Nonlinear Electron Density Research Articles

Self-focusing and defocusing of Gaussian laser beams in collisional inhomogeneous plasmas with linear density and temperature ramps

Self-focusing and defocusing of Gaussian laser beams in collisional inhomogeneous plasmas are investigated in the presence of various laser intensities and linear density and temperature ramps. Considering the ponderomotive force and using the momentum transfer and energy equations, the nonlinear electron density is derived. Taking into account the paraxial approximation and nonlinear electron density, a nonlinear differential equation, governing the focusing and defocusing of the laser beam, is obtained. Results show that in the absence of ramps the laser beam is focused between a minimum and a maximum value of laser intensity. For a certain value of laser intensity and initial electron density, the self-focusing process occurs in a temperature range which reaches its maximum at turning point temperature. However, the laser beam is converged in a narrow range for various amounts of initial electron density. It is indicated that the σ2 parameter and its sign can affect the self-focusing process for different values of laser intensity, initial temperature, and initial density. Finally, it is found that although the electron density ramp-down diverges the laser beam, electron density ramp-up improves the self-focusing process.

Instability and dynamics of two nonlinearly coupled intense laser beams in a quantum plasma

We consider nonlinear interactions between two relativistically strong laser beams and a quantum plasma composed of degenerate electron fluids and immobile ions. The collective behavior of degenerate electrons is modeled by quantum hydrodynamic equations composed of the electron continuity, quantum electron momentum (QEM) equation, as well as the Poisson and Maxwell equations. The QEM equation accounts the quantum statistical electron pressure, the quantum electron recoil due to electron tunneling through the quantum Bohm potential, electron-exchange, and electron-correlation effects caused by electron spin, and relativistic ponderomotive forces (RPFs) of two circularly polarized electromagnetic (CPEM) beams. The dynamics of the latter are governed by nonlinear wave equations that include nonlinear currents arising from the relativistic electron mass increase in the CPEM wave fields, as well as from the beating of the electron quiver velocity and electron density variations reinforced by the RPFs of the two CPEM waves. Furthermore, nonlinear electron density variations associated with the driven (by the RPFs) quantum electron plasma oscillations obey a coupled nonlinear Schrödinger and Poisson equations. The nonlinearly coupled equations for our purposes are then used to obtain a general dispersion relation (GDR) for studying the parametric instabilities and the localization of CPEM wave packets in a quantum plasma. Numerical analyses of the GDR reveal that the growth rate of a fastest growing parametrically unstable mode is in agreement with the result that has been deduced from numerical simulations of the governing nonlinear equations. Explicit numerical results for two-dimensional (2D) localized CPEM wave packets at nanoscales are also presented. Possible applications of our investigation to intense laser-solid density compressed plasma experiments are highlighted.

Temporal‐spatial modeling of electron density enhancement due to successive lightning strokes

We report results on the temporal‐spatial modeling of electron density enhancement due to successive lightning strokes. Stroke rates based on World‐Wide Lightning Location Network measurements are used as input to an axisymmetric Finite Difference Time Domain model that describes the effect of lightning electromagnetic pulses (EMP) on the ionosphere. Each successive EMP pulse interacts with a modified background ionosphere due to the previous pulses, resulting in a nonlinear electron density perturbation over time that eventually reaches a limiting value. The qualitative ionospheric response to successive EMPs is presented in 2‐D, axisymmetric space. Results from this study show that the nonlinear electron density perturbations due to successive lightning strokes must be taken into account and varies with altitude. The limiting maximum electron density is reached earlier in time for higher altitudes, and the most significant effect occurs at 88 km. The limiting modeled electron density profile in the 83–91 km altitude range does not depend on the initial electron density.

Nonlinear cooling of relativistic particles under equipartition conditions

Aims. In powerful cosmic nonthermal radiation sources with dominant magnetic-field self generation, the plasma physical processes generating these magnetic fields by relativistic plasma instabilities are closely related to the processes energising ultra-high energy radiating electrons in these sources. Then the magnetic field strength becomes time-dependent and adjusts itself to the actual kinetic energy density of the radiating electrons. As a consequence, the synchrotron radiation cooling of individual relativistic electrons exhibits a nonlinear behaviour because of the dependence of the magnetic energy density on the actual time-varying kinetic energy density. Methods. The nonlinear kinetic equation for the intrinsic temperoral evolution of relativistic electrons is solved for the case of instantaneous injection of power-law distributed electrons. Results. The properties of the resulting approximate, nonlinear electron density show significant differences compared to the standard linear solution for constant non-equipartition magnetic-field energy density as, for instance, the different time behaviour of the upper and lower cut-offs of the electron distribution. Also the differential electron fluence as a function of electron energy differs from the linear fluence. For large spectral indices s > 2 of the injected power law, the nonlinear fluence exhibits a weaker break at the lower injected electron cut-off γ1 than the linear fluence. For small spectral indices 1 2) injected power laws, the nonlinear synchrotron fluence at low frequencies approaches a power law ∝ν −0.6 , independent of the value of s, which is identical to the synchrotron fluence behaviour from monoenergetically injected relativistic electrons.

Nonlinear electron density waves and nonlinear acoustic waves in carbon nanotubes

Problems in nonlinear properties of carbon nanotubes with a strong interaction of electrons are considered if the electron mobility, the Coulomb repulsion of electrons at one site of a carbon nanotube, and variations in the distance between neighboring sites owing to acoustic oscillations are taken into account. The possible occurrence of nonlinear acoustic lattices in carbon nanotubes that are small in diameter is investigated.

