The poor man's magnetohydrodynamic (PMMHD) equations. (May 2020)

• Record Type: Journal Article
• Authors: Alberti, T; Consolini, G; Carbone, V
• Is Part Of: Journal of physics. Volume 1548(2020)
• Publication Date: 2020-05
• Subjects: Physics -- Congresses; 530.5
• DOI: 10.1088/1742-6596/1548/1/012037
• Languages: English
• ISSNs: 1742-6588

Abstract

Abstract: We present a mathematical derivation of a discrete dynamical system by following a Fourier-Galerkin approximation of the 3-D incompressible magnetohydrodynamic (MHD) equations. In this way, a 6-D map, depending on 12 bifurcation parameters, is derived as a truncated set of nonlinear ordinary differential equations (ODEs) to characterize incompressible plasma dynamical behaviors, also conserving total energy and cross-helicity in the ideal MHD approximation. Moreover, three different subspaces, associated with long-living non-trivial solutions (e.g., fixed point solutions), have been found like the fluid, magnetic, and the Alfvenic fixed points. Our set can be seen as a Lorenz-like model to investigate MHD phenomena.