During the interval 2012 March 7-11 the geospace experienced a barrage of intense space weather phenomena including the second largest geomagnetic storm of solar cycle 24 so far. Significant ultra-low-frequency wave enhancements and relativistic-electron dropouts in the radiation belts, as well as strong energetic-electron injection events in the magnetosphere were observed. These phenomena were ultimately associated with two ultra-fast (>2000 km s −1 ) coronal mass ejections (CMEs), linked to two X-class flares launched on early 2012 March 7. Given that both powerful events originated from solar active region NOAA 11429 and their onsets were separated by less than an hour, the analysis of the two events and the determination of solar causes and geospace effects are rather challenging. Using satellite data from a flotilla of solar, heliospheric and magnetospheric missions a synergistic Sun-to-Earth study of diverse observational solar, interplanetary and magnetospheric data sets was performed. It was found that only the second CME was Earth-directed. Using a novel method, we estimated its near-Sun magnetic field at 13 R e to be in the range [0.01, 0.16] G. Steep radial fall-offs of the near-Sun CME magnetic field are required to match the magnetic fields of the corresponding interplanetary CME (ICME) at 1 AU. Perturbed upstream solar-wind conditions, as resulting from the shock associated with the Earth-directed CME, offer a decent description of its kinematics. The magnetospheric compression caused by the arrival at 1 AU of the shock associated with the ICME was a key factor for radiation-belt dynamics.

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In this study, the nonlinear analysis of the sunspot index is embedded in the non-extensive statistical theory of Tsallis [5,7,8]. The triplet of Tsallis, as well as the correlation dimension and the Lyapunov exponent spectrum were estimated for the SVD components of the sunspot index timeseries. Also the multifractal scaling exponent spectrum q  ( ) f a , the generalized Renyi dimension spectrum ( ) D q and the spectrum ( ) J p of the structure function exponents were estimated experimentally and theoretically by using the q  entropy principle included in Tsallis non extensive statistical theory, following Arimitsu and Arimitsu [67,69]. Our analysis showed clearly the following: a) a phase transition process in the solar dynamics from high dimensional non Gaussian SOC state to a low dimensional non Gaussian chaotic state, b) strong intermittent solar turbulence and anomalous (multifractal) diffusion solar process, which is strengthened as the solar dynamics makes phase transition to low dimensional chaos in accordance to Ruzmakin, Zeleny and Milovanov studies [19,20,21] c) faithful agreement of Tsallis non equilibrium statistical theory with the experimental estimations of i) non-Gaussian probability distribution function ( ) P x , ii) multifractal scaling exponent spectrum ( ) f a and generalized Renyi dimension spectrum q D , iii) exponent spectrum ( ) J p of the structure functions estimated for the sunspot index and its underlying non equilibrium solar dynamics.

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