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Results for “ELECTROMAGNETIC PROPAGATION”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 1,315 records · Page 73
All sourcesNASA NTRSDOE OSTI
DOE OSTI2014

Laser pulse propagation in inhomogeneous magnetoplasma channels and wakefield acceleration

Wakefield excitation in a preformed inhomogeneous parabolic plasma channel by an intense relativistic (≃10{sup 19} W/cm{sup 2}) circularly polarized Gaussian laser pulse is investigated analytically and numerically in the presence of an external longitudinal magnetic field. A three dimensional envelope equation for the evolution of the laser pulse is derived, which includes the effect of the nonparaxial and applied external magnetic field. A relation for the channel radius with the laser spot size is derived and examines numerically to see the external magnetic field effect. It is observed that the channel radius depends on the applied external magnetic field. An analytical expression for the wakefield is derived and validated with the help of a two dimensional particle in cell (2D PIC) simulation code. It is shown that the electromagnetic nature of the wakes in an inhomogeneous plasma channel makes their excitation nonlocal, which results in change of fields with time and external magnetic field due to phase mixing of the plasma oscillations with spatially varying frequencies. The magnetic field effect on perturbation of the plasma density and decreasing length is also analyzed numerically. In addition, it has been shown that the electron energy gain in the inhomogeneous parabolic magnetoplasma channel can be increased significantly compared with the homogeneous plasma channel.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

Phonon Polaritonics in Two-Dimensional Materials

Extreme confinement of electromagnetic energy by phonon polaritons holds the promise of strong and new forms of control over the dynamics of matter. To bring such control to the atomic-scale limit, it is important to consider phonon polaritons in two-dimensional (2D) systems. Recent studies have pointed out that in 2D, splitting between longitudinal and transverse optical (LO and TO) phonons is absent at the Γ point, even for polar materials. Does this lack of LO–TO splitting imply the absence of a phonon polariton in polar monolayers? To answer this, we connect the microscopic phonon properties with the macroscopic electromagnetic response. Specifically, we derive a first-principles expression for the conductivity of a polar monolayer specified by the wave-vector-dependent LO and TO phonon dispersions. In the long-wavelength (local) limit, we find a universal form for the conductivity in terms of the LO phonon frequency at the Γ point, its lifetime, and the group velocity of the LO phonon. Our analysis reveals that the phonon polariton of 2D is simply the LO phonon of the 2D system. For the specific example of hexagonal boron nitride (hBN), we estimate the confinement and propagation losses of the LO phonons, finding that high confinement and reasonable propagation quality factors coincide in regions that may be difficult to detect with current near-field optical microscopy techniques. Finally, we study the interaction of external emitters with 2D hBN nanostructures, finding an extreme enhancement of spontaneous emission due to coupling with localized 2D phonon polaritons and the possibility of multimode strong and ultrastrong coupling between an external emitter and hBN phonons. This may lead to the design of new hybrid states of electrons and phonons based on strong coupling.

36 MATERIALS SCIENCE↗
DOE OSTI2019

GRB and blazar jets shining through their stripes

Black hole-driven relativistic astrophysical jets, such as blazars and gamma-ray bursts (GRBs), are powerful sources of electromagnetic radiation. Their emission is powered by some energy dissipation and particle acceleration mechanism operating in situ at large distances from the black hole. We propose that the formation of the dissipative structures in the jet is controlled by the time variability of the accretion disc. We argue that the open magnetic field lines through the black hole, which drive a strongly magnetized jet, may have their polarity reversing over time-scales related to the growth of the magnetorotational dynamo in the disc. Consequently, the jet is characterized by an alternating toroidal field polarity along its propagation axis, i.e. it is a ‘striped jet’. Magnetic reconnection in the current sheets that form between the stripes dissipates the alternating field energy and thus powers further jet acceleration. Here, we consider a jet with a broad distribution of stripe widths l > l min , above a dominant scale l min . We find that the bulk acceleration of the jet, driven by the annihilation of the stripes, is very gradual. The dissipation rate peaks at a distance $z_{\rm peak}\sim 10^6 R_\mathrm{ g}\, (\Gamma _\infty /30)^2\, (l_{\rm min}/1000R_\mathrm{ g})$| , where R g is the black hole’s gravitational radius and Γ ∞ the jet’s asymptotic Lorentz factor, and exhibits a very broad plateau extending by ~4–5 orders of magnitude in distance. The prolonged energy dissipation accounts for the flat-to-inverted long-wavelength spectra commonly observed in jets. The model can also account for the broad range of flaring time-scales of blazars and the fact that their bulk acceleration appears to continue out to ~100 pc scales. In GRB jets, the model predicts comparable power for the photopsheric and Thomson-thin emission components.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Attentional Ptycho-Tomography (APT) for three-dimensional nanoscale X-ray imaging with minimal data acquisition and computation time

