Transport Barriers In Tokamaks Research Articles

Shaping the edge radial electric field to create shearless transport barriers in tokamaks

Shaping the edge radial electric field to create shearless transport barriers in tokamaks

Shearless bifurcations in particle transport for reversed-shear tokamaks

Some internal transport barriers in tokamaks have been related to the vicinity of extrema of the plasma equilibrium profiles. This effect is numerically investigated by considering the guiding-centre trajectories of plasma particles undergoing $\boldsymbol {E}\times \boldsymbol {B}$ drift motion, considering that the electric field has a stationary non-monotonic radial profile and an electrostatic fluctuation. In addition, the equilibrium configuration has a non-monotonic safety factor profile. The numerical integration of the equations of motion yields a symplectic map with shearless barriers. By changing the safety factor profile parameters, the appearance and breakup of these shearless curves are observed. The shearless curve's successive breakup and recovery are explained using concepts from bifurcation theory. We also present bifurcation sequences associated with the creation of multiple shearless curves. Physical consequences of scenarios with multiple shearless curves are discussed.

Ultra long turbulent eddies, magnetic topology, and the triggering of internal transport barriers in tokamaks

Local nonlinear gyrokinetic simulations of tokamak plasmas demonstrate that turbulent eddies can extend along magnetic field lines for hundreds of poloidal turns when the magnetic shear is very small. By accurately modeling different field line topologies (e.g. low-order rational, almost rational, or irrational value of the safety factor), we show that the self-interaction of such ‘ultra long’ eddies can dramatically reduce heat transport. This extreme sensitivity of turbulent transport to the safety factor reveals novel strategies to improve confinement, constitutes experimentally testable predictions, and illuminates past observations of internal transport barriers.

Onset of internal transport barriers in tokamaks

Barriers have been identified in magnetically confined plasmas reducing the particle transport and improving the confinement. One of them, the primary shearless barriers are associated to extrema of non-monotonic plasma profiles. Previously, we identified these barriers in a model described by a map that allows the integration of charged particles motion in drift waves for a long time scale. In this work, we show how the existence of these robust barriers depends on the fluctuation amplitude and on the electric shear. Moreover, we also find control parameter intervals for which these primary barriers onset and break-up are recurrent. Another noticeable feature, in these transitions, is the appearance of a layer of particle trajectory stickiness after the shearless barrier break-up or before its onset. Besides the mentioned primary barriers, we also observe sequences of secondary shearless barriers, not reported before, created and destroyed by a sequence of bifurcations as the main control parameters, the fluctuation amplitude and electric shear, are varied. Furthermore, in these bifurcations, we also find hitherto unknown double and triple secondary shearless barriers which constitute a noticeable obstacle to the chaotic transport.

Influence of the radial electric field on the shearless transport barriers in tokamaks

In tokamaks, internal transport barriers, produced by modifications of the plasma current profile, reduce particle transport and improve plasma confinement. The triggering of the internal transport barriers and their dependence on the plasma profiles is a key nonlinear dynamics problem which is still under investigation. We consider the onset of shearless invariant curves inside the plasma which create internal transport barriers. A non-integrable drift-kinetic model is used to describe the particle transport driven by drift waves and to investigate the shearless barrier onset in tokamaks. We show that for some currently observed plasma profiles, shearless particle transport barriers can be triggered by properly modifying the electric field profile and the influence of non-resonant modes in the barrier onset. In particular, we show that a broken barrier can be restored by enhancing non-resonant modes.

Characterization of particle confinement properties in RFX-mod at a high plasma current