Density-potential relation via the single-particle kinetic energy density for one-dimensional two-level fermion systems with application to Be-like atomic ions in the(1s)2(2s)2configuration

Using the Dawson-March transformation of two-level wave functions in terms of density amplitude and phase, a differential equation is constructed relating the single-particle kinetic energy to the fermion density. Employing then the differential form of the virial theorem derived by March and Young [Nucl. Phys. 12, 237 (1959)], a nonlinear electron-density--one-body potential relation emerges. Application to the Be-like atomic ions is briefly considered.

Destructive role of hot ions in the formation of electrostatic density humps and dips in dusty plasmas

It is shown that the ion thermal energy is destructive for the ion acoustic solitons in the presence of dust, and it decreases the value of Mach number for the formation of solitary structures. The regions of ion density humps and dips are produced simultaneously, corresponding to positive and negative values of the electrostatic potential. The nonlinear electron density also behaves in a similar fashion as that of ions. However, the dust density increases in the regions where the ion and electron densities are depleted and vice versa.

Second-harmonic generation and effect of adsorbates for free-electron metal and semiconductor surfaces

We discuss aspects of a developing microscopic theory of SHG from simple metal and semiconductor surfaces. For semiconductors calculations of the dynamical nonlinear susceptibility on the basis of realistic tight-binding parametrizations of the electronic Hamiltonian provide a practical scheme. In the resulting spectra the effect of the dangling bonds on SHG is clearly seen together with a strong decrease upon saturation with H atoms. In the metal case the adsorbate induced changes of the static nonlinear electron density can be calculated self-consistently by applying density functional theory to the jellium model. The second-order dipole moment determines the effect of adsorbates on the SHG intensity in the adiabatic limit. Quite general a correlation with the nature of the adsorbate expressed by its electronegativity and the characteristic charge transfer, adsorption dipole and polarizabilities in first and second order is found.

Stimulated Brillouin and Raman scattering of laser radiation at the upper hybrid frequency in a hot, collisionless, magnetized plasma

In this paper we have made a theoretical investigation of the stimulated Brillouin and Raman backscattering of laser radiation at the upper hybrid frequency in a laser-produced plasma, taking into account the effects of a spatially uniform self-generated magnetic field of the order of a few megagauss. The Vlasov equation has been employed to obtain the nonlinear electron density perturbation due to the low-frequency short-wavelength electrostatic mode and the current density due to the high-frequency, unmagnetized, scattered laser radiation in the plasma. This kinetic treatment is valid for plasmas produced by both ${\mathrm{CO}}_{2}$ and Nd-glass lasers and short-wavelength perturbations. It is noticed that the growth rates for both Brillouin and Raman backscattering increase with the self-generated magnetic field.

Nonlinear scattering from electron Bernstein modes in a plasma

Deals with the study of the nonlinear scattering of the upper hybrid laser radiation by electron Bernstein modes in a plasma. The nonlinear current density of unmagnetized scattered laser radiation and the nonlinear electron density perturbation of the magnetized electron Bernstein modes have been derived by the kinetic approach. The validity of the present analysis is marginal for CO2 lasers but well defined for Nd glass lasers.

Nonlinear scattering of an extra-ordinary laser radiation by fast ion waves in a plasma

Presents an investigation of nonlinear scattering of an extra-ordinary laser radiation by fast ion wave in a homogeneous plasma. Vlasov equation has been used to obtain (i) the nonlinear electron density perturbation of magnetised fast ion wave and (ii) the nonlinear current density of unmagnetised scattered laser radiation. For CO2 laser produced plasma, this analysis is valid marginally whereas for Nd: glass laser produced plasma, the validity of this analysis is very well described. Typically, for Nd: glass laser produced plasma (Power density approximately=1012 W/cm2), omega p approximately=10 omega c, omega p approximately= omega 0/4, Te approximately=9 keV, the growth rate for forward scattering by fast ion wave turns out to be approximately=2.0*1012 rad s-1. It is found that this growth rate is larger than that for other resonant interactions. The threshold is considerably low.

ChemInform Abstract: ELECTRONIC STRUCTURE OF HYDROGEN‐LIKE IMPURITIES IN NEARLY FREE‐ELECTRON METALS

Recent developments in our understanding of the electronic structure of hydrogen and its isotopes in simple metals is reviewed. The role of nonlinear electron density distribution in the interpretation of the electronic properties of hydrogen-like impurities is emphasized. Calculated Knight shifts and hyperfine fields at μ+ site and electric field gradients at cubic host nuclear sites due to interstitial μ+ are compared with recent experimental data. The feasibility of using positive muon as a probe of defect structure is discussed. Future experiments and theoretical investigations aimed at a deeper understanding of the electronic properties of μ+ are suggested.

Electronic structure of hydrogen-like impurities in nearly-free-electron metals

Recent developments in our understanding of the electronic structure of hydrogen and its isotopes in simple metals is reviewed. The role of nonlinear electron density distribution in the interpretation of the electronic properties of hydrogen-like impurities is emphasized. Calculated Knight shifts and hyperfine fields at μ+ site and electric field gradients at cubic host nuclear sites due to interstitial μ+ are compared with recent experimental data. The feasibility of using positive muon as a probe of defect structure is discussed. Future experiments and theoretical investigations aimed at a deeper understanding of the electronic properties of μ+ are suggested.