The transport in the nonlinear system is briefly reviewed and the transport in continuous system is calculated through numerical computation for two typical systems. One of the systems is the two-wave system which is close to the integrable system, and a new scaling result for this system is suggested. And the other system is the more realistic tokamak including the drift along the fluctuating magnetic field.
In the two-wave system, we study the scaling of the diffusion coefficient with the fluctuation amplitude in conjunction with the E×B velocity correlation function. For high fluctuation amplitude the velocity correlation function is split into two parts. One part is the correlation for the integrable case which does not contribute to the net transport. The other part is the correlation which results from the stochasticity. The diffusion coefficient obtained from the integrals of the second part of correlation, scales as $\tilde{\phi}^0$ or $\tilde{\phi}^{-1}$ depending on the cases considered.
The electron diffusion in tokamak geometry is calculated including both the Coulomb collisional pitch angle scattering and the electromagnetic drift wave fluctuation spectrum. In the weak fluctuation limit the neoclassical banana-plateau diffusion coefficient is recovered. At higher fluctuation levels, typical of the mixing length amplitude the anomalous transport formulas of drift wave turbulence are recovered.