Transport phenomena affect the performance of fusion devices, reducing heat and particle confinement and consequently leading to a lower fusion triple product and higher fluxes on the plasma facing material. Special attention is devoted in the fusion community to the study of transport mitigation phenomena which lead to the onset of transport barriers in tokamaks, stellarators and reverse field pinch plasmas. The aim of this study is to deepen our understanding of the mechanisms driving transport in the presence of electron internal transport barriers in the RFX-mod single helical axis (SHAx) state (Lorenzini et al 2009 Nature Phys. 5 570). We discuss whether transport in the core can be described within the theory of chaotic transport. Light is also shed on the mechanisms acting at the plasma edge. The particle source is calculated using the 2D Monte-Carlo code NENE, considering the pattern of plasma–wall interaction. In the core region of the SHAx we found that the diffusivity along 90% of the radius is reduced with respect to the standard case: D ∼ 1 m2 s−1 fits well with the density profile, compared with the ∼50 m2 s−1 of a standard plasma. This result confirms a strong mitigation of magnetic chaos, although comparison with the neoclassical diffusivity Dneo ∼ 0.01–0.4 m2 s−1 indicates that transport in the SHAx is still anomalous. The same picture describes well both the particle and energy transport in the plasma core: comparison with the effective thermal diffusivity χeff indicates that the ratio χeff/D ∼ (mi/me)0.5 is consistent with the theory of chaos-dominated transport.The plasma edge is affected by a different mechanism. In the external region (the final 10% of the radius) magnetic chaos is suppressed and the edge diffusivity is likely to be ruled by electrostatic turbulence, in particular a direct link with the presence of pressure coherent structures is found.

Ion transport barriers triggered by plasma polarization in gyrokinetic simulations

The creation of ion transport barriers by externally induced sheared E × B flows is investigated with the global, full-f and flux-driven gyrokinetic code GYSELA. A gyrokinetic source of vorticity is designed and proves to be efficient in polarizing the plasma. Induced sheared electric fields develop in the turbulent core and are accompanied by the creation of a transport barrier. The barrier and the sheared flow relax quasi-periodically because of zonal flow activity and a destabilizing temperature anisotropy induced by the vorticity source. A new cyclic mechanism leading to the relaxation of transport barriers in tokamaks is discovered.

Neoclassical theory inside transport barriers in tokamaks

Inside the transport barriers in tokamaks, ion energy losses sometimes are smaller than the value predicted by the standard neoclassical theory. This improvement can be understood in terms of the orbit squeezing theory in addition to the sonic poloidal E×B Mach number Up,m that pushes the tips of the trapped particles to the higher energy. In general, Up,m also includes the poloidal component of the parallel mass flow speed. These physics mechanisms are the corner stones for the transition theory of the low confinement mode (L-mode) to the high confinement mode (H-mode) in tokamaks. Here, detailed transport fluxes in the banana regime are presented using the parallel viscous forces calculated earlier. It is found, as expected, that effects of orbit squeezing and the sonic Up,m reduce the ion heat conductivity. The former reduces it by a factor of |S|3/2 and the later by a factor of R(Up,m2)exp(-Up,m2) with R(Up,m2), a rational function. Here, S is the orbit squeezing factor.

Symmetric and asymmetric equilibria with non-parallel flows

Several classes of analytic solutions to a generalized Grad-Shafranov equation with incompressible plasma flow non-parallel to the magnetic field are constructed. The solutions include higher transcendental functions such as the Meijer G-function and describe D-shaped and diverted configurations with either a single or double X-points. Their characteristics are examined in particular with respect to the flow parameters associated with the electric field. It turns out that the electric field makes the safety factor flatter and increases the magnitude and shear of the toroidal velocity in qualitative agreement with experimental evidence on the formation of internal transport barriers in tokamaks, thus indicating a potential stabilizing effect of the electric field.

