“…Star formation (Norman and Heyvaerts, 1985;Marchand et al, 2019;Wurster et al, 2021), solar atmosphere and the solar wind at Earth distance (Galtier and Buchlin, 2007;González-Morales et al, 2019), dynamo action (Mininni et al, 2002(Mininni et al, , 2005Gómez et al, 2010) and the Earth and planetary magnetospheres (Liu et al, 2013;Dorelli et al, 2015;Xie et al, 2015;Tóth et al, 2016), are only some of the frameworks and science cases tackled in the literature employing the Hall-MHD model. Several studies have also shown that the Hall term enhances the rate of magnetic reconnection (Wang et al, 2001;Morales et al, 2005;Ma et al, 2014;Ma et al, 2018), though there is an ongoing discussion on the role of the Hall current in the emergence of magnetic structures (Mininni et al, 2007). In particular, claims are made that the Hall effect may help amplifying the large-scale magnetic field (Mininni et al, 2005) and the emergence of self-organized structures (Numata et al, 2004;Ohsaki, 2006), while some authors argue it helps instead with the generation of small-scale structures and filaments (Rheinhardt and Geppert, 2002;Miura and Araki, 2014;Martin et al, 2013).…”