Outer Scale Size Research Articles

Theoretical and computational study of a partially coherent laser beam in a marine environment

The propagation formula of a partially coherent Generalized Flattened Hermite-Cosh-Gaussian (GFHChG) beam in maritime atmospheric turbulence is derived with the help of the extended Huygens–Fresnel principle. In addition, the analytical expression for the beam width of a partially coherent GFHChG beam in the considered environment is investigated. From the numerical results based on the analytical formulae, we find that the analyzed beam can take different shapes of the profile, depending on the turbulence and beam parameters. And also, it can significantly resist turbulence with small wavelength and waist width values. On the other hand, when the medium becomes turbulent, the beam loses its characteristics and its resistance to fluctuations. Furthermore, the results reveal that the beam spreads more rapidly with the increase of the strength of turbulence, the outer scale size, and the decrease of the inner scale size. We should mention that the results gained represent a general form of numerous partially coherent laser beams such as Generalized Flattened Hermite Gaussian, Generalized Flattened Cosh-Gaussian, Hermite-Cosh-Gaussian, Cosh-Gaussian, Hermite-Gaussian and Gaussian Schell model beams.

Propagation of a Modified Complex Lorentz–Gaussian-Correlated Beam in a Marine Atmosphere

In this paper, we study the second-order statistics of a modified complex Lorentz–Gaussian-correlated (MCLGC) beam, which is a new type of partially coherent beam capable of producing an Airy-like intensity pattern in the far field, propagation through marine atmospheric turbulence. The propagation formula of spectral density is derived by the extended Huygens–Fresnel integral, which could explicitly indicate the interaction of turbulence on the beams’ spectral density under propagation. The influences of the structure constant of the turbulence, initial coherence width and wavelength on the spectral density are investigated in detail through numerical examples. In addition, analytical expressions for the r.m.s beam width, divergence angle and M2 factor of the MCLGC beam in the marine turbulence are also derived with the help of the Wigner distribution function. The results reveal that the beam spreads much faster, and the M2 factor deteriorates severely with the increase of the structure constant and the decrease of the inner scale size, whereas the outer scale size has little effect on these two quantities.

A new method for measuring the outer scale of atmospheric turbulence

A method, based on the correlation functions of the wandering (lateral fluctuations) of two separated thin parallel laser beams propagating through the atmosphere, is proposed for measuring the outer scale of atmospheric turbulence. The method utilizes the ratio between the correlation functions of the wandering in two perpendicular planes. A simple relationship to obtain the outer scale from the measured correlation functions is established for a particular model of turbulence, the modified von Karman model. The method is validated by experimental data both in the laboratory and in the open air. To this purpose special measurements, which were conducted during an outdoor measurements campaign in 2004, are analysed. An instantaneous value of the outer scale can be obtained accurately. The results show that the size of outer scale of atmospheric turbulence changes very rapidly with time and that the proposed method can be applied in real atmospheric conditions.

Atmospheric Turbulence Measurements with the Palomar Testbed Interferometer

Data from the Palomar Testbed Interferometer, with a baseline length of 110 and an observing wavelength of $2.2 \mu{\rm m}$, were used to derive information on atmospheric turbulence on 64 nights in 1999. The measured two-aperture variance coherence times at $2.2 \mu{\rm m}$ ranged from 25 msec to 415 msec (the lower value was set by instrumental limitations---the interferometer could not operate when the coherence time was lower than this). On all nights, the spectrum of the short time scale ($<600$ msec) delay fluctuations had a shallower spectrum than the theoretical Kolmogorov value of 5/3. On most nights, the mean value of the power law slope was between 1.40 and 1.50. Such a sub-Kolmogorov slope will result in the seeing improving as the $\approx 0.4$ power of wavelength, rather than the slower 0.2 power predicted by Kolmogorov theory. On four nights, the combination of delay and angle tracking measurements allowed a derivation of the (multiple) wind velocities of the turbulent layers, for a frozen-flow model. The derived wind velocities were all $\le 4 {\rm m s^{-1}}$, except for a small $10 {\rm s^{-1}}$ component on one night. The combination of measured coherence time, turbulence spectral slope, and wind velocity for the turbulent layer(s) allowed a robust solution for the outer scale size (beyond which the fluctuations do not increase). On the four nights with angle tracking data, the outer scale varied from 6 to 54 m, with most values in the 10-25 range. Such small outer scale values cause some components of visibility and astrometric errors to average down rapidly.

