Ravi Samtaney

*King Abdullah University of Science and Technology, Thuwal Kingdom of Saudi Arabia*

### **1. Introduction**

58 Topics in Magnetohydrodynamics

Uritsky, V.M., Klimas, A.J., Vassiliadis, D., et al.; (2002). Scale-free statistics of

Vörös, Z., Baumjohann, W., Nakamura, R., et al.; (2004). Magnetic turbulence in the plasma sheet, *Journal of Geophysical Research*, 109, A11215, doi: 10.1029/2004JA010404. Yankov, V.V. (1997). Magnetic field dissipation and fractal model of current sheet, *Physics of*

Yordanova, E., Bergman, J., Consolini, G., et al.; (2005). Anisotropic scaling features and

Zaslavsky, G. M.; (2002). Chaos, fractional kinetics, and anomalous transport, *Physics* 

Zelenyi, L.M. & Milovanov, A.V.; (2004). Fractal topology and strange kinetics: from

Zheng, L. J. & Furukawa, M.; (2010). Current-interchange tearing modes: Conversion of interchange-type modes to tearing modes, *Physics of Plasmas*, 17, 052508.

doi: 10.1029/2001JA000281.

*Plasmas*, 4, 571-574

*Reports*, 371, 461-580.

12, 817-825.

788.

spatiotemporal auroral emissions as depicted by Polar UVI images: The dynamic magnetosphere is an avalanching system, *Journal of Geophysical Research*, 107, 1426,

complexity in magnetospheric-cusp: a case study, *Nonlinear Processes in Geophysics*,

percolation theory to problems in cosmic electrodynamics, *Fiziki Uspekhi*, 47, 749-

A fluid description of the plasma is obtained by taking velocity moments of the kinetic equations (Vlasov or Fokker-Planck equations) for electrons and ions and employing certain closure assumptions. A hierarchy of MHD models can be derived. Generally, if the time scales of interest are larger than the electron-ion collision time scales, then one may model the plasma as a single fluid. Furthermore, the fluid description of a plasma is valid when the length scales under investigation are larger than the Debye length; and the frequencies are smaller than the cyclotron frequency. The Debye length argument can also be cast in terms of a frequency: namely the plasma frequency. In addition, it is a standard assumption that the speeds involved are much smaller than the speed of light. The oft-used term "resistive MHD" is a single-fluid model of a plasma in which a single velocity and pressure describe both the electrons and ions. The resistive MHD model of a magnetized plasma does not include finite Larmor radius (FLR) effects, and is based on the simplifying limit in which the particle collision length is small compared with the macroscopic length scales.
