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The magnetosphere is a large scale natural system powered by the solar wind that exhibits many nonequilibrium phenomena. A wide range of these phenomena are driven directly by the solar wind or arise from the storage-release processes internal to the magnetosphere. Under the influnce by the turbulent solar wind, the magnetosphere during geomagnetically active periods is far from equilibrium and storms and substorms are essentially non-equilibrium phenomena. In spite of the distributed nature of the physical processes and the apparent irregular behavior, there is a remarkable coherence in the magnetospheric response during substorms and the entire magnetosphere behaves as a global dynamical system. Alongwith the global features, the magnetosphere exhibits many multi-scale and intermittent characteristics. These features of the magnetosphere have been studied in terms of phase transitions, self-organized criticality and turbulence. In the phase transition scenario the global features are modeled as first-order transitions and the multiscale behavior is interpreted as a manifestation of the scale-free nature of criticality in second order phase transitions. In the self-organized criticality framework substorms are considered as avalanches in the system when criticality is reached. Many features of the magnetosphere, in particular the power law dependence of scale sizes, can be viewed as a feature of a turbulent system. The common theme underlying these approaches is the recognition that the nonequilibrium phenomena in the magnetosphere could be understood in terms of processes generic to such systems. In many cases the power-law behavior of the magnetosphere seen in many observations is the starting point for these studies. This chapter is an overview of the recent understanding achieved using these different approaches, and identifies the common issues and differences.

Sporadic and localized interactions of coherent structures arising from plasma resonances can be the origin of “complexity” of the coexistence of non-propagating spatiotemporal fluctuations and propagating modes in space plasmas. Numerical simulation results are presented to demonstrate the intermittent character of the non-propagating fluctuations. The technique of the dynamic renormalization-group is introduced and applied to the study of scale invariance of such type of multiscale fluctuations. We also demonstrate that the particle interactions with the intermittent turbulence can lead to the efficient energization of the plasma populations. An example related to the ion acceleration processes in the auroral zone is provided.

Recently, several observations suggested that the Earth's magnetospheric dynamics in response to solar wind changes may resemble the behavior of a complex system which operates out-of-equilibrium and near criticality. Here, we discuss the emergence of complexity and topological disorder in the magnetotail regions. In detail, we will show how several aspects regarding the multiscale nature of the magnetospheric response may be connected to the evolution of a complex topology of multiscale magnetic and plasma coherent structures.

Evidence is reviewed that suggests the presence self-organized critically dynamics in Earth's Magnetotail. It has been proposed that scale-free avalanching and spreading critical dynamics observed in auroral emissions are a reflection of these behaviors in the tail plasma sheet. Localized reconnection in the turbulent plasma sheet has been proposed as the local instability that collectively enables the avalanching process. A numerical simulation study of reconnection and magnetic field annihilation in driven current-sheet models is reviewed. Each of the models is composed of a resistive MHD component coupled to an idealized representation of an anomalous resistivity generating current-driven instability. Models in one- and two-dimensions are discussed. Behavior that indicates both models can evolve into self-organized criticality under steady driving is reviewed.

The substorm onset as a state transition is investigated from a resistive magnetohydrodynamic (MHD) simulation. The simulation uses the finite volume totalvariation diminishing (TVD) scheme on an unstructured grid system to evaluate the magnetosphere-ionosphere (M–I) coupling effect more precisely and to reduce the numerical viscosity in the near-earth plasma sheet. The calculation started from a stationary solution under a northward interplanetary magnetic field (IMF) condition with non-zero IMF . After a southward turning of the IMF, the simulation results show the progress of plasma sheet thinning in the magnetosphere. This thinning is promoted by the drain of closed flux from the plasma sheet occurring under the enhanced convection. In this stage, the reclosure process of open field lines in the plasma sheet, which determines the flux piling up from the midtail to the near-earth plasma sheet, is not so effective, since it is still controlled by the remnant of northward IMF. The substorm onset occurs as an abrupt change of pressure distribution in the near-earth plasma sheet and an intrusion of convection flow into the inner magnetosphere. After the onset, the simulation results reproduce both the dipolarization in the near-earth tail and the near-earth neutral line (NENL) at the midtail, together with plasma injection into the inner magnetosphere and an enhancement of the nightside field-aligned current (FAC). During the dipolarization process, the magnetosphere changes from the force balance in the direction to the configuration of force balance in the direction. Thus, the dipolarization is not a mere pile up of the flux ejected from the NENL Associated with the establishment of force balance in the direction, the pressure inside — 10 Re peaks to self-adjust the restored magnetic tension. It is concluded that the direct cause of these onset processes is the state (phase-space) transition of the convection system from a thinned state to a dipolarized state associated with a self-organizing criticality.

