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The aim of this study is to model the nature of nonlinear torsional magnetohydrodynamic waves propagating in solar jets as they are elevated to the outer solar atmosphere. The contribution of sequential processes to the transfer of energy is taken under consideration: the nonlinear cascade and shock formation. Thus a straight magnetic cylinder embedded in a plasma with an initial magnetic field and parallel flow to the cylinder axis is implemented. To resemble a jet where the oscillation wavelength highly exceeds the radius, the second-order thin flux tube approximation proves adequate. A Cohen–Kulsrud type equation is presented, and its solution highly depends on the parameter presented in this study, which itself is constituted of various environmental and equilibrium conditions that affect the perturbations of the variables as well as the nonlinear forces connected to Alfvén wave propagation. The shock formation time of torsional waves is inversely proportional to the density contrast of the jet, while the efficiency of energy transfer to shorter scales is directly proportional to the density contrast. While the parallel flow with a shear at the boundary expedites shock formation, its efficiency regarding energy transfer is dramatically enhanced by the plasma- β , significantly contributing to coronal heating. The observational and seismological aspect of the present study is that faster jets are less probable for observations at higher altitudes, as they experience energy transfer mostly at the base of the corona, while slow speed jets may be observed at higher altitudes contributing to solar wind acceleration.

Torsional Alfvén Wave Cascade and Shocks Evolving in Solar Jets