Space Sci Rev DOI 10.1007/s11214-010-9696-1 Physics of Magnetospheric Variability Vytenis M. Vasyliunas¯ Received: 23 July 2010 / Accepted: 3 September 2010 © Springer Science+Business Media B.V. 2010 Abstract Many widely used methods for describing and understanding the magnetosphere are based on balance conditions for quasi-static equilibrium (this is particularly true of the classical theory of magnetosphere/ionosphere coupling, which in addition presupposes the equilibrium to be stable); they may therefore be of limited applicability for dealing with time-variable phenomena as well as for determining cause-effect relations. The large-scale variability of the magnetosphere can be produced both by changing external (solar-wind) conditions and by non-equilibrium internal dynamics. Its developments are governed by the basic equations of physics, especially Maxwell’s equations combined with the unique constraints of large-scale plasma; the requirement of charge quasi-neutrality constrains the electric field to be determined by plasma dynamics (generalized Ohm’s law) and the elec- tric current to match the existing curl of the magnetic field. The structure and dynamics of the ionosphere/magnetosphere/solar-wind system can then be described in terms of three in- terrelated processes: (1) stress equilibrium and disequilibrium, (2) magnetic flux transport, (3) energy conversion and dissipation. This provides a framework for a unified formulation of settled as well as of controversial issues concerning, e.g., magnetospheric substorms and magnetic storms. Keywords Magnetic storms · Magnetospheric substorms · Solar-wind/magnetosphere interaction · Magnetosphere/ionosphere/thermosphere interaction 1 Introduction The magnetosphere is observed to be continually varying on many different time scales; some of the characteristic variations in the form of particular types of events (e.g., magnetic storms, magnetospheric substorms) are among the most challenging problems to explain, as well as often of great practical significance (e.g., for space weather). The large-scale variability of the magnetosphere can be the result both of changing external (solar-wind) V. M. Vasyliunas¯ () Max-Planck-Institut für Sonnensystemforschung, 37191 Katlenburg-Lindau, Germany e-mail: [email protected] V.M. Vasyliunas¯ conditions and of non-equilibrium internal dynamics; separating the contributions of the two is not always simple, since the solar wind is likewise continually varying on many different time scales. This review discusses the variability of the magnetosphere primarily from the point of view of physical understanding, of trying to see how the complex variable phenomena of the solar wind/magnetosphere/ionosphere/atmosphere system follow from the basic laws of physics. Essential observational results as currently understood are taken into account, but this is not intended as a review of observations as such. The aim is rather a systematic phys- ical description/formulation, in which observations may suggest and guide explanations but should not appear as explicit premises, and in which absolute primacy is given to the basic equations (including conservation laws) in their complete form, with any approximations explicitly introduced and justified. Section 2 summarizes the most important conventional methods, which mostly assume (explicitly or implicitly) an equilibrium situation and hence may need to be re-examined when applied to time-varying cases. Section 3 reviews some important differences between electrodynamics in space and in the ordinary laboratory and discusses the modifications they impose on methods mentioned in Sect. 2. Section 4 presents definitions and physi- cal descriptions of the two major types of events: magnetospheric substorms and magnetic storms. (Length limitations preclude a discussion of sawtooth and steady-magnetospheric- convection events, which might be viewed as variants of the substorm.) Finally, Sect. 5 attempts to interpret the principal types of magnetospheric-variability events in terms of a coherent set of fundamental physical processes or, where that is not yet possible, to formu- late a set of essential physical questions. The emphasis is on understanding the physical processes that underlie distinct individual events, of large spatial scale, on various time scales: substorm onset (minutes or less), sub- storm phases and similar events (tens of minutes to an hour or so), recurrence tendencies of same (typically hours), magnetic storms (hours to days). 