Thin and superthin current sheets: journey into the depths of Syrovatskii's singularity

We discuss the history of the study of thin (proton-thickness) current sheets in space plasma, which in the magnetohydrodynamic (MHD) framework were regarded as singular structures, i.e., infinitely thin MHD discontinuities. We discuss the special role of the work of S.I. Syrovatskii and his group in developing the theory and experimental studies of nonstationary thin current sheets in application to solar flares. Multisatellite scientific missions (Interball, Cluster, and MMS) have allowed looking inside the ‘singularities’ and evaluating the most complex processes of energy accumulation, transformation, and release within them. The accumulation of observational data from multisatellite space missions and the development of theoretical models of thin sheets allows their complex internal structure to be studied, including a hierarchical nesting of thinner current sheets inside wider ones. Even in a not very thin sheet, the plasma dynamics can no longer be described within the MHD approximation and requires the motion of electrons and ions to be described separately, at least. Describing ions is especially challenging because of their large Larmor radius (possibly exceeding the sheet thickness). The so-called quasiadiabatic theory of the motion of charged particles in the presence of sharp magnetic gradients plays a major role here. We reveal the key role of thin nested structures as triggers of explosive magnetic reconnection and conversion of the free energy of magnetic fields into the energy of waves and flows of accelerated particles. The relevant issue of observing and interpreting the properties of superthin (electron-scale) current sheets is covered in detail. Such sheets can be both part of multilevel nested structures and multiple independent nonstationary formations related to the magnetic energy dissipation processes in hot collisionless magnetospheric plasmas. The rapid evolution and decay of these sheets lead to the acceleration of electrons and the formation of new sheets, which also decay and give rise to new thin current structures; therefore, reconnection does occur on the electron scale, albeit in a nontrivial cascade mode. Several decades have passed since Syrovatskii constructed the MHD model of a dynamical current sheet, and the experience of improving both experimental techniques and theoretical tools that have allowed looking inside these amazing structures is instructive.