Fresnel Scale Research Articles

Images of bottomside irregularities observed at topside altitudes

We analyzed plasma and field measurements acquired by the Communication/Navigation Outage Forecasting System (C/NOFS) satellite during an eight‐hour period on 13–14 January 2010 when strong to moderate 250 MHz scintillation activity was observed at nearby Scintillation Network Decision Aid (SCINDA) ground stations. C/NOFS consistently detected relatively small‐scale density and electric field irregularities embedded within large‐scale (∼100 km) structures at topside altitudes. Significant spectral power measured at the Fresnel (∼1 km) scale size suggests that C/NOFS was magnetically conjugate to bottomside irregularities similar to those directly responsible for the observed scintillations. Simultaneous ion drift and plasma density measurements indicate three distinct types of large‐scale irregularities: (1) upward moving depletions, (2) downward moving depletions, and (3) upward moving density enhancements. The first type has the characteristics of equatorial plasma bubbles; the second and third do not. The data suggest that both downward moving depletions and upward moving density enhancements and the embedded small‐scale irregularities may be regarded as Alfvénic images of bottomside irregularities. This interpretation is consistent with predictions of previously reported theoretical modeling and with satellite observations of upward‐directed Poynting flux in the low‐latitude ionosphere.

Two-Station Interplanetary Scintillation Measurements of Solar Wind Speed near the Sun Using the X-band Radio Signal of the Nozomi Spacecraft

Interplanetary scintillation (IPS) measurements of the solar wind speed for the distance range between 13 and 37 R S were carried out during the solar conjunction of the Nozomi spacecraft in 2000 – 2001 using the X-band radio signal. Two large-aperture antennas were employed in this study, and the baseline between the two antennas was several times longer than the Fresnel scale for the X-band. We successfully detected a positive correlation of IPS from the cross-correlation analysis of received signal data during ingress, and estimated the solar wind speed from the time lag corresponding to the maximum correlation by assuming that the solar wind flows radially. The speed estimates range between 200 and 540 km s−1 with the majority below 400 km s−1. We examined the radial variation in the solar wind speed along the same streamline by comparing the Nozomi data with data obtained at larger distances. Here, we used solar wind speed data taken from 327 MHz IPS observations of the Solar-Terrestrial Environment Laboratory (STEL), Nagoya University, and in situ measurements by the Advanced Composition Explorer (ACE) for the comparison, and we considered the effect of the line-of-sight integration inherent to IPS observations for the comparison. As a result, Nozomi speed data were proven to belong to the slow component of the solar wind. Speed estimates within 30 R S were found to be systematically slower by 10 – 15 % than the terminal speeds, suggesting that the slow solar wind is accelerated between 13 and 30 R S.

Diffractive and refractive timescales at 4.8 GHz in PSR B0329+54

We present the results of flux density monitoring of PSR B0329+54 at the frequency of 4.8 GHz using the 32-meter TCfA radiotelescope. The observations were conducted between 2002 and 2005. The main goal of the project was to find interstellar scintillation (ISS) parameters for the pulsar at the frequency at which it was never studied in detail. To achieve this the 20 observing sessions consisted of 3-minute integrations which on average lasted 24 hours. Flux density time series obtained for each session were analysed using structure functions. For some of the individual sessions as well as for the general average structure function we were able to identify two distinctive timescales present, the timescales of diffractive and refractive scintillations. To the best of our knowledge, this is the first case when both scintillation timescales, t_DISS=42.7 minutes and t_RISS=305 minutes, were observed simultaneously in a uniform data set and estimated using the same method. The obtained values of the ISS parameters combined with the data found in the literature allowed us to study the frequency dependence of these parameters over a wide range of observing frequencies, which is crucial for understanding the ISM turbulence. We found that the Kolmogorov spectrum is not best suited for describing the density fluctuations of the ISM, and a power-law spectrum with beta =4 seems to fit better with our results. We were also able to estimate the transition frequency (transition from strong to weak scintillation regimes) as 10.1 GHz, much higher than was previously predicted. We were also able to estimate the strength of scattering parameter u=2.67$ and the Fresnel scale as 6.7x10^8 meters.