Abstract Noninvasive X-ray imaging of nanoscale three-dimensional objects, such as integrated circuits (ICs), generally requires two types of scanning: ptychographic, which is translational and returns estimates of the complex electromagnetic field through the IC; combined with a tomographic scan, which collects these complex field projections from multiple angles. Here, we present Attentional Ptycho-Tomography (APT), an approach to drastically reduce the amount of angular scanning, and thus the total acquisition time. APT is machine learning-based, utilizing axial self-Attention for Ptycho-Tomographic reconstruction. APT is trained to obtain accurate reconstructions of the ICs, despite the incompleteness of the measurements. The training process includes regularizing priors in the form of typical patterns found in IC interiors, and the physics of X-ray propagation through the IC. We show that APT with ×12 reduced angles achieves fidelity comparable to the gold standard Simultaneous Algebraic Reconstruction Technique (SART) with the original set of angles. When using the same set of reduced angles, then APT also outperforms Filtered Back Projection (FBP), Simultaneous Iterative Reconstruction Technique (SIRT) and SART. The time needed to compute the reconstruction is also reduced, because the trained neural network is a forward operation, unlike the iterative nature of these alternatives. Our experiments show that, without loss in quality, for a 4.48 × 93.2 × 3.92 µm 3 IC (≃6 × 10 8 voxels), APT reduces the total data acquisition and computation time from 67.96 h to 38 min. We expect our physics-assisted and attention-utilizing machine learning framework to be applicable to other branches of nanoscale imaging, including materials science and biological imaging.

47 OTHER INSTRUMENTATION↗
NASA NTRS1972

Electric dipole radiation at VLF in a uniform warm magneto-plasma.

Use of a linear full electromagnetic wave theory to calculate the input impedance of an electric antenna embedded in a uniform, lossless, unbounded warm magnetoplasma, which is assumed to consist of warm electrons and cold ions. In calculating the dipole radiation resistance for the thermal modes and the thermally modified whistler mode the analysis includes the finite temperature only for the electrons. In deriving the formal solution of the warm plasma dipole input impedance a full-wave analysis is used and two antenna orientations are considered, parallel and perpendicular to the static magnetic field. A general dispersion equation governing the modes of propagation is derived and a detailed analysis is made of the propagation characteristics of these modes.

Wang, T. N. C.↗
NASA NTRS1994

Fundamental and harmonic radiation in type III solar radio bursts

Type III solar radio bursts are investigated by modeling the propagation of the electron beam and the generation and subsequent propagation of waves to the observer. Predictions from this model are compared in detail with particle, Langmuir wave, and radio data from the International Sun Earth Explorer-3 (ISSE-3) spacecraft and with other observations to clarify the roles of fundamental and harmonic emission in type III radio bursts. Langmuir waves are seen only after the arrival of the beam, in accord with the standard theory. These waves persist after a positive beam slope is last resolved, implying that sporadic positive slopes persist for some time, unresolved but in accord with the predictions of stochastic growth theory. Local electromagnetic emission sets in only after Langmuir waves are seen, in accord with the standard theory, which relies on nonlinear processes involving Langmuir waves. In the events investigated here, fundamental radiation appears to dominate early in the event, followed and/or accompanied by harmonic radiation after the peak, with a long-lived tail of multiply scattered fundamental or harmonic emission extending long afterwards. These results are largely independent of, but generally consistent with, the conclusions of earlier works.

