Perpendicular Flow Shear Research Articles

On electromagnetic turbulence and transport in STEP

In this work, we present first-of-their-kind nonlinear local gyrokinetic (GK) simulations of electromagnetic turbulence at mid-radius in the burning plasma phase of the conceptual high-β, reactor-scale, tight-aspect-ratio tokamak Spherical Tokamak for Energy Production (STEP). A prior linear analysis in Kennedy et al (2023 Nucl. Fusion 63 126061) reveals the presence of unstable hybrid kinetic ballooning modes (KBMs), where inclusion of the compressional magnetic field fluctuation, δB∥ , is crucial, and subdominant microtearing modes (MTMs) are found at binormal scales approaching the ion-Larmor radius. Local nonlinear GK simulations on the selected surface in the central core region suggest that hybrid KBMs can drive large turbulent transport, and that there is negligible turbulent transport from subdominant MTMs when hybrid KBMs are artificially suppressed (through the omission of δB∥ ). Nonlinear simulations that include perpendicular equilibrium flow shear can saturate at lower fluxes that are more consistent with the available sources in STEP. This analysis suggests that hybrid KBMs could play an important role in setting the turbulent transport in STEP, and possible mechanisms to mitigate turbulent transport are discussed. Increasing the safety factor or the pressure gradient strongly reduces turbulent transport from hybrid KBMs in the cases considered here. Challenges of simulating electromagnetic turbulence in this high-β regime are highlighted. In particular the observation of radially extended turbulent structures in the absence of equilibrium flow shear motivates future advanced global GK simulations that include δB∥ .

Effects of the parallel flow shear on the ITG-driven turbulent transport in tokamak plasmas

The impact of the parallel flow shear on the tokamak plasma stability and turbulent transport driven by the ion temperature gradient (ITG) modes is analyzed by means of local gyrokinetic numerical analyses. It is shown that the parallel flow shear increases the ITG growth rate in the linear regime, and induces a broadening and shift of the radial spectrum. Then, the different effects of the finite parallel shear on the ITG turbulence characteristics are deeply analyzed in the nonlinear regime. These studies highlight that a reduction of the thermal-ion turbulent heat flux is induced by a complex mechanism involving the nonlinear generation of an enhanced zonal flow activity. Indeed, the turbulent sources of the zonal flows are increased by the introduction of the finite parallel flow shear in the system, beneficially acting on the saturation level of the ITG turbulence. The study has been carried out for the Waltz standard case below the critical threshold of the destabilization of the parallel velocity gradient instability, and then generalized to a selected pulse of a recent JET scenario with substantial toroidal rotation in the edge plasma region. It is, thus, suggested that the investigated complex mechanism triggered by the finite parallel flow shear reducing the ITG turbulent heat fluxes could be complementary to the well-established perpendicular flow shear in a region with sufficiently large plasma toroidal rotation.

Interplay between toroidal rotation and flow shear in turbulence stabilisation

The interplay between toroidal rotation u, parallel flow shear u′, and perpendicular flow shear γE in the stabilisation of tokamak turbulence is investigated in non-linear flux-tube gyrokinetic simulations. The simulations are performed for a reference L-mode DIII-D plasma (the so-called shortfall case) at r/a=0.8, varying the flow parameters around their nominal values. Depending on the respective signs of u, u′, and γE, turbulence is found to be enhanced, reduced, or unchanged. When the coupling is favorable, the overall effect on the non-linear heat fluxes can be very large, even at moderate flow values. The ion heat flux is, for instance, decreased by a factor of 3 when the direction of the parallel flow shear is reversed with respect to its nominal value. Even more surprising, keeping u′ and γE at their nominal values, the ion heat flux decreases by more than 50% when the toroidal flow is reversed. The relevance of this mechanism in the experiments which depends on the ability to decouple u, u′, and γE is discussed. The interplay between u and u′ observed in the non-linear simulations qualitatively follows the linear stability results and is interpreted in the frame of a simple fluid model.

