Analysis of low frequency plasma waves in turbulent magnetosheath: downstream of the Earth's bow shock

The knowledge of the dynamics and characteristics of space plasma during solar-terrestrial coupling has been greatly enriched by process that aids the determination of the instantaneous frequencies which support the non-stationary and non-linear nature of signals. Such plasmas are observed in the magnetosheath in the downstream of bow shock. In this thesis a technique was applied which extracts the various contributing oscillatory modes reflecting the waveforms observed in the space by Cluster spacecraft instruments such as FGM, CIS and EFW, and decompose the frequency of each extracted mode using Instantaneous Frequency method that is based on Simple Hilbert Transform (SHT). This is achieved through the use of Empirical Mode Decomposition (EMD). To eliminate the negative frequency of the various extracted modes referred to as intrinsic mode function which appears with Fourier transform, we apply Hilbert transform leading to analytic representation of the signals. This process aids the determination of the instantaneous frequencies of the extracted modes. The combined process of EMD and Hilbert transform is called the Hilbert-Huang transform. The results in this thesis have been based on the improved EMD. To contribute to the understanding of plasma dynamics, the computed instantaneous frequencies are compared with the results obtained from the application of Simple Hilbert Transform. Instantaneous frequencies of overriding waves are easily separated as opposed to the application of just SHT. They offer the advantage of 3-dimensional study of the spatial characteristics of waves. The understanding of the instantaneous wave number has been achieved through the EMD and SHT combination. This provides the results which give the wave vector for a known frequency at a given instant of time. The instantaneous dispersion relation is determined using the knowledge of the instantaneous frequency and wave vector in the satellite frame, the plasma bulk velocity and the spacecraft velocity (found to be negligible compared with the plasma bulk velocity). This is accomplished using a Doppler shift relation. Wave modes identifications have been carried out by considering the proton temperature anisotropies, plasma beta and plasma bulk velocity and instantaneous phase velocity in the satellite frame. We report Alfvén mode close to the bow shock, spreading out to mirror mode which dominates the middle of magnetosheath. The mirror mode then diminishes towards the magnetopause.