Dynamics of intrinsic axial flows in unsheared, uniform magnetic fields

Abstract

A simple model for the generation and amplification of intrinsic axial flow in a linear device, controlled shear decorrelation experiment, is proposed. This model proposes and builds upon a novel dynamical symmetry breaking mechanism, using a simple theory of drift wave turbulence in the presence of axial flow shear. This mechanism does not require complex magnetic field structure, such as shear, and thus is also applicable to intrinsic rotation generation in tokamaks at weak or zero magnetic shear, as well as to linear devices. This mechanism is essentially the self-amplification of the mean axial flow profile, i.e., a modulational instability. Hence, the flow development is a form of negative viscosity phenomenon. Unlike conventional mechanisms where the residual stress produces an intrinsic torque, in this dynamical symmetry breaking scheme, the residual stress induces a negative increment to the ambient turbulent viscosity. The axial flow shear is then amplified by this negative viscosity increment. The resulting mean axial flow profile is calculated and discussed by analogy with the problem of turbulent pipe flow. For tokamaks, the negative viscosity is not needed to generate intrinsic rotation. However, toroidal rotation profile gradient is enhanced by the negative increment in turbulent viscosity.

Tracing the Pathway from Drift-Wave Turbulence with Broken Symmetry to the Production of Sheared Axial Mean Flow

“…As demonstrated in Ref. [19], the spectral asymmetry results in gives ∇n crit = n 0 αω 2 * e / k θ k z ρ s c s × L z /c 2 s τ c ∼ 1.5 × 10 20 m −4 in agreement with experiment. Here, α = k 2 z v 2 te /ω * e ν ei ∼ 1 is the adiabaticity factor, the perpendicular turbulence scale length is k θ ρ s ∼ 1.5, the eddy correlation time is τ c ∼ 6 × 10 −5 s, and σ vT = k θ k z / k 2 θ ∼ 0.1.…”

“…The results presented here constitute the first experimental evidence that macroscopic radially sheared parallel flows develop from a finite residual stress which emerges from a dynamical symmetry breaking in the spectral correlator k z k θ of collisional drift wave turbulence. In this case, the symmetry breaking [19] is not due to magnetic geometry, but rather due to a phenomenon similar to modulational instability, in which a small seed axial shear is amplified by the turbulence. Note that modulational instability is also responsible for the production of zonal flows.…”

Generation of parasitic axial flow by drift wave turbulence with broken symmetry: Theory and experiment

“…To resolve this issue, a dynamical symmetry breaking mechanism has been proposed to explain the development of intrinsic axial flow in absence of magnetic shear. 23 This mechanism does not require a specific magnetic field configuration, and thus it is valid for both finite shear and zero shear regimes. This mechanism is effectively equivalent to the modulational growth of a seed axial flow shear, as in zonal flow generation.…”

“…At higher ∇n, P (ṽ r ,ṽ z ) is strongly elongated along the diagonal, suggesting large asymmetry in k z k θ . As proposed by the dynamical symmetry breaking model, 23 the mean axial flow shear modifies the drift wave growth rate, by introducing a frequency shift proportional to k z k θ V z . In our experiments, the seed axial flow shear is negative, V z < 0, because V z (r) is initially driven by the axial pressure drop and hence decreases from the core to the edge.…”

Laser induced fluorescence measurements of axial velocity, velocity shear, and parallel ion temperature profiles during the route to plasma turbulence in a linear magnetized plasma device

“…Intrinsic rotation, 12,13 driven by the residual turbulent stresses, is also of prime interest and linear plasma devices provide an ideal test bed to study intrinsic flows in a magnetic shear free regime. 14 Previous studies 15 in the Controlled Shear Decorrelation eXperiment (CSDX) have demonstrated that with increasing magnetic field (B), density gradient driven drift wave fluctuations evolve from narrow-band coherent azimuthal modes to a state of weak turbulence characterized by broadened frequency and wave number spectra. Nonlinear energy transfer analyses 16 have shown that for B ∼ 1000 G, energy is transferred from the higher frequency ( f ∼ 10 kHz, m = 3 mode) turbulent fluctuations to a low frequency ( f < 1 kHz, 17 on an upgraded CSDX (higher B, larger antenna with m = 1 helical source) have shown that a global transition occurs at a threshold magnetic field B th (which depends on the source parameters).…”