The temporal evolution of the kinetic drift-Alfven instability of plasma shear flow

The linear non-modal kinetic theory of the kinetic drift-Alfven instability, in the presence of shearing plasma flow, exhibits temporal non-modal amplitude growth with time-increasing growth rate. The drift-Alfven instability develops when the evolving frequencies of the density-gradient-driven drift wave and the kinetic Alfven wave become comparable and mode coupling increases significantly. Because the development of the instability depends on the plasma density gradient, drift-Alfven turbulence may be invoked as a possible turbulence driver in the edge pedestal, limiting the pedestal density gradients during the edge localized modes crash. In contrast to the case of shear-modified electrostatic drift-wave turbulence, the scattering of plasma ions by the shear-modified electromagnetic drift-Alven turbulence does not only suppress the turbulence, but can be responsible for transient increase in the instability's growth rate. The instability, i.e., turbulence, stabilizes when the drift and Alfven wave frequencies eventually become different enough that effective coupling between the two modes ends. So, perpendicular-flow shear can cause the growth rate to increase, decrease, become zero, and become negative as a result of shear's time-changing modification to the frequencies of the drift and Alfven waves.

Electromagnetic effects in the stabilization of turbulence by sheared flow

We have extended our study of the competition between the drive and stabilization of plasma microinstabilities by sheared flow to include electromagnetic effects at low plasma β (the ratio of plasma to magnetic pressure). The extended system of characteristic equations is formulated, for a dissipative fluid model developed from the gyrokinetic equation, using a twisting mode representation in sheared slab geometry and focusing on the ion temperature gradient mode. Perpendicular flow shear convects perturbations along the field at the speed we denote as Mcs (where cs is the sound speed). is required to make the system characteristics unidirectional and inhibit eigenmode formation, leaving only transitory perturbations in the system. This typically represents a much larger flow shear than in the electrostatic case, which only needs M > 1. Numerical investigation of the region shows the driving terms can conflict, as in the electrostatic case, giving low growth rates over a range of parameters. Also, at modest drive strengths and low β values typical of experiments, including electromagnetic effects does not significantly alter the growth rates. For stronger flow shear and higher β, geometry characteristic of the spherical tokamak mitigates the effect of an instability of the shear Alfvén wave, driven by the parallel flow shear.

Validation of gyrokinetic modelling of light impurity transport including rotation in ASDEX Upgrade

Upgraded spectroscopic hardware and an improved impurity concentration calculation allow accurate determination of boron density in the ASDEX Upgrade tokamak. A database of boron measurements is compared to quasilinear and nonlinear gyrokinetic simulations including Coriolis and centrifugal rotational effects over a range of H-mode plasma regimes. The peaking of the measured boron profiles shows a strong anti-correlation with the plasma rotation gradient, via a relationship explained and reproduced by the theory. It is demonstrated that the rotodiffusive impurity flux driven by the rotation gradient is required for the modelling to reproduce the hollow boron profiles at higher rotation gradients. The nonlinear simulations validate the quasilinear approach, and, with the addition of perpendicular flow shear, demonstrate that each symmetry breaking mechanism that causes momentum transport also couples to rotodiffusion. At lower rotation gradients, the parallel compressive convection is required to match the most peaked boron profiles. The sensitivities of both datasets to possible errors is investigated, and quantitative agreement is found within the estimated uncertainties. The approach used can be considered a template for mitigating uncertainty in quantitative comparisons between simulation and experiment.