Optimal light beams and mirror shapes for future LIGO interferometers

We report the results of a recent search for the lowest value of thermal noise that can be achieved in LIGO by changing the shape of mirrors, while fixing the mirror radius and maintaining a low diffractional loss. The result of this minimization is a beam with thermal noise a factor of 2.32 (in power) lower than previously considered Mesa Beams and a factor of 5.45 (in power) lower than the Gaussian beams employed in the current baseline design. Mirrors that confine these beams have been found to be roughly conical in shape, with an average slope approximately equal to the mirror radius divided by arm length, and with mild corrections varying at the Fresnel scale. Such a mirror system, if built, would impact the sensitivity of LIGO, increasing the event rate of observing gravitational waves in the frequency range of maximum sensitivity roughly by a factor of 3 compared to an Advanced LIGO using Mesa beams (assuming all other noises remain unchanged). We discuss the resulting beam and mirror properties and study requirements on mirror tilt, displacement, and figure error, in order for this beam to be used in LIGO detectors.

Refractive scattering evidence from multifrequency scintillation spectra observed at auroral latitudes

During October 2003 major geomagnetic storm, intensity scintillations on radio signals at 150 MHz and 400 MHz transmitted coherently from Tsykada beacon satellites have been observed. Through the analysis of intensity fluctuation spectra, evidence of refractive scattering from large scale ionospheric irregularities in the spatial plasma density distribution is found. The events can indeed be explained by using the refractive scattering theory developed by Booker and MajidiAhi (1981). The presence of refractive scattering is particularly evident in strong scintillation events, where spectral saturation may well occur. The observed intensity spectra fit the shape of theoretical predictions of the refractive theory. This provides useful insights about spectral slope, Fresnel scale, and the scale of irregularities producing the observed intensity scintillations actually present in the ionosphere.

The Stationary Phase Point Method for Transitional Scattering: Diffractive Radio Scintillation

The stationary phase point (SPP) method is introduced to treat the diffractive scintillation. From weak scattering, where the SPP number N = 1, to strong scattering (N>>1), via transitional scattering regime (N∼2, 3), we find that the modulation index of intensity experiences the monotonically increasing from 0 to 1 with the scattering strength, characterized by the ratio of Fresnel scale rF to diffractive scale rdiff.

Amplitude and Phase Fluctuations for Gravitational Waves Propagating through Inhomogeneous Mass Distribution in the Universe

When a gravitational wave (GW) from a distant source propagates through the universe, its amplitude and phase change due to gravitational lensing by the inhomogeneous mass distribution. We derive the amplitude and phase fluctuations and calculate these variances in the limit of a weak gravitational field of density perturbation. If the scale of the perturbation is smaller than the Fresnel scale ~100 pc(f/mHz)-1/2 (f is the GW frequency), the GW is not magnified due to the diffraction effect. The rms amplitude fluctuation is 1%-10% for f > 10-10 Hz, but it is reduced to less than 5% for a very low frequency of f < 10-12 Hz. The rms phase fluctuation in the chirp signal is ~10-3 rad at the LISA frequency band (10-5 to 10-1 Hz). Measurements of these fluctuations will provide information about the matter power spectrum on the Fresnel scale ~100 pc.

Solar flux dependence of coherence scales in scintillation patterns produced by ESF irregularities

