In this Letter we introduce a generalization of the Lorenz dynamical system using fractional derivatives. Thus, the system can have an effective noninteger dimension Sigma defined as a sum of the orders of all involved derivatives. We found that the system with Sigma<3 can exhibit chaotic behavior. A striking finding is that there is a critical value of the effective dimension Sigma(cr), under which the system undergoes a transition from chaotic dynamics to regular one.

Knowledge of the ion composition in the near-Earth's magnetosphere and plasma sheet is essential for the understanding of magnetospheric processes and instabilities. The presence of heavy ions of ionospheric origin in the magnetosphere, in particular oxygen (O + ), influences the plasma sheet bulk properties, current sheet (CS) thickness and its structure. It affects reconnection rates and the formation of Kelvin-Helmholtz instabilities. This has profound consequences for the global magnetospheric dynamics, including geomagnetic storms and substorm-like events. The formation and demise of the ring current and the radiation belts are also dependent on the presence of heavy ions. In this review we cover recent advances in observations and models of the circulation of heavy ions in the magne- tosphere, considering sources, transport, acceleration, bulk properties, and the influence on the magnetospheric dynamics. We identify important open questions and promising avenues for future research.

Based on high‐resolution measurements from NASA's Magnetospheric Multiscale mission, we present the dynamics of electrons associated with current systems observed near the diffusion region of magnetic reconnection at Earth's magnetopause. Using pitch angle distributions (PAD) and magnetic curvature analysis, we demonstrate the occurrence of electron scattering in the curved magnetic field of the diffusion region down to energies of 20 eV. We show that scattering occurs closer to the current sheet as the electron energy decreases. The scattering of inflowing electrons, associated with field‐aligned electrostatic potentials and Hall currents, produces a new population of scattered electrons with broader PAD which bounce back and forth in the exhaust. Except at the center of the diffusion region the two populations are collocated and appear to behave adiabatically: the inflowing electron PAD focuses inward (toward lower magnetic field), while the bouncing population PAD gradually peaks at 90° away from the center (where it mirrors owing to higher magnetic field and probable field‐aligned potentials).

No abstract

Abstract. Many phenomena in the Earth's magnetotail have characteristic temporal scales of several minutes and spatial scales of a few Earth radii (R E ). Examples of such transient and localized mesoscale phenomena are bursty bulk flows, beamlets, energy dispersed ion beams, flux ropes, traveling compression regions, night-side flux transfer events, and rapid flappings of the current sheet. Although most of these observations are linked to specific interpretations or theoretical models they are inter-related and can be the different aspects of a physical process or origin. Recognizing the inter-connected nature of the different transient and localized phenomena in the magnetotail, this paper reviews their observations by highlighting their important characteristics, with emphasis on the new results from Cluster multipoint observations. The multi-point Cluster measurements have provided, for the first time, the ability to distinguish between temporal and spatial variations, and to resolve spatial structures. Some examples of the new results are: flux ropes with widths of 0.3 R E , transient field aligned currents associated with bursty bulk flows and connected to the Hall current at the magnetic reconnection, flappings of the magnetotail current sheet with time scales of 100 s-10 min and thickness of few thousand km, and particle energization including velocity and time dispersed ion structures with the Correspondence to: A. S. Sharma (ssh@astro.umd.edu) latter having durations of 1-3 min. The current theories of these transient and localized processes are based largely on magnetic reconnection, although the important role of the interchange and other plasma modes are now well recognized. On the kinetic scale, the energization of particles takes place near the magnetic X-point by non-adiabatic processes and wave-particle interactions. The theory, modeling and simulations of the plasma and field signatures are reviewed and the links among the different observational concepts and the theoretical frameworks are discussed. The mesoscale processes in the magnetotail and the strong coupling among them are crucial in developing a comprehensive understanding of the multiscale phenomena of the magnetosphere.