Robinson, P. A.↗
NASA NTRS1995

On absorbing boundary conditions for linearized Euler equations by a perfectly matched layer

Recently, Berenger introduced a Perfectly Matched Layer (PML) technique for absorbing electromagnetic waves. In the present paper, a perfectly matched layer is proposed for absorbing out-going two-dimensional waves in a uniform mean flow, generated by linearized Euler equations. It is well known that the linearized Euler equations support acoustic waves, which travel with the speed of sound relative to the mean flow, and vorticity and entropy waves, which travel with the mean flow. The PML equations to be used at a region adjacent to the artificial boundary for absorbing these linear waves are defined. Plane waves solutions to the PML equations are developed and wave propagation and absorption properties are given. It is shown that the theoretical reflection coefficients at an interface between the Euler and PML domains are zero, independent of the angle of incidence and frequency of the waves. As such, the present study points out a possible alternative approach for absorbing out-going waves of the Euler equations with little or no reflection in computation. Numerical examples that demonstrate the validity of the proposed PML equations are also presented.

Hu, Fang Q.↗
DOE OSTI2021

Current-conserving relativistic linear response for collisional plasmas

Here we investigate the response of a relativistic plasma to electromagnetic fields in the framework of the Boltzmann equation incorporating a collision term in the relaxation rate approximation selected in a form assuring current conservation. We obtain an explicit solution for the linearized perturbation of the Fermi–Dirac equilibrium distribution in terms of the average relaxation rate k. We study the resulting covariant, gauge invariant, and current conserving form of the polarization tensor in the ultrarelativistic and non-relativistic limits. We evaluate the susceptibility in the ultrarelativistic limit and explore their dependence on k. Finally, we study the dispersion relations for the longitudinal and transverse poles of the propagator. We show that for k >2ω p , where ω p is the plasma frequency, the plasma wave modes are overdamped. In the opposite case, k$\ll$ ω p , the propagating plasma modes are weakly damped.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1994

Radio sounding of the magnetosphere from a lunar-based VLF array

Using a lunar-based active radio transmitter and receiver system operating in the 'free space' wave modes, we can obtain much information on the structures and dynamics of remote magnetospheric plasma regions in a way similar to ionosondes. Powerful, narrow-band electromagnetic pulses can be transmitted over a wide frequency range (from 10 kHz to 1 MHz). The signals would be refracted and reflected off magnetospheric structures such as the plasmapause, plasmasheet, magnetopause, and the high and low latitude boundary layers. With a series of long dipole antennas, ranging in size from 400 m to 20 km with an output voltage ranging from 6 kV to less than 0.2 kV, a target plasma region at up to 100 R(sub E) can be explored. We illustrate this remote sensing technique by using the plasmasphere as a remote target, and modeling the propagations of the sounder transmitted and received pulses by ray tracing calculations.

