Singular Integral Equations. By N.I. Muskhelishvili. Translated fromthe 2nd Russian edition by J.R.M. Radok. Pp. 447. F1. 28.50. 1953. (Noordhoff, Groningen)

This self-contained, comprehensive book describes the fundamental properties of soft x-rays and extreme ultraviolet (EUV) radiation and discusses their applications in a wide variety of fields, including EUV lithography for semiconductor chip manufacture and soft x-ray biomicroscopy. The author begins by presenting the relevant basic principles such as radiation and scattering, wave propagation, diffraction, and coherence. He then goes on to examine a broad range of phenomena and applications. The topics covered include EUV lithography, biomicroscopy, spectromicroscopy, EUV astronomy, synchrotron radiation, and soft x-ray lasers. He also provides a great deal of useful reference material such as electron binding energies, characteristic emission lines and photo-absorption cross-sections. The book will be of great interest to graduate students and researchers in engineering, physics, chemistry, and the life sciences. It will also appeal to practicing engineers involved in semiconductor fabrication and materials science.

X-Rays and Extreme Ultraviolet Radiation: Principles and Applications

When a plasma is of finite transverse cross section, space-charge waves may propagate even in the absence of a drift motion or thermal velocities of the plasma. Some of the properties of these space charge waves have been investigated by regarding the plasma as a dielectric and solving the resulting field equations. The effect of a steady axial magnetic field is considered, but motion of heavy ions and electron temperature effects are neglected. Waves are found to exist at frequencies low compared with the plasma frequency as well as waves with oppositely directed phase and group velocities (backward waves).Many of the features of these waves have been verified experimentally by measuring phase velocity and attenuation of waves along the positive column of a low pressure mercury arc in an axial magnetic field. Measurements of electron density have been made using these waves and the results are compared with those obtained by other methods. An interesting feature of these measurements, of value in plasma diagnostics, is that they can be made with frequencies which are small compared with the plasma frequency.

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Space Charge Waves in Cylindrical Plasma Columns

Dense quantum plasmas are ubiquitous in planetary interiors and in compact astrophysical objects (e.g., the interior of white dwarf stars, in magnetars, etc.), in semiconductors and micromechanical systems, as well as in the next-generation intense laser–solid density plasma interaction experiments and in quantum X-ray free-electron lasers. In contrast to classical plasmas, quantum plasmas have extremely high plasma number densities and low temperatures. Quantum plasmas are composed of electrons, positrons and holes, which are degenerate. Positrons (holes) have the same (slightly different) mass as electrons, but opposite charge. The degenerate charged particles (electrons, positrons, and holes) obey the Fermi–Dirac statistics. In quantum plasmas, there are new forces associated with (i) quantum statistical electron and positron pressures, (ii) electron and positron tunneling through the Bohm potential, and (iii) electron and positron angular momentum spin. Inclusion of these quantum forces allows the existence of very high-frequency dispersive electrostatic and electromagnetic waves (e.g., in the hard X-ray and gamma-ray regimes) with extremely short wavelengths. In this review paper, we present theoretical backgrounds for some important nonlinear aspects of wave–wave and wave–electron interactions in dense quantum plasmas. Specifically, we focus on nonlinear electrostatic electron and ion plasma waves, novel aspects of three-dimensional quantum electron fluid turbulence, as well as nonlinearly coupled intense electromagnetic waves and localized plasma wave structures. Also discussed are the phase-space kinetic structures and mechanisms that can generate quasistationary magnetic fields in dense quantum plasmas. The influence of the external magnetic field and the electron angular momentum spin on the electromagnetic wave dynamics is discussed. Finally, future perspectives of the nonlinear quantum plasma physics are highlighted.