Abstract. The coherence scale length, defined as the 50% decorrelation scale length along the magnetic east-west direction, in the ground scintillation pattern obtained at a dip equatorial location, due to scattering of VHF radio waves by equatorial spread F (ESF) irregularities, is calculated, using amplitude scintillation data recorded by two spaced receivers. The average east-west drift of the ground scintillation pattern, during the pre- and post-midnight periods, also calculated from the same observations, shows an almost linear increase with 10.7-cm solar flux. In the present paper the variability of the drift is automatically taken into account in the calculation of the coherence scale length of the ground scintillation pattern. For weak scintillations, the coherence scale depends on the Fresnel scale, which varies with the height of the irregularity layer, and also on the spectral index of the irregularity power spectrum. It is found that for weak scintillations, the coherence scales are much better organized according to the 10.7-cm solar flux, during the pre-midnight period, than during the post-midnight period, with a general trend of coherence scale length increasing with 10.7-cm solar flux except for cases with F 10.7-cm solar flux &lt;100. This indicates that, during the initial phase of ESF irregularity development, the irregularity spectrum does not have much variability while further evolution of the spatial structure in ESF irregularities is controlled by factors other than the solar flux.

Kuiper Belt Object Sizes and Distances from Occultation Observations

There are several observational campaigns underway to detect kilometer-sized foreground Kuiper belt objects (KBOs) through their occultation of background stars. The interpretation of an occultation light curve, unfortunately, is affected by a geometric degeneracy such that one is unable to determine the KBO size independently of its distance. This degeneracy can be broken through a precise measurement of the relative velocity obtained from simultaneous observations of individual events. While an array of telescopes spread over an area of few square kilometers can be employed, it is unlikely that the relative velocity can be measured to the required accuracy to help break this geometric degeneracy. The presence of diffraction fringes in KBO occultation light curves, when projected sizes of occulted stars are smaller than the Fresnel scale, improves determination of size and distance significantly. In this regard, we discuss the potential role of a dedicated satellite mission for KBO occultation observations. If dwarf stars at the V-band magnitudes of 14 and fainter can be monitored at time intervals of 0.1 s with normalized flux errors at the level of 1%, the occultation observations will allow individual KBO sizes and distances to be determined at the level of a few percent or better.

Low frequency modulation of transionospheric radio wave amplitude at low-latitudes: possible role of field line oscillations

Abstract. Ionospheric scintillations of radio waves at low-latitudes are associated with electron density irregularities. These irregularities are field-aligned and can provide excitation energy all along the field line to non-local field-aligned oscillations, such as the local field line oscillations. Eigen-periods of toroidal field line oscillations at low-latitudes, computed by using the dipole magnetic field and ion distributions obtained from the International Reference Ionosphere (IRI) for typical nighttime conditions, fall in the range of 20–25 s. When subjected to spectral analysis, signal strength of the radio waves recorded on the 250 MHz beacon at Pondicherry (4.5° N dip), Mumbai (13.4° N dip) and Ujjain (18.6° N dip) exhibit periodicities in the same range. For the single event for which simultaneous ground magnetic data were available, the geomagnetic field also oscillated at the same periodicity. The systematic presence of a significant peak in the 20–25 s range during periods of strong radio wave scintillations, and its absence otherwise suggests the possibility that field line oscillations are endogenously excited by the irregularities, and the oscillations associated with the excited field line generate the modulation characteristics of the radio waves received on the ground. The frequency of modulation is found to be much lower than the characteristic frequencies that define the main body of scintillations, and they probably correspond to scales that are much larger than the typical Fresnel scale. It is possible that the refractive mechanism associated with larger scale long-lived irregularities could be responsible for the observed phenomenon. Results of a preliminary numerical experiment that uses a sinusoidal phase irregularity in the ionosphere as a refracting media are presented. The results show that phase variations which are large enough to produce a focal plane close to the ground can reproduce features that are not inconsistent with our observations.Key words. Magnetospheric physics (magnetosphere – ionosphere interactions) Ionosphere (ionosphere – magnetoshere interactions; ionospheric irregularities)

The measurement of flow and turbulence levels using acoustical scintillation analysis

