Potato, banana, local, and nonlocal transport

The relationship between potato and banana transport theories is addressed using the solution of the drift kinetic equation. It is shown that they are two limits of a complete theory. The potato theory is the ψ→0 limit and the banana theory is the ψ→∞ limit. Here, ψ is the poloidal flux function. These local transport theories are valid even in the steep gradient situations because the real orbit width is usually smaller than the gradient scale length when the appropriate orbit squeezing effects are taken into account. The characteristic feature of a nonlocal theory is also discussed. It is shown that the equilibrium distribution in such a theory must be non-Maxwellian and nonexpandable.