An Analytical APproach to the Turbulence—Relaxed State in Tokamak Plasmas

An Analytical Approach to the Turbulence-Relaxed Statein Tokamak Plasmas

Starting from the continuity, temperature, and motion equationsof the trapped electron fluid in general tokamak magnetic fieldwith positive or reversed shear and the definition of Lagrangianinvariant, dL/dt≡(partial_t+u•▽)L=0, whereu is convective velocity, the trapped electron dynamics is considered in the following two assumptions: (i)the turbulence is low frequency electrostatic, and (ii) L is a functional only of the density n, temperature T, and magnetic field B, and the effect of perturbationpotential φ is included in the convective velocity u, i.e., u is a functional of n, T, B, and φ. The Lagrangian invariant hidden in the trapped electron dynamics is strictly found:L=ln[(n/B)^c₁(T/B^2/3)^c₂], wherec₁ and c₂ are dimensionless changeable parameters and c₁∝c₂. From this Lagrangian invariantthe turbulent particle and electronthermal transport scaling laws are derived:〈n>_ψq(ψ)=const. and〈T^3/2>_ψq(ψ)=const.,which, in the limit of large aspect ratio, reduce ton(r)q(r)=const. and T^3/2(r)q(r)=const., respectively. The latter two scalinglaws are compared with existent experimental results, being in goodagreement.