Analyzing atmospheric electric field by the European SEVAN network of particle detectors

Particle detectors of the European SEVAN network located on mountain heights in Aragats (Armenia), Lomnický štít (Slovakia) and Musala (Bulgaria) are well suited for the detection of thunderstorm ground enhancements (TGEs, enhanced fluxes of electrons, gamma rays, neutrons). The modulation of charged particles flux by the electric field of the thundercloud results in a sizable change in the count rate of detectors, which measure fluxes of electrons, gamma rays, and high energy muons in the near-vertical and near-horizontal directions. The relation between electric field strength and changes of particle flux count rates is nonlinear and depends on many unknown parameters of atmospheric electric field and meteorological conditions. Nonetheless, employing extreme TGEs as a manifestation of the strong electric field in the thundercloud and by measuring fluxes of three species of secondary cosmic rays (electrons, gamma rays, and muons) by SEVAN detectors located at altitudes of ≈ 3 km we study the extreme strength of the atmospheric electric field. With the simulation of particle traversal through the electric field with CORSIKA code (https://www.iap.kit.edu/corsika/index.php, last accessed April 21, 2021), we derive a maximum potential difference in the thunderous atmosphere to be ≈ 500 MV

An MHD spectral theory approach to Jeans’ magnetized gravitational instability

International audienceABSTRACT In this paper, we revisit the governing equations for linear magnetohydrodynamic (MHD) waves and instabilities existing within a magnetized, plane-parallel, self-gravitating slab. Our approach allows for fully non-uniformly magnetized slabs, which deviate from isothermal conditions, such that the well-known Alfvén and slow continuous spectra enter the description. We generalize modern MHD textbook treatments, by showing how self-gravity enters the MHD wave equation, beyond the frequently adopted Cowling approximation. This clarifies how Jeans’ instability generalizes from hydro to MHD conditions without assuming the usual Jeans’ swindle approach. Our main contribution lies in reformulating the completely general governing wave equations in a number of mathematically equivalent forms, ranging from a coupled Sturm–Liouville formulation, to a Hamiltonian formulation linked to coupled harmonic oscillators, up to a convenient matrix differential form. The latter allows us to derive analytically the eigenfunctions of a magnetized, self-gravitating thin slab. In addition, as an example, we give the exact closed form dispersion relations for the hydrodynamical p- and Jeans-unstable modes, with the latter demonstrating how the Cowling approximation modifies due to a proper treatment of self-gravity. The various reformulations of the MHD wave equation open up new avenues for future MHD spectral studies of instabilities as relevant for cosmic filament formation, which can e.g. use modern formal solution strategies tailored to solve coupled Sturm–Liouville or harmonic oscillator problems