Torsional Alfvén Shock Waves in Stratified Coronal Loops

Abstract The evolution of weakly nonlinear Alfvén waves in coronal loops in the density structuring both across and along the field while experiencing dissipation is highlighted. Energy transfer due to shock formation in coronal loops provides the basis for the context of the present study. Coronal loops are modeled analytically using the magnetohydrodynamic (MHD) theory in cylindrical geometry, incorporating stratification and viscosity. The effects of the external medium, along with equilibrium conditions, are considered, with the background magnetic field aligned parallel to the loop axis. The second-order thin flux tube approximation is employed to derive a Cohen–Kulsrud–Burgers type of evolutionary equation that highlights the influences of nonlinear, dissipative, and stratification terms, alongside the effect of the external medium. The Alfvén wave speed in coronal loops reaches its maximum when shocks are experienced. If not due to low amplitudes, the maximum is observed at the other footpoint. The location of shock formation is determined by the ratio of the Alfvén wave amplitude and the background Alfvén wave speed. The existence of energy transfer mechanisms due to MHD shocks at various locations of coronal loops, especially loop footpoints, brings to mind that observed energy transfers in the case of coronal loops or a set of loops not only provide coronal heating but also provide transition region heating subject to conditions. For high plasma-β values at lower altitudes, shock formation is less dependent on the external medium and depends strongly on the loop’s internal dynamics. This is contrary to open magnetic structures.