Toroidal Flow Shear Research Articles

Flow damping due to stochastization of the magnetic field.

The driving and damping mechanism of plasma flow is an important issue because flow shear has a significant impact on turbulence in a plasma, which determines the transport in the magnetized plasma. Here we report clear evidence of the flow damping due to stochastization of the magnetic field. Abrupt damping of the toroidal flow associated with a transition from a nested magnetic flux surface to a stochastic magnetic field is observed when the magnetic shear at the rational surface decreases to 0.5 in the large helical device. This flow damping and resulting profile flattening are much stronger than expected from the Rechester–Rosenbluth model. The toroidal flow shear shows a linear decay, while the ion temperature gradient shows an exponential decay. This observation suggests that the flow damping is due to the change in the non-diffusive term of momentum transport.

Fast growing resistive two fluid instabilities in hybrid-like tokamak configuration

An analytic derivation of the dispersion relation for resistive instabilities in a low-shear tokamak configuration is presented. The resistive infernal mode model (Charlton et al 1989 Phys. Fluids B 1 798) is generalized to include plasma diamagnetism, subsonic equilibrium toroidal flow shear and viscosity. An estimate of the transition point between the fast S−3/13 infernal-like (S is the Lundquist number) and the slow S−3/5 tearing-like scaling is given. A novel S−3/8 scaling is found close to the ideal ion-diamagnetic magnetohydrodynamic stability boundary. New moderately fast scalings in S are also found when sheared toroidal E × B flow and viscosity are considered. An analytic treatment of the m = n = 1 quasi-interchange mode in presence of density gradients with flat temperature profiles has been made.

Ion temperature profile stiffness: non-linear gyrokinetic simulations and comparison with experiment

Recent experimental observations at JET show evidence of reduced ion temperature profile stiffness. An extensive set of nonlinear gyrokinetic simulations are performed based on the experimental discharges, investigating the physical mechanism behind the observations. The impact on the ion heat flux of various parameters that differ within the data-set are explored. These parameters include the safety factor, magnetic shear, toroidal flow shear, effect of rotation on the magnetohydrodynamic equilibrium, R/Ln, βe, Zeff, Te/Ti, and the fast-particle content. While previously hypothesized to be an important factor in the stiffness reduction, the combined effect of toroidal flow shear and low magnetic shear is not predicted by the simulations to lead to a significant reduction in ion heat flux, due both to an insufficient magnitude of flow shear and significant parallel velocity gradient destabilization. It is however found that nonlinear electromagnetic effects due to both thermal and fast-particle pressure gradients, even at low βe, can significantly reduce the ion heat flux, and is a key factor in explaining the experimental observations. A total of four discharges are examined, at both inner and outer radii. For all cases studied, the simulated and experimental ion heat flux values agree within reasonable variations of input parameters around the experimental uncertainties.

3-D effects on viscosity and generation of toroidal and poloidal flows in LHD

Three-dimensional effects on plasma flows have been experimentally studied in the large helical device with 3D configurations. Spontaneous toroidal flow without net driving force using the combination of perpendicular neutral beam injection (NBI) heating and balanced tangential NBI heating has been investigated with two magnetic configurations. Co- and counter-directed spontaneous flows have been observed depending on the collisionality. Toroidal flow shear changes the sign at 0.4<reff<0.6 between co- and counter-flowing plasmas, where reff is a averaged minor radius. The detailed flow structures have been also examined at the edge region with stochastic magnetic field. A poloidal flow driven by the positive radial electric field has been observed at the open field region just outside of the plasma boundary. At the stochastic region, a shear of poloidal flow has been observed, while no shear of toroidal flow has been observed. The toroidal flow shear changes only in the nested magnetic flux surface region. A difference of density fluctuation property has been observed between co- and counter-flowing plasmas, where toroidal flow shears are formed.

Tearing mode stability in a toroidally flowing plasma

The effect of a sheared toroidal equilibrium flow on the tearing mode stability index, Δ′, is studied. A flow modified external kink equation for a single helicity mode is derived in a toroidal geometry. The corrections to Δ′ arising from flow contributions are estimated on the basis of a boundary layer calculation. Toroidal shear flow is seen to have a destabilizing influence on the tearing mode in a manner similar to pure axial flows in a cylindrical geometry. However, the increase in Δ′ as a function of increasing flow is seen to be smaller than the cylindrical case due to beneficial magnetic curvature effects. Shear flow associated stabilization, as observed in many recent experiments, might be arising from other physical effects such as toroidal mode couplings which are neglected in the present model.