2 Conventional (Quasi-Equilibrium) Methods and Their Limitations 2.1 Magnetic Field Configuration The configuration of the magnetic field is what in essence defines the magnetosphere. Our knowledge of it in the Earth’s magnetosphere is very extensive but is derived almost entirely from observations, often represented by empirical models (e.g. Tsyganenko 2001, and ref- erences therein) which can be quite sophisticated; physical understanding, however, in the sense of seeing how the models follow from the basic equations, is somewhat limited. Nu- merous theoretical models that describe specific regions of the configuration and its changes do exist, but they represent rather a patchwork, each model applied to a different aspect and often derived in a different way. In recent years global numerical simulations have come into widespread use, to calculate magnetic fields and other properties of a model magne- tosphere; they do constitute a unified treatment but can be as incomprehensible as the real magnetosphere. A common custom in magnetospheric and ionospheric physics, following elementary E&M textbook usage, is to preferentially describe the magnetic field configuration, whether deduced from observations or from theory, by specifying the electric currents that would produce the configuration via Ampère’s law 4πJ = c∇×B (1) Physics of Magnetospheric Variability (Gaussian units are used throughout this paper); changes of the configuration are likewise dealt with as corresponding changes of the current system. It may be noted, however, that essentially our entire empirical knowledge about the magnetic configuration of the mag- netosphere and its changes has been derived from observations of the magnetic field, any statements about currents being inferred therefrom by invoking (1). Direct determinations of J from charged-particle observations have been attempted in the magnetosphere, but, leaving aside questions of how reliable they are in view of spacecraft charging constraints, their relative contribution to our knowledge of current systems in the magnetosphere has been negligible. In the ionosphere, no direct measurements of J have ever been reported, to my knowledge, nor do I know of any practical method for making them. The relation between magnetic field and electric current, under conditions appropriate to space plasmas, is further examined in Sect. 3.2. 2.1.1 Dayside Magnetosphere The one case of a magnetic field configuration that is almost completely understood in phys- ical terms is the dayside magnetosphere, under conditions where penetration of magnetic field and of plasma across the magnetopause can be neglected (idealized as a magnetically closed magnetosphere). Unable to penetrate to any significant extent into the geomagnetic field, the solar-wind plasma is initially slowed down and compressed until the pressure has increased sufficiently so that its lateral gradient deflects the flow around the magnetosphere; the exterior pressure also deforms and compresses the magnetic field inside the magne- tosphere. In equilibrium, both the exterior plasma flow and the interior magnetic field are tangent to the boundary surface, the magnetopause; furthermore, the total pressure (plasma plus magnetic) is the same on both sides at any point of the boundary. With the idealiza- tions of negligible magnetic pressure outside and negligible plasma pressure inside, this becomes what is generally known as the Chapman-Ferraro model, which has a well-defined mathematical formulation extensively investigated in the 1960’s (see, e.g., Siscoe 1988,for detailed review and references). Calculations based on the Chapman-Ferraro model predict the location and shape of the magnetospheric boundary, the magnetic field line pattern within the magnetosphere (visu- alizable as a compressed dipole field), and the resulting geomagnetic disturbances. For the most part, with the exception primarily of intense magnetic storm periods, these predictions are in reasonable agreement with what is observed on the day side of the magnetosphere, in particular the decreasing distance of the subsolar magnetopause with increasing solar wind 2 dynamic pressure ρswVsw and the northward jumps of the low-latitude geomagnetic field 2 (sudden commencements and sudden impulses) when ρswVsw suddenly increases. The magnetic field and its changes in the Chapman-Ferraro model are usually described in terms of a current system, the Chapman-Ferraro current. Fundamentally, however, the interior magnetic field is calculated from the condition that it be tangent to the magnetopause surface, the location of which is adjusted to satisfy the condition of equal total pressure balance; the current is then obtained from the magnetic field change via (1). (The condition that the exterior flow be tangent to the magnetopause surface is satisfied by adjusting the location of the bow shock.) When the Chapman-Ferraro model was first proposed in the 1930’s, it was more or less taken for granted that there was no interplanetary magnetic field. The Chapman-Ferraro cur-