a guide of infinite transverse dimensions, the group velocity becomes c and the rest mass zero.