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.

Toroidal velocity shear Kelvin–Helmholtz instabilities in strongly rotating tokamak plasmas

Strong sheared toroidal flows are predicted to drive parallel velocity shear Kelvin–Helmholtz oscillations unstable in spherical tokamak plasmas. Numerical simulations that include rotation in the equilibrium suggest that future spherical tokamaks will have an upper limit in uni-directional injected neutral beam heating in order to keep the sheared toroidal rotation below the critical level for the onset of the global parallel velocity shear Kelvin–Helmholtz instability.

Transport bifurcation induced by sheared toroidal flow in tokamak plasmas

First-principles numerical simulations are used to describe a transport bifurcation in a differentially rotating tokamak plasma. Such a bifurcation is more probable in a region of zero magnetic shear than one of finite magnetic shear, because in the former case the component of the sheared toroidal flow that is perpendicular to the magnetic field has the strongest suppressing effect on the turbulence. In the zero-magnetic-shear regime, there are no growing linear eigenmodes at any finite value of flow shear. However, subcritical turbulence can be sustained, owing to the existence of modes, driven by the ion temperature gradient and the parallel velocity gradient, which grow transiently. Nonetheless, in a parameter space containing a wide range of temperature gradients and velocity shears, there is a sizeable window where all turbulence is suppressed. Combined with the relatively low transport of momentum by collisional (neoclassical) mechanisms, this produces the conditions for a bifurcation from low to high temperature and velocity gradients. A parametric model is constructed which accurately describes the combined effect of the temperature gradient and the flow gradient over a wide range of their values. Using this parametric model, it is shown that in the reduced-transport state, heat is transported almost neoclassically, while momentum transport is dominated by subcritical parallel-velocity-gradient-driven turbulence. It is further shown that for any given input of torque, there is an optimum input of heat which maximises the temperature gradient. The parametric model describes both the behaviour of the subcritical turbulence (which cannot be modelled by the quasi-linear methods used in current transport codes) and the complicated effect of the flow shear on the transport stiffness. It may prove useful for transport modelling of tokamaks with sheared flows.

Rotation Properties of Tokamak Plasmas

Understanding the physics that controls rotation properties of tokamaks is a crucial issue for successful ITER operation. Toroidal plasma flow and flow shear directly impact the control of turbulent transport, edge plasma physics, MHD stability, and the interaction of the MHD modes with external magnetic structures (resistive walls and resonant magnetic perturbations). Additionally, a large variety of phenomena are known to affect the properties of toroidal flows. These include 3-D magnetic fields (both resonant and nonresonant contributions), momentum sources, turbulent fluctuations, and magnetic field transients.

Resolving electron scale turbulence in spherical tokamaks with flow shear

This paper presents nonlinear gyrokinetic simulations of electron temperature gradient (ETG) turbulence based on spherical tokamak (ST) parameters. Most significantly the simulations include the strong toroidal flow and flow shear present in STs that suppress ion-scale turbulence while using kinetic ions at full mass ratio (mi/me=3600). The flow shear provides a physical long-wavelength cutoff mechanism that aids saturation of the simulations, which has previously been demonstrated to be problematic depending on magnetic shear. As magnetic shear varies widely in STs we systematically demonstrate saturation and convergence of the ETG simulations with respect to grid resolution, physical domain size, and boundary conditions. While using reduced ion mass or adiabatic ions can lessen computational expense they do not always provide reliable results. The resulting spectra from converged simulations are anisotropic everywhere in contrast to previous ETG simulations without flow shear. These results have implications for interpreting turbulence measurements, and represent an important step in determining when and where ETG turbulence is expected to be relevant in ST plasmas. They are also important in the context of validating simulations with both experimental transport analysis and turbulence measurements.

Gyrokinetic simulations of spherical tokamaks

This paper reviews transport and confinement in spherical tokamaks (STs) and our current physics understanding of this that is partly based on gyrokinetic simulations. Equilibrium flow shear plays an important role, and we show how this is consistently included in the gyrokinetic framework for flows that greatly exceed the diamagnetic velocity. The key geometry factors that influence the effectiveness of turbulence suppression by flow shear are discussed, and we show that toroidal equilibrium flow shear can sometimes entirely suppress ion scale turbulence in today's STs. Advanced nonlinear simulations of electron temperature gradient (ETG) driven turbulence, including kinetic ion physics, collisions and equilibrium flow shear, support the model that ETG turbulence can explain electron heat transport in many ST discharges.

