The extremely strong non-neutralized electric currents of the unique solar active region NOAA 13664

Context. In May 2024, the extremely complex active region National Oceanic and Atmospheric Administration (NOAA) 13664 produced the strongest geomagnetic storm since 2003.Aims.The aim of this study is to explore the development of the extreme magnetic complexity of NOAA 13664 in terms of its photospheric electric current.Methods. The non-neutralized electric current was derived from photospheric vector magnetograms, provided by the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory. The calculation method is based on image processing, thresholding, and error analysis. The spatial and temporal evolution of the non-neutralized electric current of the region as well as its constituent subregions was examined. For context, a comparison with other complex, flare-prolific active regions is provided.Results. Active region NOAA 13664 was formed by the emergence and interaction of three subregions, two of which were of notable individual complexity. It consisted of numerous persistent, current-carrying magnetic partitions that exhibited periods of conspicuous motions and strongly increasing electric current at many locations within the region. These periods were followed by intense and repeated flaring. The total unsigned non-neutralized electric currents and average injection rates reached 5.95 ⋅ 10^{13 A and 1.5 ⋅ 1013 A/day, and are the strongest observed so far, significantly surpassing other super-active regions of Solar Cycle 24 and 25.Conclusions. Active region NOAA 13664 presents a unique case of complexity. Further scrutiny of the spatial and temporal variation of the net electric currents during the emergence and development of super-active regions is paramount to understand the origin of complex regions and adverse space weather.}