For acoustical propagation in the coastal environment, small scale fluctuations in the temperature/salinity and flow velocity distorts the spherically spreading phase fronts which result in amplitude and phase fluctuations (scintillation). As the fine structure variability in the medium has a natural coherence time, it will be transported by the current. Detection of pattern motion is an essential concept exploited in acoustical scintillation and has been demonstrated in a variety of coastal channels. Important features of this approach are that the measurement is path averaged, is of the flow component perpendicular to the acoustic path and is sensitive to the Fresnel scale size which is chosen to lie within the inertial subrange of the turbulent random medium. Analysis of the signals goes beyond measurement of flow speed, and has included detection of turbulent velocity and scalar levels and turbulent anisotropy. For one-way propagation the turbulent kinetic energy dissipation rate is derived from the variance of the log-amplitude signal which is dependent on the level of the Kolmogorov spectrum dominated by current fluctuations. From reciprocal propagation, scalar and velocity turbulence levels are derived from accurate phase fluctuations. Detection of turbulent anisotropy is based on horizontal and vertical angle of arrival correlations using a square array with 1 m sides and thus sensitive to turbulent scale sizes approximately a few meters.

Nonturbulent layers in polar summer mesosphere: 2. Application of wavelet analysis to VHF scattering

In a companion paper [Alcala et al., this issue] we presented a wavelet analysis of rocket data obtained simultaneously with a VHF radar during a polar mesosphere summer echo event. Here we apply scattering theory to each of the wavelets in the reconstructed function and add up the individual electric fields scattered from the volume illuminated by the radar. The resulting scattering profile is quite similar to that observed if we take into account a small tilt of the layer, consistent with the present rocket data and with other rocket and radar measurements during similar conditions. The scattering power is overestimated by about an order of magnitude. This can be explained by either a scattering structure a factor of 5 smaller than the Fresnel scale, a tilt in the scattering layer, or a combination of the two effects.

Wavelet analysis of high&amp;hyphen;resolution temperature data with applications to radio wave scattering

High&amp;hyphen;resolution balloon&amp;hyphen;borne temperature measurements have been made in the troposphere and stratosphere during late fall over the western plains of the United States. In one such experiment the data are of remarkable quality and quite suitable for investigating methods of separating organized and turbulent features from a geophysical data stream, exploring atmospheric dynamics, and estimating VHF radar backscatter. We are particularly interested in the mechanisms creating aspect sensitivity, i.e., a nonunity ratio of vertical to well off&amp;hyphen;vertical radar backscatter. We find that very steep positive vertical temperature gradients, as high as 40.0 K&amp;sol;km, can be supported. On the other hand, negative gradients are limited to values near the marginal stability boundary. The structures are thus anisotropic and similar to ramp cliff features found in other fluids. We use wavelet analysis to isolate the organized components of the signal and, after subtraction, the residual signal is investigated to determine its character. The Fourier transform of the residual is Kolmogorov in nature, unlike that of the original data stream, and yields Cn2, the refractive index structure parameter, in good agreement with the higher&amp;hyphen;order structure function approach; this supports the success of our partition. We calculate the Fresnel reflection coefficient using the wavelet coefficients; the turbulent scatter is found using Cn2. The ratio between the Fresnel scatter and the turbulent scatter, i.e., the aspect sensitivity, is &amp;sim;10 decibels in the troposphere and over 20 decibels in the stratosphere, in agreement with published observations and supporting our assumption that the organized features have horizontal extent exceeding the Fresnel scale.

Ionospheric irregularity diagnostics from the phase structure functions of MF/HF radio echoes