http://iopscience.iop.org/article/10.3367/UFNe.0180.201001b.0055/pdf

Nonlinear aspects of quantum plasma physics

The current understanding of some important nonlinear collective processes in quantum plasmas with degenerate electrons is presented. After reviewing the basic properties of quantum plasmas, model equations (e.g., the quantum hydrodynamic and effective nonlinear Schrodinger-Poisson equations) are presented that describe collective nonlinear phenomena at nanoscales. The effects of the electron degeneracy arise due to Heisenberg’s uncertainty principle and Pauli’s exclusion principle for overlapping electron wave functions that result in tunneling of electrons and the electron degeneracy pressure. Since electrons are Fermions (spin-1/2 quantum particles), there also appears an electron spin current and a spin force acting on electrons due to the Bohr magnetization. The quantum effects produce new aspects of electrostatic (ES) and electromagnetic (EM) waves in a quantum plasma that are summarized in here. Furthermore, nonlinear features of ES ion waves and electron plasma oscillations are discussed, as well as the trapping of intense EM waves in quantum electron-density cavities. Specifically, simulation studies of the coupled nonlinear Schrodinger and Poisson equations reveal the formation and dynamics of localized ES structures at nanoscales in a quantum plasma. The effect of an external magnetic field on the plasma wave spectra and develop quantum magnetohydrodynamic equations are also discussed. The results are useful for understanding numerous collective phenomena in quantum plasmas, such as those in compact astrophysical objects (e.g., the cores of white dwarf stars and giant planets), as well as in plasma-assisted nanotechnology (e.g., quantum diodes, quantum free-electron lasers, nanophotonics and nanoplasmonics, metallic nanostructures, thin metal films, semiconductor quantum wells, and quantum dots, etc.), and in the next generation of intense laser-solid density plasma interaction experiments relevant for fast ignition in inertial confinement fusion schemes.

/pdf/colloquium-nonlinear-collective-interactions-in-quantum-1nqlatefgo.pdf

Colloquium : nonlinear collective interactions in quantum plasmas with degenerate electron fluids

The problem of the ac conductivity of a fully ionized plasma is investigated for frequencies embracing the plasma frequency. The finite duration of encounters is taken into account in a self‐consistent fashion which includes collective effects. The concomitant processes of absorption and emission of electromagnetic radiation are investigated and in particular the bremsstrahlung emission and absorption coefficients near the plasma frequency are given. The conversion of longitudinal to transverse waves by scattering from ions is discussed.

High‐Frequency Conductivity and the Emission and Absorption Coefficients of a Fully Ionized Plasma

In an earlier work the ac conductivity of a plasma was investigated by means of an elementary model. The validity of this model has been borne out by a rigorous treatment of plasma at thermal equilibrium. The elementary model is now extended to include the effects of ion correlations for arbitrary fixed ion distributions. For thermal equilibrium correlations it is found that the ion shielding reduces the maximum effective impact parameter by the factor (1 + Z)½ (i.e., both ions and electrons contribute to the shielding) for frequencies low compared to the plasma frequency ωp. For frequencies high compared to ωp, the previous results obtain. The resistance due to the excitation of longitudinal waves at frequencies just in excess of ωp is reduced by the factor (1 + Z)−1. However, if large‐amplitude (nonthermal) ion fluctuations are present, the longitudinal wave contribution to the resistance may be greatly enhanced.

Effect of Ion Correlations on High-Frequency Plasma Conductivity

A complete classical derivation of the frequency‐dependent conductivity is presented which properly takes into account collective dynamics. This treatment rests on the joint solution of the first two members of the BBGKY hierarchy, in the plasma limit, when both are able to change on the same time scale. For arbitrary frequencies this leads to an integral equation for the one‐particle distribution function which can be solved by conventional variational and/or numerical procedures. For frequencies high compared to the collision frequency, an explicit statement of the conductivity is possible. This high‐frequency limit is further examined in the limit of small electron to ion mass ratio and these limiting results are compared with those of other authors.

High‐Frequency Conductivity of a Fully Ionized Plasma

ABS>A complete classical derivation of the frequency dependent conductivity is presented that properly takes into account collective dynamics. This treatment rests on the joint solution of the first two members of the BBGKY hierarchy, in the plasma limit, when both are able to change on the same time- scale. For arbitrary frequencies this leads to an integral equation for the one- particle distribution function that can be solved by conventional variational and/ or numerical procedures. For irequencies high compared to the collision frequency, an explicit statement of the conductivity is possible. This high frequency limit is further examined in the limit of small electron to ion mass ratio, and these limiting results are compared with those of other authors. (auth)

A rigorous calculation of the high frequency conductivity of a fully ionized plasma

Of prime concern in plasma investigations is the coupling of a bounded plasma with external electromagnetic fields. In the present paper the properties of the normal modes of a cold plasma slab, and cylinder, situated in a strong magnetic field are derived, and then used to discuss the transmission and reflection of radiation, the scattering by a plasma cylinder, the response to driving sources in the vicinity of the plasma, and the radiation due to plasma oscillations.

Carl Oberman

Papers

High‐Frequency Conductivity and the Emission and Absorption Coefficients of a Fully Ionized Plasma

Effect of Ion Correlations on High-Frequency Plasma Conductivity

High‐Frequency Conductivity of a Fully Ionized Plasma

A rigorous calculation of the high frequency conductivity of a fully ionized plasma

Oscillations of a finite cold plasma in a strong magnetic field