Spectrum Of Electron Density Fluctuations Research Articles

Measurement of the magnetic field direction in a plasma by collective scattering with a CO2 laser

The effect of strongly magnetized electrons on the spectrum of collective electron density fluctuations can be used to measure the magnetic field direction in a plasma with laser light scattering. The application of this method to measure the poloidal field in tokamaks is discussed. It is shown that noncircular beam cross sections will increase the angular resolution without loss in spatial resolution. In experiments to measure the ion temperature this technique results in an increase of scattered power received. The magnetic field direction was measured for the first time in a laboratory plasma using a pulsed CO2 laser and coherent detection.

Small-scale electron density turbulence in the interstellar medium

view Abstract Citations (321) References (74) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Small-scale electron density turbulence in the interstellar medium. Cordes, J. M. ; Weisberg, J. M. ; Boriakoff, V. Abstract Diffraction phenomena associated with the scattering of pulsar radiation are used to constrain the power spectrum and galactic distribution of electron density fluctuations. The authors combine new measurements of interstellar scintillation bandwidths and pulse broadening times with those from the literature to yield information on 76 lines of sight. For individual objects, the scaling of scintillation bandwidth with frequency is in agreement with a Kolmogorov spectrum. The study of all objects, however, indicates strong disagreement with a model in which turbulence is uniformly distributed. The data suggest a two-component model for electron density turbulence: (1) a clumped medium with scale height H ⪉ 100 pc; (2) a nearly uniform medium with H ⪆ 0.5 kpc. Scattering material is ubiquitous but is preferentially located near regions of large energy input into the interstellar medium. Publication: The Astrophysical Journal Pub Date: January 1985 DOI: 10.1086/162784 Bibcode: 1985ApJ...288..221C Keywords: Electron Density (Concentration); Interstellar Matter; Pulsars; Turbulence; Cross Correlation; Line Of Sight; Radiative Transfer; Stellar Radiation; Stellar Spectra; Wave Scattering; Astrophysics full text sources ADS | data products SIMBAD (75)

Unified theory of the power spectrum of intermediate wavelength ionospheric electron density fluctuations

An extension of the Kolmogorov theory of fluid turbulence is used to develop a unified treatment of the power spectrum of intermediate wavelength electron density fluctuations in the equatorial and high‐latitude ionosphere. Favorable comparison is made between theory and experimental observations.

The ion feature in a laboratory plasma: Theory and experiment using CO2 laser light scattering

The electron density fluctuation spectrum in the range of frequencies below the ion plasma frequency (the ‘‘ion feature’’) is investigated in plasmas where the ion acoustic waves are weakly damped. The situation typical in laboratory plasmas where the electron temperature is larger than the ion temperature is considered in detail. Analytical expressions are given in the limit of weak damping and the variations of the spectrum with the relevant parameters are readily obtained, including the dependence on frequency, wavenumber, temperature ratio, drift velocity, and the concentrations of light impurity ions. Velocity distributions with non-Maxwellian tails are also considered. An experiment is described in which the scattering of CO2 laser radiation from a discharge plasma is studied. The observed fluctuation spectrum corresponds to the ion feature, in that the dependence of the observed frequencies on wavenumber corresponds to the dispersion relation of ion acoustic waves. They are only observed, however, in the edge plasma where drifting ions enhance the fluctuation level, and not in the plasma center, where light impurities in the argon plasma damp out the ion resonance.

Chemical Contributions to the Fluctuation Spectrum in a Plasma

A kinetic theory is presented for the electron density fluctuation spectrum in a chemically active plasma. Collisions as well as chemical reactions are described by means of BGK models. Approximations corresponding to mesospheric heights are invoked. It is concluded that, in general, the chemical reactions then have only rather small effects on the fluctuation spectrum.

Simultaneous measurement of magnetic field direction and ion temperature in a plasma by collective scattering with a CO2 laser

The effect of strongly magnetized electrons on the spectrum of collective electron density fluctuations was observed for the first time in a laboratory plasma. A single mode CO2 laser and coherent detection were used to scatter from a hydrogen plasma with the scattering wave vector perpendicular to the magnetic field. The results demonstrate that both the ion temperature and direction of the magnetic field can be measured simultaneously.

Analytic solution for the two‐frequency mutual coherence function for spherical wave propagation

The quadratic approximation for the phase structure function is used to obtain the two‐frequency mutual coherence function Γ(Δρ, Δω) for spherical wave propagation through a finite slab with transmitter and receiver located in free space on opposite sides of the slab. General analytic solutions are derived for two cases. In the first case the random slab is represented by a one‐dimensional power spectrum of electron density fluctuations corresponding to propagation through elongated irregularities as would occur for an equatorial satellite link to a ground station. In the second case the random slab consists of isotropic ionization irregularities. Both cases taken together represent the extremes of the range of results to be expected for propagation through ionospheric fluctuations, solar wind irregularities, or ionization irregularities caused by barium cloud instabilities. For both cases the complex general analytic results are simplified by use of the thin phase screen approximation to obtain useful analytic expressions for Γ as well as the resulting impulse response function. It is shown that the impulse response to a transmitted power delta function reduces to an exponential form in the limit of strong diffraction and to a Gaussian form in the geometrical optics limit. The Gaussian form corresponds to pulse wander while the exponential form corresponds to diffractive spreading produced by multipath effects. The relationship between the generalized power spectrum and the impulse response function is given, and results are presented for the mean time delay and time delay jitter. The accuracy of the thin phase screen calculation of these quantities is investigated in detail.