Gyrokinetic equations for strong-gradient regions

A gyrokinetic theory is developed under a set of orderings applicable to the edge region of tokamaks and other magnetic confinement devices, as well as to internal transport barriers. The result is a practical set equations that is valid for large perturbation amplitudes [qδψ/T=O(1), where δψ=δφ-ν∥δA∥/c], which is straightforward to implement numerically, and which has straightforward expressions for its conservation properties. Here, δφ and δA∥ are the perturbed electrostatic and parallel magnetic potentials, ν∥ is the particle velocity, c is the speed of light, and T is the temperature. The derivation is based on the quantity ɛ≡(ρ/λ⊥)qδψ/T≪1 as the small expansion parameter, where ρ is the gyroradius and λ⊥ is the perpendicular wavelength. Physically, this ordering requires that the E×B velocity and the component of the parallel velocity perpendicular to the equilibrium magnetic field are small compared to the thermal velocity. For nonlinear fluctuations saturated at “mixing-length” levels (i.e., at a level such that driving gradients in profile quantities are locally flattened), ɛ is of the order ρ/Lp, where Lp is the equilibrium profile scale length, for all scales λ⊥ ranging from ρ to Lp. This is true even though qδψ/T=O(1) for λ⊥∼Lp. Significant additional simplifications result from ordering Lp/LB=O(ɛ), where LB is the spatial scale of variation of the magnetic field. We argue that these orderings are well satisfied in strong-gradient regions, such as edge and scrapeoff layer regions and internal transport barriers in tokamaks, and anticipate that our equations will be useful as a basis for simulation models for these regions.

Impurity dynamics in the presence of transport barriers in tokamaks

Impurity transport in tokamak core plasmas is investigated with a three-dimensional global fluid code. The diffusion coefficient and the pinch velocity of impurity transport in tokamaks are studied using the fluid model for ion temperature gradient and trapped electron mode driven turbulence in tokamak plasmas. It is shown that in the presence of an internal transport barrier created by a reversed magnetic shear configuration or external E×B shear flow, a reversal of impurity pinch velocity is obtained, which changes from inward direction to outward direction. This scenario is favorable for expelling impurities from the central region and decontaminating the core plasma. The pinch reversal is attributed to a change of sign of the curvature pinch velocity. This modification is mostly due to the reversal of magnetic shear for the hollow q profile. When a strong E×B shear flow is externally imposed, it is rather due to a change of the turbulence mean phase velocity.

Link between self-consistent pressure profiles and electron internal transport barriers in tokamaks

Tokamak plasmas have a tendency to self-organization: the plasma pressure profiles obtained in different operational regimes and even in various tokamaks may be represented by a single typical curve, called the self-consistent pressure profile. About a decade ago local zones with enhanced confinement were discovered in tokamak plasmas. These zones are referred to as internal transport barriers (ITBs) and they can act on the electron and/or ion fluid. Here the pressure gradients can largely exceed the gradients dictated by profile consistency. So the existence of ITBs seems to be in contradiction with the self-consistent pressure profiles (this is also often referred to as profile resilience or profile stiffness). In this paper we will discuss the interplay between profile consistency and ITBs. A summary of the cumulative information obtained from T-10, RTP and TEXTOR is given, and a coherent explanation of the main features of the observed phenomena is suggested. Both phenomena, the self-consistent profile and ITB, are connected with the density of rational magnetic surfaces, where the turbulent cells are situated. The distance between these cells determines the level of their interaction, and therefore the level of the turbulent transport. This process regulates the plasma pressure profile. If the distance is wide, the turbulent flux may be diminished and the ITB may be formed. In regions with rarefied surfaces the steeper pressure gradients are possible without instantaneously inducing pressure driven instabilities, which force the profiles back to their self-consistent shapes. Also it can be expected that the ITB region is wider for lower dq/dρ (more rarefied surfaces).

Effect of electrodynamic braking force localized on rational surfaces

The experimental observation of the association of the internal heat transport barriers in tokamaks with rational q surfaces is an open problem. Often the mechanism invoked for the onset of an internal transport barrier relies on the reduction of turbulence by a local increase of the E × B velocity shear. In this paper, we present in some detail the theoretical analysis of the possible role of an externally applied electrodynamic torque, resonant on a rational surface with the support of selected Joint European Torus experimental results.

