Vol

Vol. 83, No. 41, 8 October 2002

The Correct Approach to Understanding Magnetospheric Physics

Anthony T. Y. Lui, The Johns Hopkins University Applied Physics Laboratory, Laurel, MD 20723 USA

Recently, John Greene took up the "Parker Challenge" [Parker, 1996]. Parker argued that the correct approach to understanding magnetospheric phenomena is to use the magnetic field and plasma flow velocity (B, u) as the primary quantities, with the electric field and current (E, j) being secondary, in that E and j can be determined from B and u. At the outset, it should be noted that this is strictly true only if the plasma dynamics are entirely governed by ideal magnetohydrodynamics.

The correct approach to understand magnetospheric physics depends on the phenomenon to be investigated. There is no single paradigm that is always superior to others for treating macroscopic magnetospheric problems. Insisting on one particular approach as the only correct one is unjustified and may stifle innovative pursuit in research. Thus, I am motivated to address both the limitations of the B-u paradigm, and the merits of the E-j paradigm.

Parker [1996] equated the B-u paradigm with the magnetohydrodynamics (MHD) approach as he stated that "the macroscopic behavior...of the magnetosphere is described by MHD which we refer to here as the B-u paradigm. The equations of MHD form a complete set of partial differential equations, providing a deductive approach to the theory of magnetospheric activity." Numerical simulations of the magnetosphere based on the MHD equations have indicated magnetospheric disturbances to be solely driven by X-type magnetic reconnection in various regions. This may be thought of as vindication of the B-u paradigm, but as we discuss below there is strong evidence for suggesting that MHD is insufficient to explain the physics of such disturbances.

What then is the E-j paradigm, where electric field and current are taken to be the primary quantities? What it is not is an electrical circuit approach. Rather, a focus on electric field and current as primary quantities generally requires an analysis based on particle dynamics. Therefore, we shall associate the E-j paradigm as the approach of single particle calculation or kinetic analysis (with full consideration of collective effects). The single particle approach is valid when the collective behavior of the plasma under consideration is relatively unimportant. The heart of this approach is the Boltzmann equation or the Vlasov equation in the collisionless regime. It should be recognized that the MHD equations can be derived from the Vlasov equation by adopting certain approximations, much like the classical equations in Newtonian mechanics can be obtained from the special relativity equation when the speed is small relative to the light speed.

The E-j approach is useful to treat many macroscopic magnetospheric problems that cannot be explained with the B-u approach. Injection of particles in the inner magnetosphere during magnetospheric substorms is a prime example of this. Substorm injection produces clear velocity dispersion over a large region in the inner magnetosphere, leading to the recognition of the injection boundary and the inference on the location of the particle source [McIlwain, 1974]. The substorm injection phenomenon cannot be understood in the B-u approach. Related to this inadequacy of the B-u approach is the inability of MHD simulations to produce the ring current. Many velocity dispersion features are now found in large-scale regions of the magnetosphere, such as in the low-altitude dayside cusp and the boundary of the plasma sheet. These advances are invaluable in the overall understanding of the magnetospheric dynamics.

Mounting evidence now points to the cause of a magnetospheric substorm to be a culmination of one or more physical processes occurring over multiple localized sites with intermittent disturbances rather than the consequence of a single large-scale one as once thought. Thus, substorms are analogous to terrestrial thunderstorms. Both phenomena are basically an electric discharge of the system, involving transient and localized disturbances, and yet their effects spread over regions substantially larger than that of these local discharges. The culmination of these disturbances gives the appearance of a large-scale phenomenon. This early conceptual picture presented in 1988 and documented later in 1991 [Lui, 1988, 1991] fits well with the later development of forced and/or self-organized criticality concept [Chang, 1992; Consolini, 1997]. In fact, the magnetosphere exhibits both sudden changes of state resembling the first order phase transitions and more gradual ones resembling the second order phase transitions. The system evolution in these situations calls for yet another approach, such as the renormalization group [Chang, 1992].

When compelling evidence points to the localization of these disturbances, it is postulated that the responsible process is localized magnetic reconnection. Unfortunately, this conjecture is not held up by two independent three-dimensional numerical simulations of magnetic reconnection. Pritchett and Coroniti [2000] used kinetic simulation to show magnetic reconnection in the tail plasma sheet to be essentially two-dimensional even when localized forcing is imposed at the tail magnetopause. Drake et al. [2000], also using kinetic simulation, have found magnetic reconnection to evolve quickly to a two-dimensional configuration even when it is initiated in a three-dimensional geometry. There are MHD simulations that yield localized magnetic reconnection, either intentionally by imposing arbitrarily localized resistivity or by non-physical numerical artifacts. The validity of these results is very much in question.

There are many limitations of the B-u paradigm and merits of the E-j paradigm which I shall not elaborate further here. Interested readers may find a more extensive discussion on these issues in Lui [2000], which includes also a discussion on the similarities and differences between current disruption and magnetic reconnection. In summary, however, the main objection to the B-u paradigm is its reliance on magnetohydrodynamics, when many of the processes occurring in the magnetosphere are inherently kinetic, requiring an approach that can better be summed up as the E-j paradigm.

Acknowledgments

This work was supported by National Aeronautics and Space Administration (Grant NAG5-7797) to The Johns Hopkins University Applied Physics Laboratory.

References

Chang, T. S. C., Low dimensional behavior and symmetry breaking of stochastic systems near criticality--can these effects be observed in space and in the laboratory? IEEE Trans. Plasma Sci., 20, 691, 1992.

Consolini, G., Sandpile cellular automata and magnetospheric dynamics, Proceedings of Cosmic Physics in the Year 2000, 58, Aiello et al. (eds.), SIF, Bologna, Italy, 1997.

Drake, J. F., B. N. Rogers, and M. A. Shay, The physics of collisionless magnetic reconnection, The First S-RAMP Conference Abstract, Sapporo, Japan, 2-6 October 2000, 317, 2000.

Lui, A. T. Y., What is a magnetospheric substorm expansion made of?, Eos Trans., American Geophysical Union, 69, 435, 1988.

Lui, A. T. Y., Plasma transport in the Earth's magnetotail, Modeling Magnetospheric Plasma Processes, G. R. Wilson (ed.), 41, 1991.

Lui, A. T. Y., Electric current approach to magnetospheric dynamics and the distinction between current disruption and magnetic reconnection, Magnetospheric Current Systems, AGU Monograph 118, AGU, Washington, DC, 31, 2000.

McIlwain, C. E., Substorm injection boundaries, in Magnetospheric Physics, B. M. McCormac (ed.), 143, D. Reidel, Hingham, Mass., 1974.

Parker, E. N., The alternative paradigm for magnetospheric physics, J. Geophys. Res., 101, 10587, 1996.

Pritchett, P. L., and F. V. Coroniti, Kinetic simulations of reconnection and magnetospheric disruptions, The First S-RAMP Conference Abstract, Sapporo, Japan, 2-6 October 2000, 207, 2000.