The solar wind  magnetosphere coupling exhibits both global and
multiscale characteristics due to the broad range of overlapping space and time
scales. The multiscale phenomena have been modeled in terms of many processes such
as phase transition, intermittent turbulence, and selforganized criticality. A
new theoretical foundation for multiscale processes is developed in terms of
fractional kinetics in which the probability densities are described by
FokkerPlanck equation with fractional derivatives.
A collaboration with New York University, funded by National Science Foundation under the Computational and Mathematical Geoscience (CMG), explores the multiscale phenomena in nature. In this project (PI: Dr. Surja Scharma) many approaches based on nonlinear dynamics and chaos, fractional kinetics, nonequilibrium statistical physics and nonlinear time series analysis are used. One of the main topics of research is the long term correlations and its role in extreme events. The systems under study are the large scale open systems in nature (solar windmagnetosphere interaction), financial markets, and laboratory systems. 

Thin current sheets are the sites where magnetic energy is converted to plasma energy and play a crucial role in the onset of magnetic reconnection. Building on the kinetic theory of thin current sheets developed earlier, the role of anisotropic electron pressure is investigated. Although the ions are the main current carriers in the current sheet, the electron current due to anisotropic pressure is found to yield triple peaks, as observed by CLUSTER spacecraft. 

Spacecraft observations of the relativistic electrons in the geosynchronous orbit have shown sawtooth oscillations with time scales corresponding to substorms. These oscillations reflect a strong coupling between the inner magnetosphere and the magnetotail  important in the modeling of the magnetosphere. The data from LANL satellites show different sawtooth time scales for electrons and ions, indicating different dynamical processes for the two species. 

Terestrial gammaray flashes (TGFs), detected serendipitously by Compton GRO and now observed routinely by RHESSI, have been correlated with thunderstorms, which provide the energy necessary to accelerate electrons capable of generating the gamma rays. The cosmic ray showers during thunderstorms provide the seed electrons necessary for a runaway discharge in the thunderstorm electric field. However these electric fields are in the 10 15 km height, and the runaway discharge can not extend to the satellite altitudes. A mechanism in which the electrons propagate upward in the channels formed by the selffocusing of whistler waves, commonly observed during lightning discharges, was suggested (Kaw et al., Phys. Plasmas, 8, 4954, 2001). The whistler waves are found to be unstable in the thundercloud region and can grow to amplitudes necessary for the nonlinear instability (Milikh et al., J. Geophys. Res., 110, A02308, 2005). The nonlinear evolution of the plasma ducts formed due to the whistler waves are simulated using a numerical code, and yields the conditions for the upward propagation of the relativistic electrons and the characteristics of the gamma rays generated by bremsstrahlung in the vicinity of the satellite. These compare well with the RHESSI and groundbased ELF/VLF wave observations. 

The global MHD simulations of the solar windmagnetosphere coupling have shown a strong interrelationship between the processes in the different regions starting from the solar wind to the ionosphere. An increased ionospheric conductivity leads to changes in the field aligned currents and the shape of the magnetopause. This in turn leads to a reconfiguration of the magnetosheath flow and a reduction in the reconnection rate. The net result is a saturation of the transpolar potential, as observed by many ground and spacecraftborne instruments. 

Space weather specifies the state of the geospace environment and forecasts are essential to protect the technological infrastructure of our society. Many extreme space weather events have severely damaged satellites, power transmission systems, aircraft communication and many other civil and military systems. The geospace environment is continuously driven by the solar wind, bringing the disturbances from the sun. The complexity of this interaction makes space weather forecasting a challenge and many approaches are used to develop space weather forcasts. The nonlinear dynamical systems approach has provided a characterization of the geospace environment as a dynamical system and thus provided the basis for its predictability (Sharma, 1995). With this approach the state of the magnetosphere can be forecast readily, as shown in the case of the Aprill 2002 geospace storm.
The relativistic electron at geosynchronous orbit can cause severe damage to the hundreds of spacecraft in that region and these "killer" electrons are a major concern from the space weather perspective. The data of the electron fluxes from LANL spacecraft and of the solar wind from upstream spacecraft are used to develop dataderived models that predict the average daily intensity of the relativistic electrons and the probabilities of extreme events (Ukhorskiy et al., 2004). The research on space weather forecasting has been funded (PI: Dr. Surja Sharma) by NSF and the National Space Weather Program. 

Magnetic reconnection is fundamental plasma process in nature and is responsible for the fast energy release in space plasmas such as in the solar atmosphere and the Earth's magnetotail, in laboratory plasmas and many astrophysical settings. Understanding magnetic reconnection in collisionless plasmas has been a long standing problem and new theories and numerical simulations continue to provide new advances. The thin current sheets are the sites of the onset and evolution of reconnection and an understanding of the structure and dynamics is closely tied to the reconnection processes. Many aspects of thin current sheets, such as its kinetic equilibrium, embedded structure, stability are studied using theory, modeling and simulations. The finest scale processes are studied using an electronmagnetohydrodynamic simulations and shows the development of a quadrupole magnetic field structure and stretching of the current sheet. The shortest length of the current sheet is found to be about six electron skin depths and such structures are expected to be measured by the forthcoming NASA Magnetospheric Multiscale Mission (MMS). In the project (PI: Dr. Surja Sharma) funded by NASA the physics at the shortest scales one studied using computer simulations using the EMHD, twofluid, global MHD and particleincell (PIC) models. 

The computer Simulations of plasmas uses many models and techniques such as the global MHD, two  fluid, electron  magnetohydrodynamics (EMHD), and particleincell (PIC). The global MHD model is now among the most widely used computational tool for the solar wind  magnetosphere interaction. The EMHD model studies the fastest and shortest processes in a variety of plasmas, such as magnetic reconnection. The PIC codes are used to study the plasma conditions in which the kinetic processes are important, e.g. wave particle interactions. 