Zero-Turbulence Manifold in a Toroidal Plasma

Sheared toroidal flows can cause bifurcations to zero-turbulent-transport states in tokamak plasmas. The maximum temperature gradients that can be reached are limited by subcritical turbulence driven by the parallel velocity gradient. Here it is shown that q/ϵ (magnetic field pitch/inverse aspect ratio) is a critical control parameter for sheared tokamak turbulence. By reducing q/ϵ, far higher temperature gradients can be achieved without triggering turbulence, in some instances comparable to those found experimentally in transport barriers. The zero-turbulence manifold is mapped out, in the zero-magnetic-shear limit, over the parameter space (γ(E), q/ϵ, R/L(T)), where γ(E) is the perpendicular flow shear and R/L(T) is the normalized inverse temperature gradient scale. The extent to which it can be constructed from linear theory is discussed.

Understanding the effect of sheared flow on microinstabilities

The competition between the drive and stabilization of plasma microinstabilities by sheared flow is investigated, focusing on the ion temperature gradient mode. Using a twisting mode representation in sheared slab geometry, the characteristic equations have been formulated for a dissipative fluid model, developed rigorously from the gyrokinetic equation. They clearly show that perpendicular flow shear convects perturbations along the field at a speed we denote by Mcs (where cs is the sound speed), whilst parallel flow shear enters as an instability driving term analogous to the usual temperature and density gradient effects. For sufficiently strong perpendicular flow shear, M > 1, the propagation of the system characteristics is unidirectional and no unstable eigenmodes may form. Perturbations are swept along the field, to be ultimately dissipated as they are sheared ever more strongly. Numerical studies of the equations also reveal the existence of stable regions when M < 1, where the driving terms conflict. However, in both cases transitory perturbations exist, which could attain substantial amplitudes before decaying. Indeed, for M ≫ 1, they are shown to exponentiate times. This may provide a subcritical route to turbulence in tokamaks.

Simultaneous, co-located parallel-flow shear and perpendicular-flow shear in low-temperature, ionospheric-plasma relevant laboratory plasma

Shear in plasma flow can lead to either suppression or enhancement of plasma fluctuations, as illustrated by a variety of laboratory experiments. The plasma equilibrium conditions associated with flow shear are discussed in terms of test-particle simulations and experimental observations. The demonstration of producing and controlling simultaneous, co-located shears in both parallel flow and perpendicular flow are reported. Ion-cyclotron and lower-hybrid waves associated with this two-dimensional flow-shear configuration are observed. It is concluded that laser-induced fluorescence measurements of ion-velocity profiles both make it possible to document shear flow and aid significantly the interpretation of kinetic effects that influence the mechanisms invoked to explain flow-shear-driven plasma fluctuations.

Flow Shear Effects on Plasma Microinstability in Open-Ended Magnetic Configurations

The external and independent control of parallel and perpendicular flow shears in collisionless magnetized plasmas is realized using segmented plasma sources. Then, ion flow velocity shears parallel to the magnetic-field lines are observed to destabilize not only the drift-wave but also the ion-cyclotron instabilities depending on the sign of the parallel shear in the absence of field-aligned electron drift flow in laboratory experiments. On the other hand, perpendicular ion flow velocity shears are demonstrated to suppress both the drift-wave and the ion-cyclotron instabilities, and furthermore, the suppressions are found to take place independently of the sign of the perpendicular shear.

Sheared Flow Excitation and Suppression of Electrostatic Instabilities in Laboratory Collisionless Magnetoplasmas

The ion-cyclotron instabilities in a collisionless magnetoplasma are observed to be stabilized by a perpendicular plasma flow shear independently of the sign of the shear. This suppression of the ion-cyclotron instabilities is caused only when the perpendicular flow shear exists outside the disk electrode which excites the instabilities by applying a positive bias voltage to it. This phenomenon can be explained by the excitation mechanism of ion-cyclotron instabilities such as potential driven model.

Effects of Controlled Flow-Shear on Low-Frequency Instabilities in Magnetized Plasmas

The external and independent control of parallel and perpendicular flow shears in collisionless magnetized plasmas are realized using two newly-developed plasma sources. The ion flow velocity shears parallel to the magnetic-field lines are then observed to destabilize not only the D’Angelo mode but also the drift-wave instability depending on the sign of the parallel shear in the absence of field-aligned electron drift flow in laboratory experiments. On the other hand, perpendicular ion flow velocity shears are demonstrated to suppress the drift-wave and the ion-cyclotron instabilities, and furthermore, these suppressions are found to take place independently of the sign of the perpendicular shear.

