Advanced spectral and statistical data analysis techniques have greatly contributed to shaping our understanding of microphysical processes in plasmas. We review some of the main techniques that allow for characterising fluctuation phenomena in geosp
ace and in laboratory plasma observations. Special emphasis is given to the commonalities between different disciplines, which have witnessed the development of similar tools, often with differing terminologies. The review is phrased in terms of few important concepts: self-similarity, deviation from self-similarity (i.e. intermittency and coherent structures), wave-turbulence, and anomalous transport.
Turbulent spectra of magnetic fluctuations in the free solar wind are studied from MHD to electron scales using Cluster observations. We discuss the problem of the instrumental noise and its influence on the measurements at the electron scales. We co
nfirm the presence of a curvature of the spectrum $sim exp{sqrt{krho_e}}$ over the broad frequency range $sim[10,100]$ Hz, indicating the presence of a dissipation. Analysis of seven spectra under different plasma conditions show clearly the presence of a quasi-universal power-law spectrum at MHD and ion scales. However, the transition from the inertial range $sim k^{-1.7}$ to the spectrum at ion scales $sim k^{-2.7}$ is not universal. Finally, we discuss the role of different kinetic plasma scales on the spectral shape, considering normalized dimensionless spectra.
Magnetic fluctuations in the solar wind are distributed according to Kolmogorovs power law $f^{-5/3}$ below the ion cyclotron frequency $f_{ci}$. Above this frequency, the observed steeper power law is usually interpreted in two different ways: a dis
sipative range of the solar wind turbulence or another turbulent cascade, the nature of which is still an open question. Using the Cluster magnetic data we show that after the spectral break the intermittency increases toward higher frequencies, indicating the presence of non-linear interactions inherent to a new inertial range and not to the dissipative range. At the same time the level of compressible fluctuations raises. We show that the energy transfer rate and intermittency are sensitive to the level of compressibility of the magnetic fluctuations within the small scale inertial range. We conjecture that the time needed to establish this inertial range is shorter than the eddy-turnover time, and is related to dispersive effects. A simple phenomenological model, based on the compressible Hall MHD, predicts the magnetic spectrum $sim k^{-7/3+2alpha}$, which depends on the degree of plasma compression $alpha$.