We present a new approach to investigating ionospheric irregularities, using the temporal structure function of totally reflected radio echo phase variations. Modern digital ionosondes (e.g., the dynasonde) measure the echo phase with very high resolution and precision, at closely spaced antennas, frequencies, and times. A “stringing” procedure gives continuous and unambiguous phase variation data for time intervals of any desired length. Quasi‐periods of tens of seconds up through several minutes are caused by large‐scale movements of the ionospheric plasma, while shorter‐period phase variations result from the interaction of the sounding signal with small‐scale irregularities. The relevant irregularity spatial domain extends from decameter radio wavelengths to the first Fresnel scale, a few kilometers. We obtain a theoretical relation between structure functions of the temporal phase variations and spatial irregularities with a simple model of frozen horizontal drift. The relation permits solutions of both the direct and inverse problems. Although long‐period phase measurements are practicable and essential to exploring larger irregularity scales, they require observing modes dedicated to multiple fixed‐frequency time series, and this undesirably limits the number of altitudes that can be monitored simultaneously. An alternative “rudimentary structure function” is obtainable from standard dynasonde “B‐mode” ionograms; it offers good altitude and time resolution for irregularity studies while permitting other established diagnostics (electron density profiles, vector velocities, critical frequencies, etc.) with the same data. We show some example analyses by these methods as applied to auroral and magnetic‐equatorial dynasonde observations. We find irregularity amplitudes in the range 0.001 &lt; ΔN/N &lt; 0.1 (for a nominal scale of 1 km) and spectral indices in the range 2 &lt; v &lt; 4, with evidence of diurnal variation in both quantities at both locations.

Simultaneous Global Positioning System observations of equatorial scintillations and total electron content fluctuations

One aspect of the Global Positioning System (GPS) is the potential to conduct geophysical research, and worldwide networks of GPS receivers have been established to exploit this potential. Several research groups have begun using this global GPS data to study ionospheric total electron content (TEC) variations, also referred to as GPS phase fluctuations, as surrogates for ionospheric scintillations. This paper investigates the relationship between GPS amplitude scintillations and TEC variations for the same line of sight using observations from Ancón, Peru. These observations were taken under equatorial spread F conditions for three nights in April 1997. As expected, only when the spectrum of TEC fluctuations includes significant power at the Fresnel scale do scintillations appear. We also find that when the TEC fluctuation spectrum includes the Fresnel scale, the S4 scintillation index is roughly proportional to measures of TEC fluctuation for the weak scintillations observed. The proportionality constant varies from night to night, however, casting doubt on the ability to predict GPS S4 successfully from TEC fluctuation data alone. We also present a simple theoretical phase screen model and show that if a relationship between TEC fluctuation measures and S4 exists, that relationship depends on the power spectrum of phase variations at the screen. Unfortunately, the available TEC data, at 30 s per sample (with some aliasing apparently permitted), offer limited spectral information. A preliminary comparison of 1 s/sample data with the same data decimated to a 30 s/sample interval suggests, however, that the level of successful S4 prediction, based on TEC fluctuation measures alone, is comparable at either sample rate.

Microlab‐1 experiment: Multipath effects in the lower troposphere

Interpretation of the Doppler‐shifted radio frequencies from the proof‐of‐concept GPS/MET radio occultation experiment is impeded by the effects of multipath propagation caused by strong variations of atmospheric refractivity. In this paper, we describe and validate a method of deciphering the ray structure of the measured electromagnetic field in regions of multipath propagation. The method is based on diffraction theory and the principles of the synthesized aperture, which allows for the refinement of the vertical resolution beyond the Fresnel scale as well as for the improvement of the signal/noise ratio. The validation of the method is based on artificial occultation data simulated using global fields from a NCEP analysis. An example of the application of the diffraction correction algorithm for the processing of real GPS/MET data is given. The comparison of the inversion results with and without diffraction correction indicates a very significant role of multipath propagation in the lower troposphere, which suggests that the diffraction correction can significantly improve the quality of the data processing.

Onset of strong scintillation with application to remote sensing of turbulence inner scale