Electron density power spectrum in the local interstellar medium

Interstellar scintillation (ISS), fluctuations in the amplitude and phase of radio waves caused by scattering in the interstellar medium, is important as a diagnostic of interstellar plasma turbulence. ISS is also of interest because it is noise for other radio astronomical observations. The unifying concern is the power spectrum of the interstellar electron density. Here we use ISS observations through the nearby (less than or approximately =1 kpc) (ISM) to estimate the spectrum. From measurements of angular broadening of pulsars and extragalactic sources, decorrelation bandwidth of pulsars, refractive steering of features in pulsar dynamic spectra, dispersion measured fluctuations of pulsars, and refractive scintillation index measurements, we construct a composite structure function that is approximately power law over 2 x 10(exp 6) m less than scale less than 10(exp 13) m. The data are consistent with the structure function having a logarithmic slope versus baseline less than 2; thus there is a meaningful connection between scales in the radiowave fluctuation field and the scales in the electron density field causing the scattering. The data give an upper limit to the inner scale, l(sub o) less than or approximately 10(exp 8) m and are consistent with much smaller values. We construct a composite electron density spectrum that is approximately power law over at least the approximately = 5 decade wavenumber range 10(exp -13)/m less than wavenumber less than 10(exp -8)/m and that may extend to higher wavenumbers. The average spectral index of electron density over this wavenumber range is approximately = 3.7, very close to the value expected for a Kolmogorov process. The outer scale size, L(sub o), must be greater than or approximately = 10(exp 13) m (determined from dispersion measure fluctuations). When the ISS data are combined with measurements of differential Faraday rotation angle, and gradients in the average electron density, constraints can be put on the spectrum at much smaller wave numbers. The composite spectrum is consistent with a Kolmogorov-like power law over a huge range (10 or more decades) of spatial wavenumber with an infrared outer scale L(sub o) greater than or approximately 10(exp 18)m. This power-law subrange-expressed as ratio of outer to inner scales-is comparable to or larger than that of other naturally occurring turbulent fluids, such as the oceans or the solar wind. We outline some of the theories for generating and maintaining such a spectrum over this huge wavenumber range.

Remote sensing of auroral E region plasma structures by radio, radar, and UV techniques at solar minimum

The unique capability of the Polar BEAR satellite to simultaneously image auroral luminosities at multiple ultraviolet (UV) wavelengths and to remote sense large‐scale (hundreds to tens of kilometers) and small‐scale (kilometers to hundreds of meters) plasma density structures with its multifrequency beacon package is utilized to probe the auroral E region in the vicinity of the incoherent scatter radar (ISR) facility near Sondrestrom. In particular, we present coordinated observations on two nights obtained during the sunspot minimum (sunspot number &lt;10) January–February 1987 period when good spatial and temporal conjunction was obtained between Polar BEAR overflights and Sondrestrom ISR measurements. With careful coordinated observations we were able to confirm that the energetic particle precipitation responsible for the UV emissions causes the electron density increases in the E region. These E region electron density enhancements were measured by the ISR at Sondrestrom. The integrations up to the topside of these ISR electron density profiles were consistent with the total electron content (TEC) measured by the Polar BEAR satellite. An electron transport model was utilized to determine quantitatively the electron density profiles which could be produced by the particle precipitation, which also produced multiple UV emissions measured by the imager; these profiles were found to be in good agreement with the observed ISR profiles in the E region. Surprisingly large magnitudes of phase and amplitude scintillations were measured at 137 and 413 MHz in the regions of TEC enhancements associated with the particle precipitation. Steep phase spectral slopes with spectral index of 4 were found in these regions. Strength‐of‐turbulence computations utilizing the ISR electron density profiles and observed characteristics of phase and amplitude scintillations are interpreted in terms of an irregularity amplitude varying between 10 and 20% at a several‐kilometer outer scale size in the E region extending approximately 50 km in altitude. This outer scale size is also consistent with the measured phase to amplitude scintillation ratio. An estimate of the linear growth rate of the gradient‐drift instability in the E region shows that these plasma density irregularities could have been generated by this process. The mutual consistency of these different sets of measurements provides confidence in the ability of the different techniques to remote sense large‐ and small‐scale plasma density structures in the E region at least during sunspot minimum when the convection‐dominated high‐latitude F region is fairly weak.

