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.

Solar energetic particle (SEP) events are a serious radiation hazard for spacecraft as well as a severe health risk to humans traveling in space. Indeed, accurate modeling of the SEP environment constitutes a priority requirement for astrophysics and solar system missions and for human exploration in space. The European Space Agency's Solar Energetic Particle Environment Modelling (SEPEM) application server is a World Wide Web interface to a complete set of cross‐calibrated data ranging from 1973 to 2013 as well as new SEP engineering models and tools. Both statistical and physical modeling techniques have been included, in order to cover the environment not only at 1 AU but also in the inner heliosphere ranging from 0.2 AU to 1.6 AU using a newly developed physics‐based shock‐and‐particle model to simulate particle flux profiles of gradual SEP events. With SEPEM, SEP peak flux and integrated fluence statistics can be studied, as well as durations of high SEP flux periods. Furthermore, effects tools are also included to allow calculation of single event upset rate and radiation doses for a variety of engineering scenarios.

As the current solar cycle 25 progresses and moves towards solar maxima, solar activity is increasing and extreme space weather events are taking place. Two severe geomagnetic storms accompanied by two large Forbush decreases in galactic cosmic ray intensity were recorded in March and May, 2024. More precisely, on 24 March 2024, a G4 (according to the NOAA Space Weather Scale for Geomagnetic Storms) geomagnetic storm was registered, with the corresponding geomagnetic indices Kp and Dst equal to 8 and −130 nT, respectively. On the same day, the majority of ground-based neutron monitor stations recorded an unusual Forbush decrease. This event stands out from a typical Forbush decrease because of its high amplitude decrease phase and rapid recovery phase, i.e., 15% decrease and an extremely rapid recovery of 10% within 1.5 h, as recorded at the Oulu neutron monitor station. Furthermore, on 10–13 May 2024, an unusual G5 geomagnetic storm (geomagnetic indices Kp = 9 and Dst = −412 nT) was registered (the last G5 storm had been observed in 2003). In addition, the polar neutron monitor stations recorded a Ground Level Enhancement (GLE74) during the recovery phase of a large Forbush decrease of 15%, which started on 10 May 2024. In this study, a detailed analysis of these two severe events in regard to the accompanying solar activity, interplanetary conditions and solar energetic particle events is provided. Moreover, the results of the NKUA “GLE Alert++ system”, the NKUA/IZMIRAN “FD Precursory Signals” method and the NKUA “ap Prediction tool” concerning these events are presented.

The space environment is forever changing on all spatial and temporal scales. Energy releases are observed in numerous dynamic phenomena (e.g. solar flares, coronal mass ejections, solar energetic particle events) where measurements provide signatures of the dynamics. Parameters (e.g. peak count rate, total energy released, etc.) describing these phenomena are found to have frequency size distributions that follow power-law behavior. Natural phenomena on Earth, such as earthquakes and landslides, display similar power-law behavior. This suggests an underlying universality in nature and poses the question of whether the distribution of energy is the same for all these phenomena. Frequency distributions provide constraints for models that aim to simulate the physics and statistics observed in the individual phenomenon. The concept of self-organized criticality (SOC), also known as the "avalanche concept", was introduced by Bak et al. (1987, 1988), to characterize the behavior of dissipative systems that contain a large number of elements interacting over a short range. The systems evolve to a critical state in which a minor event starts a chain reaction that can affect any number of elements in the system. It is found that frequency distributions of the output parameters from the chain reaction taken over a period of time can be represented by power-laws. During the last decades SOC has been debated from all angles. New SOC models, as well as non-SOC models have been proposed to explain the power-law behavior that is observed. Furthermore, since Bak's pioneering work in 1987, people have searched for signatures of SOC everywhere. This paper will review how SOC behavior has become one way of interpreting the power-law behavior observed in natural occurring phenomenon in the Sun down to the Earth.

A ground-level enhancement (GLE) event is a sudden increase in cosmic ray intensity originated by solar sources and recorded by ground-based detectors. GLEs are invariably associated with large solar flares that can release and accelerate solar particles at high energies. The minimum kinetic energy of particles reaching the Earth’s surface is >433 MeV at sea level and about 300 MeV/n at high-mountain altitude of about 3000 m a.s.l. Even though these abrupt events linked to solar activity are quite rare, they can have a great impact on technological systems and human health when recorded. Therefore, the accurate and effective prognosis of such events is of great importance. In this paper, an overview of the most recently recorded GLE event and the first of solar cycle 25, i.e., GLE73, as well as a post-event analysis is presented. GLE73 was detected on 28 October 2021 and was associated with the active region AR12887 on the central part of the solar disk, which produced an X1.0 solar flare. The event was registered by several stations of the worldwide ground-based neutron monitor network. An accurate alert was issued successfully by the ESA R-ESC federated product GLE Alert Plus, as well as the updated GLE Alert++ System of the Athens Neutron Monitor Station (A.Ne.Mo.S.). It should be emphasized that the GLE Alert++ signal by NKUA/A.Ne.Mo.S. was issued 45 min earlier than the one issued by GOES. A short description and the advantages of this last system are provided.

The main source of the ionization of the Earth’s atmosphere is the cosmic radiation that depends on solar activity as well as geomagnetic activity. Galactic cosmic rays constitute a permanent radiation background and contribute significantly to the radiation exposure inside the atmosphere. In this work, the cosmic-ray-induced ionization of the Earth’s atmosphere, due to both solar and galactic cosmic radiation during the recent solar cycles 23 (1996–2008) and 24 (2008–2019), was studied globally. Estimations of the ionization were based on the CRAC:CRII model by the University of Oulu. The use of this model allowed for extensive calculations from the Earth’s surface (atmospheric depth 1033 g/cm²) to the upper limit of the atmosphere (atmospheric depth 0 g/cm²). Monte Carlo simulations were performed for the estimation quantities of radiobiological interest with the validated software DYASTIMA/DYASTIMA-R. This study was focused on specific altitudes of interest, such as the common flight levels used by commercial aviation.