The magnetosphere is a prototypical open system driven by the turbulent solar wind and exhibits complex behavior with global and multiscale characteristics. The multiscale behavior, characterized by the ubiquitous power law distributions of many variables, arises from the internal magnetospheric dynamics and the turbulence in the solar wind. On the other hand the overarching global dynamical behavior originates mainly from the internal dynamics and is evident in processes such as plasmoid formation and release. This combination of global and multiscale behavior is a nonequilibrium phenomenon typical of plasmas in Nature and in many laboratory settings. The global nature of the magnetosphere is characterized by low-dimensionality and is evident in the numerical simulations using global MHD models. The multiscale aspects have been studied using many approaches, such as multifractality, self-organized criticality, turbulence, intermittency, etc. Phase transitions, which exhibit global behavior (first order) and scale invariance (second order), provide a framework for a comprehensive model of the magnetosphere.

The paper reviews main observational features and suggested interpretations of magnetic field variations at frequencies below 10 Hz in the Earth's plasma sheet. Such wave activity is widely believed to be important for the magnetotail structure and substorm dynamics. This range contains tail flapping modes, MHD, ion cyclotron and lower hybrid range waves. As compared with the solar wind, the analysis is complicated by non-linearity of fluctuations, non-stationarity of the plasma sheet and relative shortness of data samples. The primary attention is devoted to discussion of the modern approach, considering fluctuations as the stochastic scale-invariant wave field. Basic analysis methods are illustrated with data examples from the Interball-1 mission.

The physical processes in the magnetosphere span a wide range of space and time scales and due to the strong cross-scale coupling among them the fundamental processes at the smallest scales are critical to the large scale processes. For example, many key features of magnetic reconnection and particle acceleration are initiated at the smallest scales, typically the ion gyro-radii, and then couples to meso-scale and macro-scale processes, such as plasmoid formation. The Magnetospheric Muliscale (MMS) mission is a multi spacecraft mission dedicated to the study of plasma physics at the smallest scales and their cross-scale coupling to global processes. Driven by the turbulent solar wind, the magnetosphere is far from equilibrium and exhibits complex behavior over many scales. The processes underlying the multi-scale and intermittent features in the magnetosphere are fundamental to sun-earth connection. Recent results from the four spacecraft Cluster and earlier missions have provided new insights into magnetospheric physics and will form the basis for comprehensive studies of the multi-dimensional properties of the plasma processes and their inter-relationships. MMS mission will focus on the boundary layers connecting the magnetospheric regions and provide detailed spatio-temporal data of processes such as magnetic reconnection, thin current sheets, turbulence and particle acceleration. The cross-scale exploration by MMS mission will target the microphysics that will enable the discovery of the chain of processes underlying sun-earth connection.

Experimental observations of intermittency phenomena in the edge plasma turbulence of fusion devices are summarized. New results from ADITYA tokamak are presented which show that the intermittent particle flux obeys a stable Lévy distribution. The distribution function is self-similar over a range of time-scales extending upto 50 decorrelation times. The distribution of waiting time between successive bursts of particle flux follows an asymptotic power-law. These observations indicate that the intermittent particle flux is caused by a mechanism involving “storage and release”. An attempt is made to present a perspective for the intermittency in edge turbulence in comparision to similar phenomena observed in fluid turbulence.

Shear flow stabilization of edge turbulence leads to self-organized high (H) confinement modes in tokamak plasmas. Thus understanding the mechanisms for generation of shear/zonal flow and fields in finite plasmas is an important area of research. A brief review of various mechanisms for shear flow generation and discussion of our recent theory which yields a criterion for bifurcation from low to high (L-H) confinement mode is presented. The predicted threshold based on this parameter shows good agreement with edge measurements on discharges undergoing L-H transitions in DIII-D with ▽ both towards and away from the X-point, as well as for pellet induced H-modes.