25 Years of Self-organized Criticality: Concepts and Controversies

Introduced by the late Per Bak and his colleagues, self-organized criticality (SOC) has been one of the most stimulating concepts to come out of statistical mechanics and condensed matter theory in the last few decades, and has played a significant role in the development of complexity science. SOC, and more generally fractals and power laws, have attracted much comment, ranging from the very positive to the polemical. The other papers (Aschwanden et al. in Space Sci. Rev., 2014, this issue; McAteer et al. in Space Sci. Rev., 2015, this issue; Sharma et al. in Space Sci. Rev. 2015, in preparation) in this special issue showcase the considerable body of observations in solar, magnetospheric and fusion plasma inspired by the SOC idea, and expose the fertile role the new paradigm has played in approaches to modeling and understanding multiscale plasma instabilities. This very broad impact, and the necessary process of adapting a scientific hypothesis to the conditions of a given physical system, has meant that SOC as studied in these fields has sometimes differed significantly from the definition originally given by its creators. In Bak’s own field of theoretical physics there are significant observational and theoretical open questions, even 25 years on (Pruessner 2012). One aim of the present review is to address the dichotomy between the great reception SOC has received in some areas, and its shortcomings, as they became manifest in the controversies it triggered. Our article tries to clear up what we think are misunderstandings of SOC in fields more remote from its origins in statistical mechanics, condensed matter and dynamical systems by revisiting Bak, Tang and Wiesenfeld’s original papers

Alternating bursts of low energy ions and electrons near the substorm onset

The substorm associated behavior of the low energy particles (30 eV–28.5 keV) near the earthward edge of the plasma sheet is examined using data from CRRES during the late growth and early expansion phases of a substorm on 12 March 1991 and their significance for the substorm onset mechanism is discussed. In this substorm, the CRRES was located on <i>L</i> ~6.3 and ~20° westward of the substorm onset and observed the sequence of the alternating bursts of the low energy ions and electrons. The bursts of the 0.633–9.6 keV ions occurred 1–2 min before the (7.31–21.7 keV) electron bursts. The first ion burst happened 2min before the substorm onset, at the moment of weak brightening of the most equatorial pre-breakup arc near the latitude ~62°. The alternation of the ion and electron bursts may be a signature of a drift-Alfvén ballooning instability on the inner edge of the plasma sheet near substorm onset

Studies of the substorm on March 12, 1991: 1. Structure of substorm activity and auroral ions

The substorm on March 12, 1991 is studied using the data of ground-based network of magnetometers, all-sky cameras and TV recordings of aurora, and measurements of particle fluxes and magnetic field onboard a satellite in the equatorial plane. The structure of substorm activity and the dynamics of auroral ions of the central plasma sheet (CPS) and energetic quasi-trapped ions related to the substorm are considered in the first part. It is shown that several sharp changes in the fluxes and pitch-angle distribution of the ions which form the substorm ion injection precede a dipolarization of the magnetic field and increases of energetic electrons, and coincide with the activation of aurora registered 20 degrees eastward from the satellite. A conclusion is drawn about different mechanisms of the substorm acceleration (injection) of electrons and ions

Optical complex for the study of pulsating aurora with sub-millisecond time resolution on the basis of the Verkhnetulomsky observatory

International audienceA new telescope-spectrometer was installed at Verkhnetulomsky observatory (68?36'N, 31?47'E) to supplement the data from all-sky cameras with measurements of the fine space-time structure of the auroral luminescence. The telescope uses 5 cm ultraviolet (UV) transparent lens as an optical system and a matrix of multi-anode photomultiplier tubes as a photo detector. The angular resolution of the telescope is 1.2? and the temporal resolution is 0.3 ms. The telescope observes a central part (20?) of the all-sky camera field of view (FOV). Description of both optical instruments and results of the first joint measurements are presented

25 Years of Self-Organized Criticality: Solar and Astrophysics

Shortly after the seminal paper “Self-Organized Criticality: An explanation of 1/fnoise” by Bak et al. (1987), the idea has been applied to solar physics, in “Avalanches and the Distribution of Solar Flares” by Lu and Hamilton (1991). In the following years, an inspiring cross-fertilization from complexity theory to solar and astrophysics took place, where the SOC concept was initially applied to solar flares, stellar flares, and magnetospheric substorms, and later extended to the radiation belt, the heliosphere, lunar craters, the asteroid belt, the Saturn ring, pulsar glitches, soft X-ray repeaters, blazars, black-hole objects, cosmic rays, and boson clouds. The application of SOC concepts has been performed by numerical cellular automaton simulations, by analytical calculations of statistical (powerlaw-like) distributions based on physical scaling laws, and by observational tests of theoretically predicted size distributions and waiting time distributions. Attempts have been undertaken to import physical models into the numerical SOC toy models, such as the discretization of magneto-hydrodynamics (MHD) processes. The novel applications stimulated also vigorous debates about the discrimination between SOC models, SOC-like, and non-SOC processes, such as phase transitions, turbulence, random-walk diffusion, percolation, branching processes, network theory, chaos theory, fractality, multi-scale, and other complexity phenomena. We review SOC studies from the last 25 years and highlight new trends, open questions, and future challenges, as discussed during two recent ISSI workshops on this theme.Fil: Aschwanden, Markus J.. Lockheed Martin Corporation; Estados UnidosFil: Crosby, Norma B.. Belgian Institute For Space Aeronomy; BélgicaFil: Dimitropoulou, Michaila. University Of Athens; GreciaFil: Georgoulis, Manolis K.. Academy Of Athens; GreciaFil: Hergarten, Stefan. Universitat Freiburg Im Breisgau; AlemaniaFil: McAteer, James. University Of New Mexico; Estados UnidosFil: Milovanov, Alexander V.. Max Planck Institute For The Physics Of Complex Systems; Alemania. Russian Academy Of Sciences. Space Research Institute; Rusia. Enea Centro Ricerche Frascati; ItaliaFil: Mineshige, Shin. Kyoto University; JapónFil: Morales, Laura Fernanda. Canadian Space Agency; Canadá. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Nishizuka, Naoto. Japan National Institute Of Information And Communications Technology; JapónFil: Pruessner, Gunnar. Imperial College London; Reino UnidoFil: Sanchez, Raul. Universidad Carlos Iii de Madrid. Instituto de Salud; EspañaFil: Sharma, A. Surja. University Of Maryland; Estados UnidosFil: Strugarek, Antoine. University Of Montreal; CanadáFil: Uritsky, Vadim. Nasa Goddard Space Flight Center; Estados Unido