Self‐organized criticality in the substorm phenomenon and its relation to localized reconnection in the magnetospheric plasma sheet

Abstract

Abstract. Evidence is presented that suggests that there is a significant self-organized criticality (SOC) component in the dynamics of substorms in the magnetosphere. We assume that observations ofbursty bulk flows, fast flows, localized dipolarizations, plasma turbulence, etc. show that multiple localized reconnection sites provide the basic avalanche phenomenon in the establishment of SOC in the plasma sheet. First results are presented from a study of this avalanche process based on this working assumption. A magnetic field reversal model is discussed. Resistivity, in this model, is self-consistently generated in response to the excitation of an idealized currentdriven instability. When forced by convection of magnetic flux into the field reversal region, the model yields rapid magnetic field annihilation through a dynamic behavior that is shown to exhibit many of the characteristics of SOC. Over a large range of forcing strengths, the annihilation rate is shown to self-adjust to balance the rate at which flux is convected into the reversal region. Several analogies to magnetotail dynamics are discussed: (1) It is shown that the presence of a localized criticality in the model produces a remarkable stability in the global configuration of the field reversal while simultaneously exciting extraordinarily dynamic internal evolution. (2) Under steady forcing it is shown that a loading-unloading cycle may arise that, as a consequence of the global stability, is quasi-periodic and, therefore, predictable despite the presence of internal turbulence in the field distribution. Indeed, it is shown that the global loading-unloading cycle is a consequence of the internal turbulence. (3) It is shown that under steady, strong forcing the loading-unloading cycle vanishes. Instead, a recovery from a single unloading persists indefinitely. The field reversal is globally very steady while internally it is very dynamic as field annihilation goes on at the rate necessary to match the strong forcing. From this result we speculate that steady magnetospheric convection events result when the plasma sheet has been driven close to criticality over an extended spatial domain. During these events we would expect to find localized reconnection sites distributed over the spatial domain of near criticality, and we would expect to find plasma sheet transport in that domain to be closely related to that of BBF and fast flow events.

The magnetosphere as a complex system

“…This deceivingly simple diffusion equation will provide the starting point to understand the complex behavior required to establish a global SO state. Klimas et al, (2000) introduced (see Lu 1995) sporadic dissipation through a spatio-temporal evolution for η as…”

“…Recent observations seem to suggest that plasmas, under certain conditions, demonstrate very complex behavior, that includes self-similar behavior, emergence and self-organization, phase transitions, turbulence, spatio-temporal chaos, and so on (Lu and Hamilton, 1991;Carreras et al, 1996;Boffeta et al, 1999;Klimas et al, 2000;Tangri et al, 2003;Valdivia et al, 2003;Borovsky et al, 2003).…”

“…Even though these models are a clear simplification of the complete equations, they are claimed to represent the energy flow in a qualitative manner (Boffeta et al, 1999;Biskamp, 2000). Klimas et al (2000) and Valdivia et al(2003) derived from the plasma equations, but using anomalous localized dissipation, a continuous model of magnetic annihilation that displays selfsimilar event behavior, reminiscent of a self-organized critical state. A similar model was postulated earlier as a possible continuous representation of a sandpile (Lu, 1995).…”

Intermittency and multifractional Brownian character of geomagnetic time series

“…Its complex dynamics, which results from the superposition of the internal dynamics and the external driving due to the changes of solar wind conditions, has been widely investigated during the past two decades. Several studies have been devoted to examine the occurrence of chaos, turbulence and criticality during geomagnetic storms and substorms, which are the most important manifestations of the magnetospheric activity (e.g., Klimas et al, 1996Klimas et al, , 2000Consolini and Chang, 2001;Dobias and Wanliss, 2009). These studies have clearly evidenced that the magnetospheric evolution is characterized by a near-criticality dynamics, which manifests both in the scale-invariant nature of magnetotail relaxation events and fractal properties of geomagnetic time series.…”

Nonclassical Transport and Particle-Field Coupling: from Laboratory Plasmas to the Solar Wind

“…These types of transport behavior have been observed both in space and laboratory plasmas, and a substantial effort has been made to characterize these regimes and understand the physical mechanisms that cause them. Examples are provided by the dynamics of solar flares (Lu and Hamilton 1991), magnetic substorms in Earth's magnetosphere (Klimas et al 2000), and radial turbulent transport in fusion devices and basic plasma experiments Fasoli et al 2010) to name just a few.…”