Green, James L.↗
DOE OSTI2012

Light-Front Holographic QCD

The relation between the hadronic short-distance constituent quark and gluon particle limit and the long-range confining domain is yet one of the most challenging aspects of particle physics due to the strong coupling nature of Quantum Chromodynamics, the fundamental theory of the strong interactions. The central question is how one can compute hadronic properties from first principles; i.e., directly from the QCD Lagrangian. The most successful theoretical approach thus far has been to quantize QCD on discrete lattices in Euclidean space-time. Lattice numerical results follow from computation of frame-dependent moments of distributions in Euclidean space and dynamical observables in Minkowski spacetime, such as the time-like hadronic form factors, are not amenable to Euclidean lattice computations. The Dyson-Schwinger methods have led to many important insights, such as the infrared fixed point behavior of the strong coupling constant, but in practice, the analyses are limited to ladder approximation in Landau gauge. Baryon spectroscopy and the excitation dynamics of nucleon resonances encoded in the nucleon transition form factors can provide fundamental insight into the strong-coupling dynamics of QCD. New theoretical tools are thus of primary interest for the interpretation of the results expected at the new mass scale and kinematic regions accessible to the JLab 12 GeV Upgrade Project. The AdS/CFT correspondence between gravity or string theory on a higher-dimensional anti-de Sitter (AdS) space and conformal field theories in physical space-time has led to a semiclassical approximation for strongly-coupled QCD, which provides physical insights into its nonperturbative dynamics. The correspondence is holographic in the sense that it determines a duality between theories in different number of space-time dimensions. This geometric approach leads in fact to a simple analytical and phenomenologically compelling nonperturbative approximation to the full light-front QCD Hamiltonian 'Light-Front Holography'. Light-Front Holography is in fact one of the most remarkable features of the AdS/CFT correspondence. The Hamiltonian equation of motion in the light-front (LF) is frame independent and has a structure similar to eigenmode equations in AdS space. This makes a direct connection of QCD with AdS/CFT methods possible. Remarkably, the AdS equations correspond to the kinetic energy terms of the partons inside a hadron, whereas the interaction terms build confinement and correspond to the truncation of AdS space in an effective dual gravity approximation. One can also study the gauge/gravity duality starting from the bound-state structure of hadrons in QCD quantized in the light-front. The LF Lorentz-invariant Hamiltonian equation for the relativistic bound-state system is P{sub {mu}}P{sup {mu}}|{psi}(P)> = (P{sup +}P{sup -} - P{sub {perpendicular}}{sup 2})|{psi}(P)> = M{sup 2}|{psi}(P)>, P{sup {+-}} = P{sup 0} {+-} P{sup 3}, where the LF time evolution operator P{sup -} is determined canonically from the QCD Lagrangian. To a first semiclassical approximation, where quantum loops and quark masses are not included, this leads to a LF Hamiltonian equation which describes the bound-state dynamics of light hadrons in terms of an invariant impact variable {zeta} which measures the separation of the partons within the hadron at equal light-front time {tau} = x{sup 0} + x{sup 3}. This allows us to identify the holographic variable z in AdS space with an impact variable {zeta}. The resulting Lorentz-invariant Schroedinger equation for general spin incorporates color confinement and is systematically improvable. Light-front holographic methods were originally introduced by matching the electromagnetic current matrix elements in AdS space with the corresponding expression using LF theory in physical space time. It was also shown that one obtains identical holographic mapping using the matrix elements of the energy-momentum tensor by perturbing the AdS metric around its static solution. A gravity dual to QCD is not known, but the mechanisms of confinement can be incorporated in the gauge/gravity correspondence by modifying the AdS geometry in the large infrared (IR) domain z {approx} 1 = {Lambda}{sub QCD}, which also sets the scale of the strong interactions. In this simplified approach we consider the propagation of hadronic modes in a fixed effective gravitational background asymptotic to AdS space, which encodes salient properties of the QCD dual theory, such as the ultraviolet (UV) conformal limit at the AdS boundary, as well as modifications of the background geometry in the large z IR region to describe confinement. The modified theory generates the point-like hard behavior expected from QCD, instead of the soft behavior characteristic of extended objects.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Design of multi neutron-to-gamma converter array for measuring time resolved ion temperature of inertial confinement fusion implosions

The ion temperature varying during inertial confinement fusion implosions changes the amount of Doppler broadening of the fusion products, creating subtle changes in the fusion neutron pulse as it moves away from the implosion. A diagnostic design to try to measure these subtle effects is introduced—leveraging the fast time resolution of gas Cherenkov detectors along with a multi-puck array that converts a small amount of the neutron pulse into gamma-rays, one can measure multiple snapshots of the neutron pulse at intermediate distances. Further, precise measurements of the propagating neutron pulse, specifically the variation in the peak location and the skew, could be used to infer time-evolved ion temperature evolved during peak compression.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Symmetry Protected Two-Photon Coherence Time

We report the observation of symmetry protected two-photon coherence time of biphotons generated from backward spontaneous four-wave mixing in laser-cooled 87 Rb atoms. When biphotons are nondegenerate, nonsymmetric photonic absorption loss results in exponential decay of the temporal waveform of the two-photon joint probability amplitude, leading to shortened coherence time. In contrast, in the case of degenerate biphotons, when both paired photons propagate with the same group velocity and absorption coefficient, the two-photon coherence time, protected by space-time symmetry, remains unaffected by medium absorptive losses. Furthermore, our experimental results validate these theoretical predictions. This outcome highlights the pivotal role of symmetry in manipulating and controlling photonic quantum states.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2016

