Cross-Phase Analysis of ITG and ETG Particle Transport for Understanding I Mode

The tokamak I mode has proved difficult to explain because it is not clear how an anomalous heat flux is suppressed while the particle flux remains robust. We investigate details of transport cross-phases in a model with L and I mode representations, since cross phases can differ from one regime to another. We assume L mode is dominated by ITG turbulence and I mode by ETG turbulence, as suggested by observations, and calculate the respective particle fluxes from kinetic theory. To enable analytic calculations, flow shear is not included but is accounted for by assuming that the shearing rate is larger in I mode and tends to reduce all fluxes. Non-adiabatic particles govern transport; in ITG they are trapped electrons and require collisions to produce radial transport, even in hot plasmas. This gives a ▽T-driven pinch that offsets outward diffusion, weakening particle transport in L mode. The non-adiabatic ions of ETG are collisionless, with non-zero transport requiring an ion spectrum feature to create a magnetic-drift resonance. If ITG is a subdominant instability in I mode all flux terms are outward, yielding more robust particle transport than in L mode. The requirement of an ion frequency is discussed in relation to linear and nonlinear effects in the frequency spectrum.