Multi-scale transport simulation of toroidal momentum source profile effect on internal transport barrier collapse

The mechanism of internal transport barrier (ITB) collapse in the reversed magnetic shear configuration is investigated using a global ion temperature gradient (ITG) driven drift wave turbulence code. A heating source and a toroidal momentum source are introduced to follow the self-consistent evolution of the ion temperature and flow profiles. A scenario of transport barrier collapse driven by a meso-scale mode excited in the barrier region is suggested. The importance of the quasi-linear effect due to profile modification as well as three-wave coupling is clearly shown by means of energy transfer analysis. The effect of the toroidal flow shear (TFS) profile on the dynamics of ITB evolution is investigated. It is found that the decorrelation between meso-scale modes and ITG driven modes due to the TFS can prevent global relaxation.

Sawtooth control and the interaction of energetic particles

Long-period sawteeth have been observed to result in the low-β triggering of neo-classical tearing modes (NTMs), which can significantly degrade plasma confinement. In ITER, the stabilizing effects of the fusion-born α particles are likely to exacerbate this. Consequently, in order to avoid triggering NTMs, many techniques have been proposed to control, and in particular, to destabilize the sawtooth oscillations. Here, sawtooth behaviour in off-axis NBI-heated plasmas in JET and ASDEX Upgrade is presented. It is found that the energetic particles born outside the q = 1 surface due to off-axis NBI can destabilize the sawteeth, even in the presence of stabilizing on-axis fast particles. In order to model the stability of the n = 1 internal kink mode, which is associated with the sawtooth oscillations, both a magnetohydrodynamic code including toroidal rotation and a drift kinetic code have been employed. The modelling highlights the significant role played by both the passing energetic particles and the toroidal flow shear in determining the kink mode stability in the presence of an energetic particle population.

Stability and dynamics of the edge pedestal in the low collisionality regime: physics mechanisms for steady-state ELM-free operation

Understanding the physics of the edge pedestal and edge localized modes (ELMs) is of great importance for ITER and the optimization of the tokamak concept. The peeling–ballooning model has quantitatively explained many observations, including ELM onset and pedestal constraints, in the standard H-mode regime. The ELITE code has been developed to efficiently evaluate peeling–ballooning stability for comparison with observation and predictions for future devices. We briefly review recent progress in the peeling–ballooning model, including experimental validation of ELM onset and pedestal height predictions, and nonlinear 3D simulations of ELM dynamics, which together lead to an emerging understanding of the physics of the onset and dynamics of ELMs in the standard intermediate to high collisionality regime. We also discuss new studies of the apparent power dependence of the pedestal, and studies of the impact of sheared toroidal flow. Recently, highly promising low collisionality regimes without ELMs have been discovered, including the quiescent H-mode (QH) and resonant magnetic perturbation (RMP) regimes. We present recent observations from the DIII-D tokamak of the density, shape and rotation dependence of QH discharges, and studies of the peeling–ballooning stability in this regime. We propose a model of the QH-mode in which the observed edge harmonic oscillation (EHO) is a saturated kink/peeling mode which is destabilized by current and rotation, and drives significant transport, allowing a near steady-state edge plasma. The model quantitatively predicts the observed density dependence and qualitatively predicts observed mode structure, rotation dependence and outer gap dependence. Low density RMP discharges are found to operate in a similar regime, but with the EHO replaced by an applied magnetic perturbation.

Effect of sheared equilibrium plasma rotation on the classical tearing mode in a cylindrical geometry

The effect of sheared equilibrium plasma rotation on the stability of tearing modes in an Ohmic (low plasma β) regime is investigated. It is found, by means of numerical MHD simulations in a cylindrical geometry, that plasma rotation in the equivalent toroidal direction can result either in the increase or in the decrease of the instability growth rate. Perpendicular plasma viscosity and plasma rotation shear at the modes’ rational surface play a key role on assessing the effect of shear flow. While destabilizing for low viscosity plasmas (ratio of the resistive to viscous diffusion time scales τR∕τV≪1), for viscous plasmas (τR∕τV>1) shear flow reduces the growth rate. Above a given threshold in the rotation shear (that depends on the ratio τR∕τV) a tearing mode, unstable in the absence of rotation, can be stabilized. The effect of sheared toroidal flow on mode stability, in both viscosity regimes that are considered in the paper, is qualitatively independent of the aspect ratio.

