3.3.2 SCINTILLATIONS DUE TO AMBIENT FLUCTUATIONS AND SELF- FOCUSING INSTABILITIES Electron density fluctuations in the upper ionosphere will cause correlated random differential phase shifts across the wave front of a microwave beam as it propagates through the irregularities. As a result, a spherical wavefront becomes corrugated (Figure 3-8) and the ensuing diffraction produces phase and amplitude scintillations at some distant surface. Assuming that the correlation function of index of refraction fluctuations is Gaussian with scale length r , then the correlation length of phase fluctuations along the wavefront of a control beam at the transmitting antenna face will be given approximately by , where is the distance to the location (or mean location) of the irregularities and Z is the distance to the satellite. It follows that only small scale lengths contribute to phase noise across the array. One expects that these small scale (50 meters and less) irregularities will be weak and therefore not produce a large phase shift. The theory of phase and amplitude fluctuations due to propagation through ionospheric irregularities is developed in Appendix A. Temporal decorrelation occurs when density irregularities drift through a correlation length (see Appendix A-32 and A-33). A computer program has been written to compute phase and amplitude correlation functions at the transmitting antenna in terms of the power spectrum of the electron density fluctuations. In addition, the program determines the rms phase deviations and amplitude fades and the temporal correlation function for phase changes. Typical results are given in Figure 3-9 for a Gaussian model of the density correlation function and a frequency of 1 GHz. The rms phase fluctuation $rms scales inversely with frequency. A double Gaussian distribution provides a better fit (see Appendix A) to nonlinear self-induced density fluctuations(11), assuming that a self-focusing plasma instability (Appendix B) causes irregularities at microwave frequencies that are similar to those observed during high power HF heating of the ionosphere. Results of this model are tabulated in Table 3-3).
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