MODELING OF L-BAND SIGNALS SCINTILLATION IN THE CONDITIONS OF EQUATORIAL PLASMA BUBBLES Vadim Gherm and Nikolay Zernov,
Department of Radiophysics
University of St.Petersburg, St.Petersburg, Russia
Hal Strangeways,
School of Electronic and Electrical Engineering
University of Leeds, Leeds, U.K.

Slide3:

Hybrid model for prediction of the field scintillation on transionospheric paths of propagation was developed as the combination of the complex phase method (CPM) and random screen technique. The model was described in detail in a recent paper [1] by V.E.Gherm, N.N.Zernov, and H.J.Strangeways, «Propagation model for transionospheric fluctuating paths of propagation: Simulator of the transionospheric channel», published in Radio Science, 40, RS1003, doi:10.1029/2004RS003097, 2005.
To extend the initially developed propagation model ([2] - V.E.Gherm, N.N.Zernov, S.M.Radicella and H.J.Strangeways, Propagation model for signal fluctuations on transionospheric radio links, Radio Science, 35, 5, 1221-1232, 2000) solely based on the CPM, or the generalized Rytov’s approximation, which is not capable of describing the case of strong scintillation, the CPM was combined with the random screen technique.

In the contrast with widely employed (e.g. WBMOD) effective phase screen, the random screen being introduced in the present method is a physical screen with log-amplitude and phase fluctuations relevant to a real field on a plane surface located below the ionosphere. To generate this random field the phase and log-amplitude correlation functions, as well as their cross-correlation function are utilized. They are derived in the framework of the CPM.According to the CPM the complex amplitude of the field passed through the ionosphere is represented as follows undisturbed field random factor:

In the contrast with widely employed (e.g. WBMOD) effective phase screen, the random screen being introduced in the present method is a physical screen with log-amplitude and phase fluctuations relevant to a real field on a plane surface located below the ionosphere. To generate this random field the phase and log-amplitude correlation functions, as well as their cross-correlation function are utilized. They are derived in the framework of the CPM. According to the CPM the complex amplitude of the field passed through the ionosphere is represented as follows undisturbed field random factor

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Correlation functions of fluctuations of and S and their cross -
correlation are represented as integrals in ray-centred variables with the longitudinal variable oriented along a path of propagation determined by positions of the receiver and transmitter.
Having obtained the correlations one can generate the random realizations of the field on the screen. Random factor is treated in terms of the complex phase complex phase phase log-amplitude The equation for the complex phase is then solved by the perturbation method assuming the smallness of the refractive index fluctuations.

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As a result of non-linear evolution of the bubble the strong plasma turbulence is generated inside it, so that the variance of the fractional electron density fluctuations inside the bubble and around it is greater than in the ambient ionosphere.
We model this non-uniform distribution of the variance empirically employing the same function as for the modelling of the depletion.

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Correlation functions of the complex phase Correlation and cross-correlation functions of phase and log-amplitude

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The model bubble drifts in the East direction with the speed 150 m/s Upper graph demonstrates the electron density distribution along the slant path of propagation, so that the vertical axis is the distance along the ray. The slant depletion region corresponds to the crossing of the ray path by the bubble.
Below is the time dependence of the TEC along the slant path, in TEC units

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Simulated time series of amplitude at the receiver (upper panel). Focusing and defocusing due to the large-scale structure are observed Simulated time series of phase at the receiver (bottom panels). Left – full phase, right – detrended phase (stochastic part)

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Simulated time dependence of S4 index calculated using 60 sec intervals of generated amplitude data Experimentally measured S4 (Courtesy B. Arbesser-Rastburg, ESA-ESTEC)

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Simulation example 2
3D time dependent model PBMOD describes the development and time evolution of structures on scales from a few km to hundreds of km (PBMOD, J.M.Retterer (ARFL)).
Results of simulation for Jicamarca, November 2004. Data were provided by Keith Groves (ARFL).
In the figure the vertical distribution of the electron density is plotted as a function of time for a fixed position of the receiver on the Earth. Time dependence of the vertical total electron content (TEC) corresponding to the electron density distribution from the upper figure.

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Realizations of log-amplitude (upper figure) and stochastic phase (lower figure) on the random screen

Slide18:

Simulated time series of amplitude at the receiver. Strong focusing and defocusing due to the large-scale structure are observed. Simulated time series of phase at the receiver.

Slide19:

Simulated time dependence of S4 index calculated using 60 sec intervals of generated amplitude data. Simulated time dependence of phase variance calculated using 60 sec intervals of generated phase data, detrended using high-pass filter with 0.1 Hz cut-off frequency.

Slide20:

Conclusions
A propagation model for transionospheric fluctuating paths of propagation has been further extended to describe the effects caused by the localized ionospheric structures (e.g. plasma bubbles in the low-latitude ionosphere).
The extended model takes into account both quasi-regular and random structures typical of the equatorial bubbles. The model is capable of generating the random time series including the case of propagation through the bubble structures and producing the statistical moments of the signal (power spectra, correlation functions, scintillation index, etc.).
The simulated random time series of the field demonstrate the characteristic non-stationary behaviour caused by the presence and motion of the localized deterministic and irregular structures through the path of propagation. In particular, the results of modeling demonstrate that strong enhancements of the scintillation index (S4) can occur depending on the parameters of the bubble and the path.
The results of modeling L-band signals for the case of the geostationary satellite shows reasonable agreement with the experimentally measured data.

Slide22:

Ionospheric irregularities and scintillation
The irregularities in the F region of the ionosphere in the equatorial region occur in the form of depletions, frequently referred to as “bubbles”. The depletions that originate over the magnetic equator in the postsunset hours extend in both horizontal and vertical directions. The bubbles are upwelled by electrodynamic E x B drift over the magnetic equator and map down to off-equatorial locations along magnetic field lines in the form of “bananas”. These bubbles may sometimes rise to great heights, exceeding 1000 km above the magnetic equator. Radar maps show that the irregularities extend in the east-west direction over several hundred kilometers near the magnetic equator.
The moving depletions produce large horizontal gradients on which smaller scale structures can grow. These irregularities of the electron density of the ionosphere inside the volume of the bubble produce rapid changes both in amplitude and phase of the signal passing through the bubble. This phenomenon is called ionospheric scintillation.

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