Numerical simulation of propagation through atmospheric turbulence of an initially spherical wave is used to calculate irradiance variance σ(2)(I), variance of log irradiance σ(2)(ln I), and mean of log irradiance ?In I? for 13 values of l(0)/R(f) (i.e., of turbulence inner scale l(0) normalized by Fresnel scale R(F)) and 10 values of Rytov variance σ(2)(Rytov), which is the irradiance variance, including the inner-scale effect, predicted by perturbation methods; l(0)/R(f) was varied from 0 to 2.5 and σ(2)(Rytov) from 0.06 to 5.0. The irradiance probability distribution function (PDF) and, hence, σ(2)(I), σ(2)(In I), and ?ln I? are shown to depend on only two dimensionless parameters, such as l(o)/R(F) and σ(2)(Rytov). Thus the effects of the onset of strong scintillation on the three statistics are characterized completely. Excellent agreement is obtained with previous simulations that calculated σ(2)(I). We find that σ(2)(I), σ(2)(In I), and ?ln I? are larger than their weak-scintillation asymptotes (namely, σ(2)(Rytov), σ(2)(Rytov), and - σ(2)(Rytov)/2, respectively) for the onset of strong scintillation for all l(0)/R(f). An exception is that for the largest l(0)/R(f), the onset of strong scintillation causes σ(2)(ln I) to decrease relative to its weak-scintillation limit, σ(2)(Rytov). We determine the efficacy of each of the three statistics for measurement of l(0), taking into account the relative difficulties of measuring each statistic. We find that measuring σ(2)(I) is most advantageous, although it is not the most sensitive to l(0) of the three statistics. All three statistics and, hence, the PDF become insensitive to l(0) for roughly 1 < β0(2) < 3 (where β0(2) is σ (2)(Rytov) for l(0) = 0); this is a condition for which retrieval of l(0) is problematic.

Irradiance variance of optical waves through atmospheric turbulence by numerical simulation and comparison with experiment

Irradiance variance for optical propagation through atmospheric turbulence is calculated by numerical simulation. Let l0 be the inner scale, Rf be the Fresnel scale, and β02 be the weak-fluctuation irradiance variance at zero inner scale. Then results in the strong-focusing regime just past the peak can be summarized by σI2 = 1.74 − 0.092β0 + 0.60(l0/Rf) for a plane wave and σI2 = 3.02 − 0.35β0 + 5.56(l0/Rf) for a point source. These numerical results are in excellent agreement with experimental results.

Acoustic propagation and oceanic fine structure.

Internal waves distort the sound-speed field in the sea. This time variable distortion causes fluctuations in acoustic intensity and phase in forward transmission experiments. Initial efforts to predict the spectrum of internal wave-induced phase fluctuations were successful. Corresponding success was not achieved in the prediction of acoustic intensity, which is sensitive to smaller vertical scales than phase. Are the oceanic environmental models inaccurate or are the relevant scattering models in error? Here, a statistical picture of the fine-scale wave field is presented. The data consist of 10 000 profiles of density and sound speed, from the sea surface to 560 m, collected over a 20-day period. Vertical wave-number-frequency spectra of sound-speed anomaly are estimated from these profiles. Of relevance is the frequency dependence of the spectrum at the vertical wave number corresponding to the Fresnel scale of a given acoustic experiment. In an Eulerian frame, where vertical advection influences the observations, the frequency dependence varies significantly with vertical wave number. The form, as well as level, of the power spectrum of log intensity is dependent on the Fresnel scale of the experiment. Since estimation of the Fresnel scale is sometimes associated with significant uncertainty, the shape of the log amplitude spectrum might prove a valuable guide to the scattering physics.

Variance of focal-plane centroids

The variance of the unbiased focal-plane estimates of image centroids from a point source is derived for arbitrary strength of scattering by using path-integral methods. The Markov approximation and narrow angular scattering are assumed. Results are presented for an ideal focusing telescope with an aperture transmission that produces no phase errors. Calculations of the leading term are performed for a circular telescope aperture and the case of homogeneous atmospheric turbulence described by the Hill spectrum [ J. Fluid Mech.88, 541– 562 ( 1978)]. When there are irradiance fluctuations, the variance of the unbiased estimate of image centroids depends on the choice of the origin of the weighting vector. The variance of the centroid of a single image depends on three physical parameters related to the Fresnel scale, the inner scale, and the strength of scattering. The variance of the separation between two images from two separated telescope apertures depends on the same parameters in addition to the normalized separation of the apertures. The important contributions from propagation distance and spectral wave number are identified for the different parameter regimes. The magnitude of centroid motion compared to the average image size is also discussed.