Analytic regimes of tokamak plasma

The paper suggests certain regimes of fusion plasma with magnetic confinement, when the Larmor radius $\lambda$ and the angle $\alpha$ (determining the orientation of the local coordinates) form an analytic function $w=\lambda e^{i\alpha}$ of complex variable $z=x_1+i x_2$ ($x_1$ and $x_2$ are coordinates of tokamak cross-section). It is known that an efficient nuclear fusion requires transport barriers, which might be due to zonal/poloidal flow; and the emergence of such flow is implied by the adiabatic extra conservation (established in a local slub). The suggested analytic regimes are based on the global extension of this extra conservation; transport barriers could spread to the entire tokamak plasma. It is interesting that in these regimes, plasma temperature reaches maximum often not at a single location (of tokamak cross-section), but at several points separated by regions of lower temperature.