Computing nonlinear magnetohydrodynamic edge localized instabilities in fusion plasmas

The onset and nonlinear evolution of Edge Localized Modes (ELMs) in toroidally confined plasmas are known to shed thermal energy from the edge of the confinement region, and may also affect the core plasma through nonlinear mode coupling. The physics of this process is not well understood, although the concomitant large bursts of thermal energy transport are a major concern for future burning plasma experiments. The evolution of ELMs is inherently nonlinear and analytic approaches are limited by the complexity of the problem. Save a handful of recent important theoretical works, the nonlinear consequences of ELMs are mainly unexplored. Recent developments in the NIMROD code [http://nimrodteam.org] have enabled the computational study of ELMs in tokamaks in the extended magnetohydrodynamic (MHD) framework, and a new initiative was formed to understand the basic physics of their nonlinear evolution. The results of these investigations are presented for both model equilibria and accurate reconstructions from the DIII-D experiment at General Atomics [http://fusion.gat.com/diii-d/]. These results show a filamentary high temperature structure propagating radially outward, which is strongly damped by experimentally relevant toroidal flow shear. Two fluid and gyroviscous terms are included linearly as a preliminary indication of these important physical effects, and stabilization of higher wave number modes is observed.

Modeling the effect of toroidal plasma rotation on drift-magnetohydrodynamic modes in tokamaks

A new code, MISHKA-F (Flow), has been developed as an extension of the ideal magneto-hydrodynamic (MHD) code MISHKA-1 [Mikhailovskii et al., Plasma Phys. Rep. 23, 844 (1997)] in order to investigate the linear MHD stability of ideal and resistive eigenmodes with respect to the effects of toroidal rotation in tokamaks in general toroidal geometry with the ion diamagnetic drift effect taken into account. Benchmark test results of the MISHKA-F code show good agreement with analytic theory [A. B. Mikhailovskii and S. E. Sharapov, Plasma Phys. Controlled Fusion 42, 57 (2000)] for the stability limits of the ideal n∕m=1∕1 internal kink mode. The combined stabilizing effects of the ion diamagnetic drift frequency, ω*i, and the toroidal flow shear are also studied. The ω*i stabilization of the internal kink mode is found to be more effective at finite flow shear. Finite-n ballooning modes are studied in plasmas with the toroidal flow shear effect included. The stabilization of the ballooning modes by toroidal rotation is found to agree well with earlier predictions [Webster et al., Phys. Plasmas 11, 2135 (2004)]. The effect of high flow shear is analyzed for a sawtoothing discharge typical in the Mega Ampère Spherical Tokamak (MAST) [Sykes et al., Nucl. Fusion 41, 1423 (2001)]. It is found that the ideal n=1 internal kink mode can be stabilized by toroidal rotation at values observed experimentally.

Creation of localized sheared flow by ion trapping

Radially localized sheared toroidal flow may be driven in a toroidal plasma by using ion cyclotron heating to assymmetrically trap ions.

Experimental Observation of the Toroidal Flow Shear in the Edge of the SUNIST

In the edge plasma of the SUNIST spherical tokamak, the toroidal flow velocity vφ, the poloidal shear layer and the fluctuation-driven particle transport fluxes Γr have been simultaneously measured with Mach probe and Langmuir probe arrays, respectively. The results indicate that the vφ has a radial gradient dvφ/dr. The change of the dvφ/dr positively correlates with both the poloidal shear and the suppression of the Γr. Such coincidence suggests that the toroidal sheared flow may play an important role in the suppression of the edge fluctuation-driven transport in STs.

Geometrical improvements of rotational stabilization of high-n ballooning modes in tokamaks

We have found numerically that damping phases appear in the time evolution of the perturbation energy of high-n ballooning modes in the presence of toroidal flow shear, where n is a toroidal mode number. The damping dominates exponential growth which occurs in the bad curvature region, resulting in stabilization of ballooning modes. D-shaping of plasma cross-section, reduction of aspect ratio, and arrangement of an X-point at inner side of the torus enhance the stabilization effect of the toroidal flow shear through this mechanism.