Sheared Poloidal Flow Research Articles

Full-wave calculation of sheared poloidal flow driven by high-harmonic ion Bernstein waves in tokamak plasmas

A full-wave, one-dimensional spectral model is developed to study sheared poloidal flow driven by high-harmonic ion Bernstein waves (IBWs) in tokamak plasmas. The local plasma conductivity is corrected to lowest order in ρ/L where ρ is the ion Larmor radius and L is the equilibrium scale length. This correction takes into account gradients in equilibrium quantities and is necessary for conservation of energy. It is equivalent to the “odd-order derivative” terms in finite difference models. No assumption is made regarding the smallness of the ion Larmor radius relative to wavelength, and results are applicable to all orders in k⊥ρ where k⊥ is the perpendicular wave number. Previous numerical results for flow drive have relied on expansions in k⊥ρ, and are thus limited to cyclotron harmonics of two and below. In this article, we consider higher-harmonic cases corresponding to recent IBW flow drive experiments on the Tokamak Fusion Test Reactor [B. P. LeBlanc, R. E. Bell, S. Bernabei et al., Phys. Rev. Lett. 82, 331 (1999)] and the Frascati Tokamak Upgrade [R. Cesario, C. Castaldo, V. Pericoli-Ridolfini et al., “Recent Results of the Ion Bernstein Wave Heating Experiment on FTU,” in Proceedings of the 13th Topical Conference on Radio Frequency Power in Plasmas, 1999, Annapolis, MD, edited by S. Bernabei and F. Paoletti (American Institute of Physics, New York, 1999), p. 100]. In these cases, a directly launched high-harmonic IBW is used to drive poloidal flow near the fourth- and fifth-harmonic ion cyclotron layers. Other applications include high-harmonic fast wave heating in low aspect ratio tokamaks such as the National Spherical Torus Experiment [S. M. Kaye, M. Ono, Y.-K. M. Peng et al., Fusion Technol. 36, 16 (1999)].

Poloidal flows and enhanced reverse shear bifurcation in tokamaks

The effect of poloidal flow shear on transition to enhanced reverse shear (ERS) mode in tokamaks is studied. A model is examined where the flow-fluctuation equilibrium evolves in time as a function of pressure gradients. Under some conditions the transition to the ERS phase occurs via as s-fold catastrophe and is accompanied by a spike in poloidal flow generation where poloidal flow shear is reversed. The nature of the transition is found to depend critically on the ratio of factors controlling the damping and generation of poloidal flow shear. The turbulence level shows a periodic bursting behavior which is suppressed in the ERS phase. The relevance of these results to recent observations from the Tokamak Fusion Test Reactor [R. E. Bell et al., Phys. Rev. Lett. 81, 1429 (1998)] is briefly discussed.

Generation of sheared poloidal flows via Reynolds stress and transport barrier physics

A view of the latest experimental results and progress in the understanding of the role of poloidal flows driven by fluctuations via Reynolds stress is given. Reynolds stress shows a radial gradient close to the velocity shear layer location in tokamaks and stellarators, indicating that this mechanism may drive significant poloidal flows in the plasma boundary. Observation of the generation of E×B sheared flows via Reynolds stress at the ion Bernstein resonance layer has been noticed in toroidal magnetized plasmas. The experimental evidence of sheared E×B flows linked to the location of rational surfaces in stellarator plasmas might be interpreted in terms of Reynolds stress sheared driven flows. These results show that E×B sheared flows driven by fluctuations can play an important role in the generation of transport barriers.

Role of reynolds stress-induced poloidal flow in triggering the transition to improved ohmic confinement on the HT-6M tokamak

Time and space resolved measurements of electrostatic Reynolds stress, radial electric field E(r), and plasma rotations have been performed across the transition to improved Ohmic confinement in the Hefei Tokamak-6M (HT-6M). The first experimental evidence of the correlation between the enhanced Reynolds stress gradient and the poloidal flow acceleration in the edge plasma is presented. The results indicate that the turbulence-induced Reynolds stress might be the dominant mechanism to create the sheared poloidal flow and E(r), which may further trigger the transition.

ICRF heating and profile control techniques in TFTR

In fast wave to ion Bernstein wave mode conversion experiments in DT supershot plasmas, localized efficient ion heating rather than electron heating was observed, which was due to Doppler broadened tritium cyclotron resonance overlap into the mode conversion region. The ion temperature heat pulse associated with RF power modulation in this regime could provide a diagnostic tool for measuring the local ion thermal conductivity in various confinement regimes. In direct launch ion Bernstein wave heating experiments, core power coupling was limited by the excitation of parasitic edge modes. However, a sheared poloidal flow was observed that is consistent in both magnitude and direction with theoretical models based on RF driven Reynolds stress. With the modest power coupled to the core (∼360 kW), the magnitude of the shear in the observed flow was estimated to be a factor of 3-4 too low to trigger transport barrier formation through localized shear suppression of turbulence.

