Optimized up–down asymmetry to drive fast intrinsic rotation in tokamaks

Abstract

Breaking the up-down symmetry of the tokamak poloidal cross-section can significantly increase the spontaneous rotation due to turbulent momentum transport. In this work, we optimize the shape of flux surfaces with both tilted elongation and tilted triangularity in order to maximize this drive of intrinsic rotation. Nonlinear gyrokinetic simulations demonstrate that adding optimally-tilted triangularity can double the momentum transport of a tilted elliptical shape. This work indicates that tilting the elongation and triangularity in an ITER-like device can reduce the energy transport and drive intrinsic rotation with an Alfvén Mach number of roughly 1%. This rotation is four times larger than the rotation expected in ITER and is approximately what is needed to stabilize MHD instabilities. It is shown that this optimal shape can be created using the shaping coils of several present-day experiments.

Physics research on the TCV tokamak facility: from conventional to alternative scenarios and beyond

“…Gyrokinetic simulations have suggested a correlation between the toroidal rotation inversion observed when crossing a density threshold with a transition from an ion-temperature-gradient (ITG) dominated to a mixed ITG-trapped-electron-mode (TEM) turbulence regime [61]. Turbulence-driven residual stress is predicted to depend strongly on the up-down asymmetry of the plasma cross-section, which can be parametrized in terms of elongation, triangularity, and tilt angle [62]: these predictions are also being tested in a broad shaping scan. A detailed study of the evolution of rotation during the sawtooth cycle has shown that a co-current torque occurs in the core at the sawtooth crash, in addition to the expected fast outward transport of momentum [63].…”

A generalized Grad-Shafranov equation with plasma flow under a conformal coordinate transformation

“…2. It is noted that up-down asymmetry may drive fast intrinsic rotation in tokamaks [6]. The bounding flux surface, shown in blue corresponds to ψ b = −1.49 while on the magnetic axis, also shown in blue, we have ψ a = −2.15.…”

Impact of shaping on microstability in high-performance tokamak plasmas

“…One of the performance-limiting factors on tokamak experiments is the significant turbulence-dominated radial transport of heat, momentum and particles from the core plasma out to the edge. One method of affecting this turbulent transport is to change the shape of the axisymmetric fluxsurfaces traced out by the confining magnetic field; this has been validated both experimentally and in numerical simulations [1][2][3][4][5][6][7][8]. Flux-surface shape is often characterised by the elongation κ and triangularity δ, where κ(r) ≡ Z(r, θ max )/r and δ(r) ≡ [R 0 (r) − R(r, θ max )]/r, where R(r, θ) is the plasma major radius, θ is the poloidal angle, Z(r, θ) is the vertical distance above the midplane, r ≡ [R(r, 0) − R(r, π)]/2 is the plasma half-diameter at the flux-surface midplane, R 0 (r) ≡ [R(r, 0) + R(r, π)]/2 is the major radius of the flux-surface center and θ max is the poloidal angle of the maximum Z.…”

“…The impact of shaping on transport due to microinstabilities has been less-thoroughly studied, and those studies that have been performed have focussed only on a relatively small region of the vast multi-dimensional shaping parameter space. Despite this, increased elongation is generally thought to be stabilizing [1][2][3][4], whereas triangularity can have varying effects. Both the TCV and DIII-D experiments have reported that negative triangularity yields improved performance, allowing performance comparable to H-mode whilst maintaining L-mode edge profiles [5][6][7].…”