Physics of non-diffusive turbulent transport of momentum and the origins of spontaneous rotation in tokamaks

Abstract

Abstract. The theory of turbulent transport of toroidal momentum is discussed in the context of the phenomenon of spontaneous/intrinsic rotation. We review the basic phenomenology and survey the fundamental theoretical concepts. We then proceed to an in-depth discussion of the radial flux of toroidal momentum, with special emphasis on the off-diagonal elements, namely the residual stress (the portion independent of V) and the pinch. A simple model is developed which unifies these effects in a single framework and which recovers many of the features of the Rice scaling trends for intrinsic rotation. We also discuss extensions to finite beta and the effect of SOL boundary conditions. Several issues for future consideration are identified.

Neoclassical physics in full distribution function gyrokinetics

“…3 and 4. On the other hand, the accurate computation of the self-consistent radial electric field is a known central problem for full-f gyrokinetics, 21,69 part of it being due to the following degeneracy, intrinsic in neoclassical theory: prediction in an axisymmetric system is on the combination E r À v u B h , which is degenerate in the absence of toroidal symmetry-breaking mechanisms, should they be (i) of geometric nature -ripple, 70,71 error fields-or should they appear (ii) through the onset of the turbulence -E Â B shear, 72 turbulent Reynolds stresses, [73][74][75] or intensity gradients-or (iii) through the inclusion of sources of toroidal momentum. The restriction of the conventional neoclassical equilibrium in Eq.…”

Residual parallel Reynolds stress due to turbulence intensity gradient in tokamak plasmas

“…The idea presented here is consistent with ͑and inspired by͒ the fact that the turbulent momentum transport can be linked to turbulent wavemomentum transport and the wave kinetic equation, and computed by considering the wave-momentum flux. 30,37 In this formulation, two residual terms appear, one proportional to the E ϫ B shear ͑which thus corresponds to Ref. 29͒, and another one proportional to the intensity gradient.…”

Conversion of poloidal flows into toroidal flows by phase space structures in trapped ion resonance driven turbulence

“…[7,8,9] To elaborate this point, it is useful to recall that toroidal flow evolution equation generally takes the form:…”

“…Here χ ζ is the anomalous viscosity, V pinch is the pinch [31,32,33], Π res rζ is the residual stress [7,8,9], and a is a parallel acceleration [7,34] which acts as a local source. Π res rζ and a are required to spin-up plasmas from rest [8,9].…”

“…Π res rζ and a are required to spin-up plasmas from rest [8,9]. Physically, a originates from acoustic coupling, which includes refractive force [7] or turbulent acceleration [34].…”