The measurement of large-scale density fluctuations in toroidal plasmas from the 'phase scintillation' of a probing electromagnetic wave

The plasma electron density fluctuation spectrum can be obtained from the measurement of the phase fluctuation spectrum of a probing electromagnetic wave measured some distance from the plasma. If the mean square fluctuation of the probing beam is much less than unity and the observer-plasma distance is well within the Fresnel distance of the irregularities, a direct relationship exists between the density and phase spectra. As an example of this procedure, an experiment is described which uses a probing beam wavelength of 2 mm to measure the density irregularities. It is then proposed that a suitable wavelength for the present large toroidal plasma devices is in the 10 mu m region.

Plasma oscillations and sound waves in collision-dominated two-component plasmas

Charge, mass, and electron density fluctuation spectra of strongly correlated, fully ionized two-component plasmas within the framework of the Mori–Zwanzig memory function formalism are analyzed. All dynamical correlation functions are expressed in terms of the memory functions of the ion and electron velocity autocorrelation functions by a generalized effective field approximation which preserves the exact initial values (i.e., static correlations). The theory reduces correctly to the mean field (or collisionless Vlasov) results in the weak coupling limit, and yields charge density fluctuation spectra in good agreement with available computer simulation data, as well as reasonable estimates of the transport coefficients. The collisional damping and frequency shift of the plasma oscillation mode are sizeable, even in the long wavelength limit. The theory also predicts the propagation of well-defined sound waves in dense plasmas in thermal equilibrium.

Coronal investigations with occulted spacecraft signals

The radio telemetry links between Earth and a spacecraft near superior conjunction penetrate the corona at ranges well within the acceleration regime of the solar wind. Occultation experiments in the solar corona have been performed on many interplanetary missions beginning with the Mariner and Pioneer series and extending up to the more recent data on Helios, Viking, and Voyager. The changes in group and phase velocity of the radio signal are measured to determine the total electron content of the corona and its fluctuations. The broadening of the carrier signal may be used in combination with the electron content data to derive a solar wind velocity profile. The wave number spectrum of electron density fluctuations in the corona may be inferred from amplitude and phase scintillations of the received signal. Linearly polarized signals, which are rotated along the propagation path by the Faraday effect, can provide information on the coronal magnetic field and its variations.

Sound wave contributions to the electron density fluctuation spectrum in plasmas

Theimer’s general theory of the electron density fluctuation spectrum in a plasma is extended to include collision-induced sound wave formation. This is achieved in two steps. First, therandom fluctuation spectrum, which is formally free of Coulomb correlations, is calculated by Theimer’s general theory, from a Vlasov equation with modified BGK collision term. The modification introduces a pressure term, (mυν)·υ/kBT, which is usually neglected; it is shown to represent the average pressure force per particle. Secondly, thecollective fluctuation spectrum is calculated from therandom spectrum, by means of Theimer’s general formalism. The resulting collective spectrum contains the effects of collision-induced sound wave formation. The most conspicuous of these effects is the collisionnarrowing of ion-acoustic resonance lines, which exhibit collisionbroadening when calculated without using the pressure term. This is demonstrated for a pure-hydrogen plasma and for a plasma containing ionized impurities.

Effects of very high collision frequencies on the electron density fluctuation spectrum of plasmas

This is a generalization of an earlier theory for calculating the electron density fluctuations in a plasma containing strongly ionized impurities. This earlier theory is based on the simplifying assumption that the collision parameter yμ is small so that only linear terms of first order in yμ have to be kept in the formalism. The present theory removes this unnecessary and unrealistic limitation and shows that a theory, nonlinear in yμ, can be deduced from the general principles of density fluctuations as easily as the linear theory. Some numerical results are presented which illustrate the difference between the linear and nonlinear theory.

Spacecraft radio scattering observations of the power spectrum of electron density fluctuations in the solar wind

Solar wind electron density power spectra in the solar equatorial region are inferred from observations of phase scintillations and spectral broadening made with the Viking, Helios, and Pioneer spacecraft. The heliocentric distance range covered is 2–215 RS, and for some observations close to the sun the spectra extend to fluctuation frequencies as high as 100 Hz. For heliocentric distances ≳20 RS the equivalent spacecraft‐measured one‐dimensional density spectrum Vne is well modeled by a single power law (f−α) in the frequency range 10−4‐5 × 10−2 Hz. The mean spectral index α is 1.65, very close to the Kolmogorov value of 5/3. Under the assumption of constant solar wind speed, Vne varies as R−3.45, where R is heliocentric distance. Within 20 RS, Vne can still be modeled by a single power law over the frequency range 10−3‐10¹ Hz, but the spectral index becomes smaller, α ∼ 1.1. The flattening of the density spectrum within 20 RS is presumably associated with energy deposition in the near‐sun region and acceleration of the solar wind.

