Toroidal rotation in neutral beam heated discharges in DIII-D

Abstract

It is known that the toroidal angular momentum and the ion thermal energy are correlated in tokamak discharges heated by neutral beam injection. Here, data from ten years of measurements on DIII-D are considered, for representative discharges from all types and all conditions. The ratio of simple replacement times for momentum and energy is found to order this correlation indicating that these times are approximately equal, across the minor radius. Representative discharges of several types are discussed in more detail, as well as transport analysis results for the momentum and thermal ion diffusivities.

Dimensionless size scaling of intrinsic rotation in DIII-D

“…The correlation of V ϕ with T i as shown in Figure (2), and described in other experiments [10,18,[32][33][34] is also captured in equation (1). Equation (1) can be cast in a form that reveals its relation to the PS [10], V φ~Ti /I p , as shown in equation (4), although we apply it to a region where the gradient in V ϕ is negative, rather than positive as done in [10].…”

“…The correlation of the local V ϕ with the local T i is clear. The line drawn at a slope of 45 km/s/keV is the scaling value described in reference [34] for unidirectional co-I p NBI in DIII-D, with the DIII-D NBI D + beams at 60 keV for these data in Figure 2. The lines drawn at 18 and 10 km/s/keV will be related to the Parra scaling [10] discussed in Section VII.…”

“…Another experimental observation that guided this search for a dimensionless scaling is the correlation of the intrinsic toroidal velocity with the local T i [10,19] or the gradient in T i [33]. This correlation also holds in conditions with significant NBI-torque drive [34,35].…”

Perturbative studies of toroidal momentum transport using neutral beam injection modulation in the Joint European Torus: Experimental results, analysis methodology, and first principles modeling

“…On the experimental side, a significant improvement in the characterization of the steady-state behaviour of toroidal rotation has been achieved, both in plasmas with external torque source [11][12][13][14] and in plasmas without external torque sources [15][16], which still exhibit non-zero toroidal rotation, the so-called "intrinsic rotation", whose physical origin is still under investigation. A rather surprising recent observation from steady-state momentum studies is that the effective momentum diffusivity is much lower than the ion heat diffusivity (P r eff = χ φ eff / χ i eff~0 .4 using the definition of χ φ as in Eq.1) [11,[13][14], apparently contradicting the theoretical expectations.…”

Electromagnetic effects on toroidal momentum transport

“…1 The global confinement times and the diffusivities of energy and momentum have previously been assumed to be equal or predicted to be comparable. [2][3][4] Recent experimental studies 5,6 do, however, contradict these results and have yielded an effective Prandtl number ͑ratio of the effective momentum diffusivity ͑ ,eff ͒ and an effective ion heat diffusivity ͑ i,eff ͒͒ substantially below 1. This discrepancy could be resolved as suggested by various studies through the existence of momentum pinch ͑inward flow of momentum flux͒, which is anticipated as the result of symmetry breaking effects on toroidal momentum transport.…”