Computer Code For Calculation Of The Mutual Coherence Function

We present a computer code in FORTRAN 77 for the calculation of the mutual coherence function (MCF) of a plane wave normally incident on a stochastic half-space. This is an exact result. The user need only input the path length, the wavelength, the outer scale size, and the structure constant. This program may be used to calculate the MCF of a well-collimated laser beam in the atmosphere.

Preliminary numerical study of the outer scale size of ionospheric plasma cloud striations

The one‐level (one for the plasma cloud and neglect of cloud‐background ionosphere interaction), two‐dimensional fluid equations modeling striation development in large F region ionospheric plasma clouds have been numerically solved, by using an initial one‐dimensional cloud geometry, for three different initial Pedersen conductivity gradient scale lengths L=3, 6, and 10 km. In the nonlinear regime, evidence is presented for an outer scale size of well‐developed striations in a direction (y) perpendicular to the E × B drift (x) of the plasma cloud whose initial Pedersen conductivity varies only along the drift direction. The perpendicular outer scale size 2π/k0y is proportional to the initial gradient scale length L through a constant of order unity, i.e., k0yL/2π ≃1. In addition, for the three scale lengths L studied, the one‐dimensional x power spectra ∝kx−n x with n x ≃2 for 2π/k x between 1 and 80 km, while the y power spectra ∝ky−n y with n y ≃2–2.5 for 2π/k y between 1 and 10 km. These results are consistent with recent experimental and theoretical studies of plasma cloud striations.

Measurements of electron density irregularities in the ionosphere of Jupiter by Pioneer 10

It is demonstrated that when the frequency spectrum of log amplitude fluctuations is used, the radio-occultation experiment is a powerful tool for detecting, identifying, and studying ionospheric irregularities. Analysis of Pioneer 10 radio-occultation measurements reveals that the Jovian ionosphere possesses electron-density irregularities which are very similar to those found in the earth's ionosphere. This is the first time such irregularities have been found in a planetary ionosphere other than that of the earth. The Pioneer 10 results indicate that the spatial wave-number spectrum of the electron-density irregularities is close to the Kolmogorov spectrum and that the outer scale size is greater than the Fresnel size (6.15 km). This type of spectrum suggests that the irregularities are probably produced by the turbulent dissipation of irregularities larger than the outer scale size.

Effects of turbulence in a planetary atmosphere on radio occultation

There has been considerable interest in the amplitude and phase fluctuations of the radio signal received from a flyby spacecraft during occultation by a planetary atmosphere. For planetary flyby missions, the Fresnel-zone size exceeds the outer scale size of turbulence, and existing formulations for the frequency spectra of the amplitude and phase fluctuations are inadequate because they do not account for the inhomogeneity of the turbulence in the direction transverse to the propagation path. In this paper, the formulation is given for the correlation functions for the log-amplitude and phase fluctuations of both spherical and plane waves propagating in a turbulent medium whose correlation function for refractive index fluctuations is described by the product of a function of the average coordinate and a function of the difference coordinate. The results are applied to radio occultation of a flyby space probe by the atmosphere of Venus, assuming that the turbulence in the atmosphere exists as a layer, that it is localized, isotropic, and smoothly varying, and that the localized turbulence is described by the Kolmogorov spectrum. Closed-form solutions for both variances and frequency spectra of the log-amplitude and phase fluctuations are obtained using Rytov's method, and it is seen that the shape of the frequency spectra depends a great deal on the characteristics and extent of the turbulence.