# Equatorial Plasma Bubbles: A Review
## 2 Observations of EPBs and Associated Irregularities
### Ionospheric Scintillation Measurements
#### 2.3.1 Dependence of Scintillation Parameters on Irregularity Characteristics  
A brief discussion of some of the theoretical aspects of ionospheric scintillations is presented here to make it easier for the reader to understand the relationship between the parameters estimated from scintillation data and irregularity characteristics. This forms the basis for extraction of information about intermediate-scale irregularities in EPBs from scintillation observations [40]. The most commonly used parameter derived from amplitude scintillation data is the \(S_{4}\) index, which is the standard deviation of normalized intensity of the signal and indicates the strength of amplitude scintillations. Scintillations during an interval of time are considered to be weak if \(S_{4}<0.5\). In the theory of ionospheric scintillations, a stochastic description of the irregularities is used. Scattering of the radio signal is due to variations in the refractive index \(\mu\) of the ionosphere which are directly related to fluctuations in electron density \(N\) expressed as: \(\Delta\mu\ \ =\ -\lambda^{2}\ r_{e}\ \Delta N/\ 2\ \pi\), where \(r_{e}\) is the 'classical radius' of the electron [39]. It is seen from this relationship that the higher the frequency of the radio signal, the smaller the change in ionospheric refractive index for a particular variation in electron density. Therefore, ionospheric scintillations are expected to be stronger on lower frequency radio signals than on higher frequency signals. The phase screen approximation has been widely used in theoretical investigations of ionospheric scintillations [41]. In this approximation, the layer of irregularities traversed by the radio signal is replaced by a phase-changing screen so that a phase perturbation is imposed on the radio wave as it emerges from the screen. For a two-dimensional phase screen, this phase perturbation has a spatial variation given by \(\varphi(\rho)\ =\ -\lambda\ r_{e}\ \Delta Nt(\rho)\), where the two-dimensional vector \(\rho\) specifies the location in the screen and \(\Delta Nt(\rho)\) is the variation of the total electron content along the signal path to that location which occurs due to the presence of irregularities. After emerging from the phase screen, as the radio waves propagate to a ground receiver, phase perturbation imposed on the incoming radio waves by the irregularities gives rise to amplitude and phase scintillations. As the EPBsand associated irregularities are aligned with the geomagnetic field, which is horizontal at the dip equator, a phase screen varying only in one direction, along the geomagnetic east-west, is often used in modeling scintillations in the equatorial and low-latitude regions. Scintillation characteristics, such as the \(S_{4}\) index, correlation functions, or power spectra, are statistical in nature and are theoretically related to statistical features of the irregularities. In such theories, the stochastic nature of the irregularities is described by their spatial power spectrum [39; 40]. Rocket and satellite measurements have shown that one-dimensional spectra of plasma density variations in ESF irregularities have a power-law form, which sometimes show a break in slope [14; 15; 16; 17; 18; 19]. Scintillations recorded by a receiver are temporal fluctuations which are related to spatial variations in the ground scintillation pattern in the plane of the receiver through the speed with which the pattern moves across the receiver.