Effects of Controlled Flow Velocity Shear in Open-Ended Magnetized Plasmas

The effects of ion flow velocity shears parallel and perpendicular to the magnetic-field lines, which are precisely controlled by a segmented electrode, are investigated in open-ended magnetized plasmas. The perpendicular flow velocity shears are demonstrated to suppress drift-wave, flute, and ion-cyclotron instabilities. On the other hand, parallel flow velocity shears are observed to destabilize D’Angelo mode, drift-wave, and ion-cyclotron instabilities depending on the sign of the parallel shear. The combined effects of the parallel and perpendicular flow shears will be important for controlling instabilities in magnetized plasmas.

Plasma Flow-Shear Driven Instabilities and Efficient Cyclotron-Wave Absorption in Open Magnetic-Field Configurations

The two plasma sources using a concentrically three-segmented plasma emitter are developed, with which the parallel and perpendicular flow shears can be controlled, respectively. Here the drift-like and Kelvin-Helmholtz instabilities are observed to be excited and suppressed depending on the parallel and perpendicular flow shears, respectively. On the other hand, propagation and absorption of right-hand (R) and left-hand (L) circularly polarized waves, which are related to plasma heating, are investigated under magnetic-mirror configurations. Not only R wave but also L wave is absorbed in the electron cyclotron resonance (ECR) region in the same way, which is considered to be caused by the polarization reversal from the L wave to the R wave. It is actually observed that the L wave is converted into the R wave near the ECR point depending on the electron temperature.

Anomalous momentum transport from drift wave turbulence

A sheared slab magnetic field model B=B0[ẑ+(x/Ls)ŷ], with inhomogeneous flows in the ŷ and ẑ directions, is used to perform a fully kinetic stability analysis of the ion temperature gradient (ITG) and dissipative trapped electron (DTE) modes. The concomitant quasilinear stress components that couple to the local perpendicular (y component) and parallel (z component) momentum transport are also calculated and the anomalous perpendicular and parallel viscous stresses obtained. A breakdown of the ITG-induced viscous stresses are generally observed at moderate values of the sheared perpendicular flow. Even in the absence of external momentum sources, ion diamagnetic effects can generate an inhomogeneous radial electric field which gives rise to a sheared perpendicular flow which can sustain a sheared parallel flow. The effect of the perpendicular stress component in the momentum balance equations is generally small while the parallel stress component, which is primarily determined by the perpendicular flow shear, can dominate the usual neoclassical viscous stress terms. The large anomalous effect suggests that the neoclassical explanation of poloidal flows in tokamaks may be incorrect. The present results are in general agreement with existing experimental observations on momentum transport in tokamaks.

Kinetic quasitoroidal ion temperature gradient instability in the presence of sheared flows

The gyrokinetic integral equations for the study of the ion temperature gradient driven mode (ηi mode) in toroidal geometry, at low plasma pressure, are extended to include equilibrium ion parallel v0∥(r) and perpendicular vE(r) sheared flows, where r is the minor radius of the flux surface. Magnetic gradient and curvature drifts of the ions, as well as finite ion Larmor radius effects, are included. The parallel sheared flow is shown to be destabilizing. The perpendicular sheared flow is a stabilizing mechanism. Mixing length estimates show that the ηi-mode induced ion thermal transport increases with increasing parallel flow shear, and decreases with perpendicular flow shear. The decrease of the ion transport is due not only to the decrease of the mode growth rate, but also to the shrinking of the mode width. Using the mixing length formulas for the thermal transport associated with the unstable modes, it is shown that the results are consistent with the experimental observations concerning the improvement of confinement in H-mode discharges coincident with the increase of cross-field sheared flows.