ner_tags: O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O
tokens: due to the forces connected to the torsional Alfvén wave. Therefore, by having these expressions to hand, the efficiency of collimation due to the atmospheric and equilibrium conditions together with the nonlinear forces connected to the torsional Alfvén wave can be better understood. This provides a helpful tool and a robust standing point for observation purposes and coronal seismology. If one asks how, the answer lies in Figures 2 and 3 , where the interplay of the plasma- β and the shear flow on the density perturbations and jet cross section is highlighted. It can clearly be seen that the efficiency of the shear flow is highly elevated in higher plasma- β regions. This means that in the solar photosphere, where the plasma- β equals unity, the density perturbation amplitude due to the nonlinear forces and the external pressure force increases to over twice that of the solar corona. Note in the absence of the shear flow, the plasma- β acts mutually for the density perturbations due to the nonlinear effects connected to the torsional Alfvén wave. Figure 2. Interplay of the plasma- β and the shear flow ( u 0 ) effective on the density perturbations inside the jet due to the nonlinear forces (left panel) and the external pressure force (right panel). The surface plot is created from Equation ( 25 ), and the shear flow is normalized by the Alfvén speed. The interplay of the plasma- β and the shear flow on the perturbations of the jet cross section is pictured in the two panels of Figure 3 . By glancing over the surface plots of Figure 3 it can beseen that for coronal conditions (low plasma- β ) the perturbations of the jet cross section are anti-phase with those inside the jet. This means that for coronal conditions the forces effective on the jet collimation prove more efficient compared with the photospheric conditions. Figure 3. Interplay of the plasma- β and the shear flow ( u 0 ) effective on the jet cross section perturbation due to the nonlinear forces (left panel) and the external pressure force (right panel. The surface plot is created from Equation ( 33 ), and the shear flow is normalized by the Alfvén speed. The reason for this anti-phase behavior for coronal conditions can be better understood when the parallel speed perturbations surf against the shear flow and plasma- β . Figure 4 shows that the parallel speed perturbations due to the forces working on the jet collimation connected to the torsional wave are in phase with the density perturbations. In the low plasma- β regime, an increase in the perturbation amplitude of the density is accompanied by an increase in the parallel speed of the plasma. The decrease in the jet cross section is therefore due to the Bernoulli effect. However for photospheric conditions (finite plasma- β regime), the jet cross section is in phase with the density and parallel speed perturbations connected to the nonlinear torsional Alfvén wave. Figure 4. Interplay of the plasma- β and the shear flow (