Fluid Closure, Theory, Relations to Particle Pinches, Fluid Resonances

The fluid closure in a toroidal plasma is discussed. In particular the relation to particle and temperature pinches is considered. Implications for the radial growth of transport coefficients are given. A particularly significant effect of dissipative kinetic resonances is that they reduce particle pinches. This is shown both for a gyrofluid and a quasilinear kinetic model. In particular the fact that the ITG and Trapped electron modes are resonant modes and that the effect of dissipative kinetic resonanses is ignorable for impurities but not for main ions shows that the closure aspect in a fluid description and strongly nonlinear effects in a kinetic description are instrumental for a proper description of particle pinches. We assume here that only the ITG mode due to main ions is unstable. The ITG mode due to impurities would, of course, be sensitive to the resonance with impurities. This also addresses the question of sources in the Fokker‐Planck equation. The point is that we need only to worry about resonant sources for the wave dynamics, since RF heating with phase velocity or NBI heating with beam velocity far from the drift waves will appear only as ideal heat sources. The difference in phase velocity between drift waves and RF waves is much larger than the difference in thermal velocity of main ions and typical impurity ions.