  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.
