The difference between the guiding center phase-space Lagrangians derived in [J.W. Burby, J. Squire, and H. Qin, Phys. Plasmas {bf 20}, 072105 (2013)] and [F.I. Parra, and I. Calvo, Plasma Phys. Control. Fusion {bf 53}, 045001 (2011)] is due to a dif
ferent definition of the guiding center coordinates. In this brief communication the difference between the guiding center coordinates is calculated explicitly.
The effect of momentum injection on the temperature gradient in tokamak plasmas is studied. A plausible scenario for transitions to reduced transport regimes is proposed. The transition happens when there is sufficient momentum input so that the velo
city shear can suppress or reduce the turbulence. However, it is possible to drive too much velocity shear and rekindle the turbulent transport. The optimal level of momentum injection is determined. The reduction in transport is maximized in the regions of low or zero magnetic shear.
