Fusion, space and solar plasmas as complex systems

Complex systems science seeks to identify simple universal models that capture the key physics of extended macroscopic systems, whose behaviour is governed by multiple nonlinear coupled processes that operate across a wide range of spatiotemporal scales. In such systems, it is often the case that energy release occurs intermittently, in bursty events, and the phenomenology can exhibit scaling, that is a significant degree of self-similarity. Within plasma physics, such systems include Earth's magnetosphere, the solar corona and toroidal magnetic confinement experiments. Guided by broad understanding of the dominant plasma processes—for example, turbulent transport in tokamaks or reconnection in some space and solar contexts—one may construct minimalist complex systems models that yield relevant global behaviour. Examples considered here include the sandpile approach to tokamaks and the magnetosphere and a multiple loops model for the solar coronal magnetic carpet. Such models can address questions that are inaccessible to analytical treatment and are too demanding for contemporary computational resources; thus they potentially yield new insights, but risk being simplistic. Central to the utility of these models is their capacity to replicate distinctive aspects of observed global phenomenology, often strongly nonlinear, or of event statistics, for which no explanation can be obtained from first principles considerations such as the underlying equations. For example, a sandpile model, which embodies critical-gradient-triggered avalanching transport associated with nearest-neighbour mode coupling and simple boundary conditions (and little else), can be used to generate some of the distinctive observed elements of tokamak confinement phenomenology such as ELMing and edge pedestals. The same sandpile model can also generate distributions of energy-release events whose distinctive statistics resemble those observed in the auroral zone. Similarly, a multiple loops model, which embodies random footpoint motion combined with reconnection of intersecting loops (and little else), can generate global magnetic field structure resembling the solar coronal magnetic carpet, with power law distributions for energy-release events also similar to those observed in the solar corona. These reduced models thus focus on identifying the key physical ingredients that are necessary and sufficient to generate the observed phenomenology.