Full-wave modeling of EMIC waves near the He + gyrofrequency

Electromagnetic ion cyclotron (EMIC) waves are known to be excited by the cyclotron instability associated with hot and anisotropic ion distributions in the equatorial region of the magnetosphere and are thought to play a key role in radiation belt losses. Although detection of these waves at the ground can provide a global view of the EMIC wave environment, it is not clear what signatures, if any, would be expected. One of the significant scientific issues concerning EMIC waves is to understand how these waves are detected at the ground. In order to solve this puzzle, it is necessary to understand the propagation characteristics of the field-aligned EMIC waves, which include polarization reversal, cutoff, resonance, and mode coupling between different wave modes, in a dipolar magnetic field. However, the inability of ray tracing to adequately describe wave propagation near the crossover cutoff-resonance frequencies in multi-ion plasmas is one of reasons why these scientific questions remain unsolved. Using a recently developed 2-D full-wave code that solves the full-wave equations in global magnetospheric geometry, we demonstrate how EMIC waves propagate from the equatorial region to higher magnetic latitude in an electron-proton-He+ plasma. We find that polarization reversal occurs at the crossover frequency from left-hand polarization (LHP) to right-hand (RHP) polarization and such RHP EMIC waves can either propagate to the inner magnetosphere or reflect to the outer magnetosphere at the Buchsbaum resonance location. Lastly, we also find that mode coupling from guided LHP EMIC waves to unguided RHP or LHP waves (i.e., fast mode) occurs.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Electromagnetic Inhomogeneous-Energy-Density-Driven Instability in the UCLA Large Plasma Device (EM-IEDDI in LAPD) (Final Technical Report)

Using the Large Plasma Device (LAPD), the electromagnetic signatures associated with the inhomogeneous-energy-density-driven (IEDD) instability were targeted for documentation in a lab experiment. Exploitable features of LAPD are the extreme-length, high-beta, low-collisionality, and excellent reproducibility. The signatures of interest were mode amplitude, mode structure, frequency spectrum, phase velocity, and excitation threshold. The abrupt inhomogeneity at the interface between two coaxial plasma columns, that have disparate space potential values, were expected to generate a strong, localized, transverse, dc electric field and form a strong ExB-flow inhomogeneity that was expected to trigger broadband, intermediate-frequency waves that propagate many gyroradii beyond the interfacial source region. WVU was unable to destabilize the IEDDI mode in LAPD. Experimental limitation of three different parameters conspire to prevent IEDDI-favorable conditions even though Alfven-favorable conditions are met. Electron-neutral collision frequency is too high, Structuring of the radial profile of the radial electric field is negligible and the control of that structure is minimal, and the Magnetic field is too large for some purposes and too small for other purposes. WVU designed a new antenna and relied on externally-driving the IEDDI (instead of spontaneous destabilization). The antenna operation failed for unforeseen reasons and lack of electrician time and availability.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS2016

Mixing the Solar Wind Proton and Electron Scales: Effects of Electron Temperature Anisotropy on the Oblique Proton Firehose Instability

The double adiabatic expansion of the nearly collisionless solar wind plasma creates conditions for the firehose instability to develop and efficiently prevent the further increase of the plasma temperature in the direction parallel to the interplanetary magnetic field. The conditions imposed by the firehose instability have been extensively studied using idealized approaches that ignore the mutual effects of electrons and protons. Recently, more realistic approaches have been proposed that take into account the interplay between electrons and protons, unveiling new regimes of the parallel oscillatory modes. However, for oblique wave propagation the instability develops distinct branches that grow much faster and may therefore be more efficient than the parallel firehose instability in constraining the temperature anisotropy of the plasma particles. This paper reports for the first time on the effects of electron plasma properties on the oblique proton firehose (PFH) instability and provides a comprehensive vision of the entire unstable wave-vector spectrum, unifying the proton and the smaller electron scales. The plasma β and temperature anisotropy regimes considered here are specific for the solar wind and magnetospheric conditions, and enable the electrons and protons to interact via the excited electromagnetic fluctuations. For the selected parameters, simultaneous electron and PFH instabilities can be observed with a dispersion spectrum of the electron firehose (EFH) extending toward the proton scales. Growth rates of the PFH instability are markedly boosted by the anisotropic electrons, especially in the oblique direction where the EFH growth rates are orders of magnitude higher.

