3D Dynamics of Magnetic Flux Ropes Across Scales: Solar Eruptions and Sun-Earth Plasma Coupling

Central to the understanding of the eruptive phenomena on the Sun and their impact on the terrestrial plasma environment is the dynamics of coronal mass ejections (CMEs)---a 3D magnetic flux rope configuration---and the evolution of their magnetic fields. I will discuss the basic physics of CME eruption and solar flare energy release in the context of the analytic erupting flux rope model of CMEs. In this ideal MHD model, a CME is treated as a 3D flux rope with its two stationary footpoints anchored in the Sun. The model structure is non-axisymmetric and embedded in a model corona/solar wind. The initial flux rope is driven out of equilibrium by ``injection'' of poloidal flux and propagates under the Lorentz hoop force from the Sun to 1 AU, across a wide range of spatial and temporal scales. Comparisons of the model results and recent STEREO observations show that the solutions that best fit the observed CME position-time data (to within 1-2\% of data) also correctly replicate the temporal profiles of associated flare X-ray emissions (GOES data) and the {\it in situ} magnetic field and plasma data of the CME ejecta at 1 AU where such data are available (e.g., ACE and STEREO/IMPAXCT/PLASTIC data), providing a unified basis of understanding CME dynamics and flare energetics.