Predicting core and edge transport barriers in tokamaks using the GLF23 drift-wave transport model

The density and temperature profiles are predicted in core and edge transport barriers in the DIII-D tokamak [J. L. Luxon and L. G. Davis, Fusion Technol. 8, 441 (1985)] using the GLF23 drift-wave model. The GLF23 model has been retuned to yield a better fit to the linear gyrokinetic growth rates for reversed magnetic shear and H-mode pedestal parameters. The turbulent saturation levels are determined using nonlinear gyrokinetic simulations. Using a large profile database, it is found that the retuned and original GLF23 models yield comparable results for discharges with monotonic safety factor profiles and no discernable internal transport barriers (ITBs). Examples of using retuned GLF23 model to predict the temperature profiles in simulations of several DIII-D strongly reversed magnetic shear ITB discharges are provided. Particle transport simulations show that the model is successful in predicting the density profile in discharges without ITBs but that some additional background particle diffusivity is needed in order to reproduce the measured density profiles within the barrier region of ITB plasmas where the ion temperature gradient and trapped electron mode transport have been quenched by rotational shear stabilization.

Inductive Current Density Perturbations to Probe Electron Internal Transport Barriers in Tokamaks

Improved electron energy confinement in tokamak plasmas, related to internal transport barriers, has been linked to nonmonotonic current density profiles. This is difficult to prove experimentally since usually the current profiles evolve continuously and current injection generally requires significant input power. New experiments are presented, in which the inductive current is used to generate positive and negative current density perturbations in the plasma center, with negligible input power. These results demonstrate unambiguously for the first time that the electron confinement can be modified significantly solely by perturbing the current density profile.

Derivation of an analytical area-preserving map to describe transport barriers in tokamaks

Transport barriers have been observed in tokamak experiments involving negative magnetic shear. The use of non-twist maps has been proposed in order to explain the underlying dynamical mechanism of such barriers. In this work we derive an area-preserving analytical map to describe the formation of a transport barrier in a chaotic field line region of a tokamak with an ergodic magnetic limiter. The map so obtained is used to investigate the radial diffusion of field lines in such a configuration.

Particle flows in dusty plasmas of the tokamak edge

In this Brief Communication the plasma flows and ambipolar electric field induced due to the temperature stresses on ions are estimated. These flows are similar to the plasma “residual” rotations in tokamaks, but are related to dust contamination of tokamak plasmas. The induced electric field might be very important for creating transport barriers in tokamaks.

Tokamak MHD equilibria with reversed magnetic shear and sheared flow**A preliminary version of this study was presented in the 29th EPS Conf. on Plasma Phys. and Control. Fusion (Montreux, Switzerland, 17–21 June 2002) [1

Analytical solutions of the magnetohydrodynamic equilibrium equations for a cylindrically symmetric magnetically confined plasma with reversed magnetic shear, s < 0, and sheared flow are constructed by prescribing the safety factor, poloidal velocity and axial velocity profiles consistently with experimental ones. On the basis of the solutions obtained, in most of the cases considered, it turns out that an increase of |s| and of the velocity components result in larger absolute values for the radial electric field, Er, its shear, , and the E × B velocity shear, ωE × B = |(d/dr)(E × B/B2)|, which may play a role in the formation of internal transport barriers in tokamaks. In particular for a constant axial magnetic field, ωE × B at the point where is proportional to 1−s. Also, and ωE × B increase as the velocity shear takes larger values. The results clearly indicate that s < 0 and sheared flow acts synergetically in an increase of ωE × B with the impact of the flow, in particular the poloidal one being stronger than that of s < 0.

Analysis of turbulent-transport suppression in non-neutral plasmas by turbulence theory based on mass-weighted averaging

Turbulent-transport suppression is investigated on the basis of the turbulence theory founded on the mass-weighted averaging. Effects of plasma non-neutrality occur twofold. One is a direct electric-field effect, and the other is an indirect effect through the E×B flow. The results are discussed in light of transport barriers in tokamaks. Specifically, it is shown that the electric-field curvature and the bulk poloidal flow generating a centripetal force contribute to the suppression of turbulence and heat transport, but that the shear part of the flow leads to the enhancement of turbulence.

Kinetic ballooning stability of internal transport barriers in tokamaks

Steep plasma pressure gradient can be stably sustained in tokamaks if the magnetic shear s is weak, either positive or negative. A fully kinetic integral equation code has been developed to investigate stability of the drift and ballooning modes in tokamaks. For small shear |s|≪1 where the magnetohydrodynamic ballooning mode is known to be stable, the kinetic ballooning mode is stable only if the pressure gradient exceeds a threshold.