Non-standard magnetohydrodynamics equations and their implications in sunspots

Abstract

In this work, we study the physics of plasma waves and magnetohydrodynamic (MHD) equilibrium of sunspots based on the concept of non-standard Lagrangians which play an important role in several branches of science. We derived the modified fluid equations from the Maxwell–Vlasov equation using the moment conventional procedure. Several new interaction terms between physical quantities arise in the non-standard MHD (NS-MHD) equations that give rise to additional features in plasma MHD. A number of fundamental problems in plasma physics are discussed including the non-relativistic dynamics of inviscid fluid subject to the gravitational field, linear waves in plasma MHD and MHD equilibrium of sunspots. For the case of magnetoacoustic wave, it was observed that the NS-MHD equations modify the dispersion relation and its corresponding velocity depends on the sign (positive or negative) of the free parameters introduced in the theory. The non-standard Alfvén velocity is greater than the standard Alfvén velocity for the negative sign and smaller for the positive sign. Besides, in the MHD equilibrium of sunspots, non-standard MHD extends the conventional problem by adding several constraints that lead to an emergence of very low temperature inside the magnetic flux tube comparable to what is observed in low-temperature superconductors. Additional consequences are discussed accordingly.