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Abstract. We consider the problem of the canonical profiles for tokamak
plasma with arbitrary cross-section, taking into account two principles: 1)
the free plasma energy minimum with the constraint of total current
conservation and 2) the profile consistency. We deduce the Euler
differential equation for the canonical profile of 
= 1/q with two
types of the boundary conditions: soft and stiff. The soft conditions
correspond to the Kadomtsev solution for the circular cylinder. The stiff
conditions describe a fast response of the plasma over the whole
cross-section on the edge impact. Using the canonical profile of the current
density, we calculate the critical gradients for the temperature, and create
the transport model for the electron and ion temperatures and density. We
show that, when the aspect ratio is diminished, or when the elongation
increases, the canonical profiles become flatten. The similar tendency for
the real profiles of the electron temperature was found in analyzis of JET
and START experiments. The obtained critical gradients were used to analysis
of the experiments in tokamaks with moderate and tight aspect ratios.
IAEA 2003