The Crab Nebula pulsar - Variability of dispersion and scattering

Previous investigations of the effects of interstellar dispersion and scattering on the waveform of the Crab Nebula pulsar (NP 0532) have indicated a two-screen scattering model with one variable screen and have revealed anomalously large phase residuals at 73.8 MHz. The relevant observational data are reanalyzed in order to bring the two-screen model into better agreement with theoretical models of the interstellar medium and to account for the low-frequency (73.8-MHz) phase anomaly. The wavenumber spectrum of electron-density fluctuations is examined along with its role in scattering models involving an extended medium, a thick screen, or a thin screen. A tenable unit impulse response is constructed for a thin screen, its Fourier transform is analyzed, and an attempt is made to obtain the dispersion measure and scattering constants for two screens. A comparison of the resulting pulse-broadening and delay effects with other theoretical predictions shows that all observed pulse-broadening and delay effects in NP 0532 are consistent with scattering by a single thick slab of plasma occupying no more than one quarter of the line of sight.

Plasma irregularities in the comet's tail

Scintillation theory is invoked to explain fluctuations in radio intensity observed during occultation of the extragalactic radio source PKS 2025-15 by the plasma tail of comet 1973 XII on Jan. 5, 1975. Plasma irregularities and turbulence in the tail of the comet (Kohoutek 1973f) are fitted to a Gaussian spectrum and to a Kolmogorov power-law spectrum in analyzing the scintillation data. The rms fluctuation of electron density in the cometary tail is reported at 80 electrons per cu mm, the inner scale of the fluctuation at 800 km, and the largest scale of fluctuation at possibly 400,000 km. A hump in the comet power-law spectrum is noted. Use of the power spectrum of electron density fluctuations to predict the power spectrum of magnetic field fluctuations for irregularities associated with hydromagnetic turbulence is recommended.

Nonlinear optical effects for plasma diagnostics

We compare two nonlinear optical effects which show promise of yielding directly plasmon frequencies, damping rates, and intensities in small, transient (submicrosecond) plasmas. The Raman-induced Kerr effect is shown to offer significant advantages over three-wave mixing when the plasma screening length is much smaller thanc÷[plasmon frequency]. When the screening length is much smaller than the optical wavelengths, then the former effect can yield an electron-density fluctuation spectrum with laser powers (∼MW) that are readily available.

Microwave scattering from a turbulently heated plasma

The electron density fluctuation spectrum during the turbulent heating of a toroidal plasma column is derived from the scattering of lambda 0=2.4 mm and 8.8 mm microwave beams. A multi-antenna receiver array and heterodyne detection are used to obtain the frequency spectrum of fluctuations with wavevectors aligned across and parallel to the exciting plasma current. The minimum detectable fluctuation levels were S(k)=6*104 (at lambda 0=2.4 mm) and S(k)=2*104 ( lambda 0=8.8 mm), set by the plasma radiation level. Evidence is obtained of ion sound fluctuations with k perpendicular to B are observed whose origin has not yet been explained.

Resonances in light scattered from a plasma in a magnetic field

Expressions are developed for the electron density fluctuation spectrum for monochromatic radiation incident upon a magnetized plasma in thermal equilibrium. The method is based upon the full−wave derivation of a formal relation between the autocorrelations of particle density and dielectric tensor. Collisions are introduced into the formulation via a BGK and a Fokker−Planck collision term in the Boltzmann equation. An enhancement of the scattered spectra due to the excitation of longitudinal slow−wave resonances is predicted when the differential scattering vector is aligned primarily perpendicular to the magnetic field, provided that the collision−to−cyclotron frequency ratio satisfies the relation ν/Ω ≪ 1 in the BGK model or ν/Ω ≪ Ω2m/k2KT in the Fokker−Planck model.

Effect of collisions on the plasma line of the electron density fluctuation spectrum

The Klimontovich-Dupree formalism is used to investigate the effect of electron-neutral collisions on the plasma line of the electron density fluctuation spectrum. The Fourier transform of the fluctuation electron number density is calculated by integrating along electron trajectories consisting of straight-line segments joined at electron-neutral scattering sites. It is shown that the scattering process itself results in the excitation of plasma oscillations and contributes to the plasma line intensity. The electron density autocorrelation is calculated by ensemble averaging over the initial positions and velocities of all the electrons in the system and averaging over a transition probability describing the electron-neutral collisions. The transition probability is expanded as a power series in the collision frequency. The plasma line spectrum is calculated in the limit that the electron travels many wavelengths between collisions. The principal result of this is that collisions enhance the intensity of the plasma line by as much as a factor of six when the collision frequency exceeds the Landau damping decrement. This result is of most interest in attempts to observe the electron plasma line with the incoherent-scatter radar in the E-region of the ionosphere when the electron density is enhanced by auroral bombardment.

Relativistically induced instellar density fluctuations

The spectrum of cold electron density fluctuations induced by a relativistic electron gas is investigated and the results discussed in relation to the interstellar medium.