plasmas↗
NASA NTRS2019

Electromagnetic Scattering by Discrete Random Media. I: The Dispersion Equation and the Configuration-Averaged Exciting Field

We consider the scattering of a plane electromagnetic wave obliquely incident on a plane-parallel layer of discrete random medium with non-scattering boundaries. We solve the Lax integral equation for the conditional configuration-averaged exciting field coefficients by assuming a special-form solution, that is, by representing the conditional configuration-averaged exciting field coefficients as a linear combination of the coefficients corresponding to an up-going and a down-going wave. This solution representation is supposed to be valid within the whole domain occupied by the particles, even in the close proximity of the boundaries. By balancing the waves with different propagation directions and wavenumbers we derive two homogeneous systems of equations corresponding to the generalized Lorenz–Lorentz law and two inhomogeneous systems of equations corresponding to the generalized Ewald–Oseen extinction theorem. It is shown that (i) the two homogeneous systems of equations of the generalized Lorenz–Lorentz law reduce to a single homogeneous system of equations corresponding to a semi-infinite discrete random medium at normal incidence; (ii) the dispersion equation is direction and polarization independent; and (iii) the two inhomogeneous systems of equations of the generalized Ewald–Oseen extinction theorem can be reduced to two scalar equations by means of the addition theorem for vector spherical harmonics. It is also shown that the same dispersion equation can be obtained without assuming a special-form solution representation in the proximity of the boundaries.

Adrian Doicu↗
DOE OSTI2012

Propagation of gamma rays and production of free electrons in air

This paper is devoted to the analysis of production of free electrons in air by gamma-rays leaking from radioactive materials. A model based on the Klein-Nishina scattering theory is used to calculate scattering cross sections and approximate the electron production rate. The model includes the effects of primary gamma-quanta radiated by the source as well as that scattered in air. Comparison of the model with the mcnpx kinetic code (http://mcnpx.lanl.gov/) in a sample problem shows excellent agreement. The motivation for this research comes from the recently proposed concept of remote detection of concealed radioactive materials [V. L. Granatstein and G. S. Nusinovich, J. Appl. Phys. 108, 063304 (2010)]. The concept is based on the breakdown in air at the focal point of a high-power beam of electromagnetic waves produced by a THz gyrotron with a 10-20 {mu}s pulse. The presence of a radioactive material can greatly exceed the production rate of free electrons over the natural background rate. Additional electrons act as seeds to initiate the breakdown and create sufficiently dense plasma at the focal region. The dense plasma can then be remotely detected as an unambiguous effect of the concealed radioactive material.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2017

Elliptically polarised normal modes under conditions of nonstationary electromagnetically induced transparency

We report the results of numerical simulation of the evolution of a weak elliptically polarised input probe pulse in the case of electromagnetically induced transparency in the field of elliptically polarised control light. It is shown that the electric field strength of any input probe pulse can be represented as a sum of the electric field strengths of two subpulses whose polarisation ellipses have the same constant eccentricities and mutually perpendicular directions of the major axes, one of these axes being parallel to the major axis of the polarisation ellipse of the control light. The directions of rotation of the electric field strength vectors of subpulses are mutually opposite. Subpulses move with different velocities in a medium, which leads to their spatial separation. In the propagation of subpulses, their polarisation characteristics (eccentricities and directions of major axes of polarisation ellipses) remain unchanged. At any stage of evolution, including the instants of significant spatial overlapping of subpulses, the intensity of the probe light in the medium is the sum of their intensities. Consequently, these subpulses are nonstationary mutually orthogonal elliptically polarised normal modes of the probe field whose existence is related to the medium anisotropy caused by the control field. The simulation is carried out for a scheme of degenerate quantum transitions between {sup 3}P{sub 0}, {sup 3}P{sup 0}{sub 1} and {sup 3}P{sub 2} levels of the 208Pb isotope, taking into account the Doppler broadening of the spectral lines under the assumption that the probe field has a higher frequency than the control field. (nonlinear optical phenomena)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