Stabilization of the kinetic internal kink mode by a sheared poloidal flow

The effects of a sheared poloidal flow on the m = 1 (poloidal mode number) and n = 1 (toroidal mode number) kinetic internal kink mode are simulated by the linearized version of the gyro-reduced MHD code, GRM3D-2F, based on a two-field and two-fluid gyro-reduced MHD model, including the kinetic effects of electron inertia and the perturbed electron pressure gradients along the magnetic field. A parameter study for different values of de (collisionless electron skin depth) with a fixed value of ρs = 0 (ion Larmor radius estimated by the electron temperature) shows that the smaller-de case, which has the smaller growth rate, is stabilized by the smaller sheared poloidal flow. When ρs is raised to ρs > de for a fixed value of de, the instability is stabilized by the smaller shear flow compared with the case of ρs < de, although the growth rate without the flow is larger for ρs > de. Since de is very much less than the minor radius, and ρs > de for the existing and future experiments, it is possible that even a quite small sheared poloidal flow may have a crucial influence on the kinetic internal kink mode.

Flow-curvature effect on linear Rayleigh–Taylor instability in magnetized plasmas

The effect of sheared poloidal flow on the linear Rayleigh–Taylor (RT) instability of magnetized plasma is reexamined. In the weak curvature flow limit (V⊥0″≪1) the linear RT mode stabilization effect is recovered. In the strong flow curvature limit (V⊥0″≫1) it is shown that the RT mode may not stabilize.

Effects of supersonic beam and pellet injection on edge electric field and plasma rotation in HL-1M

Experimental measurements of edge electric field and plasma rotation have been carried out on both of scrape-off layer (SOL) and the boundary region of HL-1M for Ohmic, Supersonic Beam Injection (SBI) and Multi-shot Pellet Injection (MPI) with a Mach/Langmuir probe array. The radial profiles of the toroidal flow Mach number M, the poloidal flow rotation velocity V pol and the electric field E r are measured during experiments of MPI and SBI respectively. The effects of supersonic beam injection and multi-shot pellet injection on the edge electric field, plasma rotation and fluctuation have been observed. The results show that the change of the radial electric field E r is generated and becomes more negative at the tokamak plasma edge and the sheared poloidal flow relates to the reduction in fluctuation level. During SBI and MPI, poloidal rotation velocities of 3.8 km/s and 10 km/s in the electron diamagnetic direction are measured, respectively. From the measurements we also obtain radial electric fields of −8 and −14 kV/m, respectively in the plasma edge region. It appears that the poloidal velocity is mainly dominated by the E × B drift.

Dynamics of axisymmetric and poloidal flows in tokamaks

As a result of turbulence and finite Larmor radius effects, random radial currents are present in a tokamak plasma and these drive sheared axisymmetric poloidal flows. We model these currents with a noise source with given statistical properties and calculate the linear kinetic response to this source. Without collisions, there is no long term damping of these flows; when collisions are included, poloidal flows are damped. The mean square potential associated with these flows is given in terms of the linear response function we calculate and a model correlation function for the current source. Without collisions, the mean square flow increases linearly with time, but with collisions, it reaches a steady state. In the long correlation time limit, the collisionless residual flows are important in determining the mean square flow.

Steady state drift vortices in plasmas with shear flow in equilibrium

The Hasegawa–Mima equation in the presence of sheared poloidal flow is solved for two-dimensional steady state vortex. It is shown that when the phase velocity of the vortex is the same as the diamagnetic drift velocity, an exact solution in the form of counter-rotating vortices may appear. In the small amplitude limit near the origin this solution reduces to a localized Lamb-dipole.

Magnetohydrodynamic behaviour during core transport barrier experiments with ion Bernstein wave heating in PBX-M: I ELMs, fluctuations and crash events

If the ion Bernstein wave (IBW) heating power in an H mode discharge of the PBX-M experiment exceeds a threshold power of about 200 kW, a core transport barrier is created in the central region of the plasma. At lower neutral beam injection (NBI) powers, the core barrier is accompanied by an edge L mode. The high edge localized mode (ELM) repetition frequency (1 kHz) prevents the creation of a strong barrier, so the edge first has to make an H-to-L transition before a strong core transport barrier can be created. At higher NBI powers, the ELM repetition frequency is lowered to less than 200 Hz, which allows the immediate creation of a strong core barrier. Edge localized mode loss, which propagates radially first on a fast (non-diffusive) and then on a slow (diffusive) time-scale all the way to the plasma core, is strongly reduced in the core barrier region. Correlated with the reduced ELM loss, the fluctuations in the core barrier region are also strongly reduced, both during the ELM and during the quiet periods between the ELMs. There is strong evidence that the IBW induced poloidal flow shear is responsible for the stabilization of core turbulence and the creation of the core transport barrier. The large perpendicular E × B flow shear component of the measured toroidal velocity in co-injection neutral beam heated discharges seems to be largely cancelled by the ion diamagnetic drift shear produced by large ion pressure gradients in the core barrier region. The value of IBW induced poloidal flow has not been experimentally determined, but its numerical value is found to be a factor of 4 larger than either the toroidal velocity or the ion diamagnetic drift shear components, leaving only IBW induced flow shear as the most probable cause for the turbulence stabilization. The core turbulence suppression and the creation of the core transport barrier is also consistent with expectations from a comparison between the E × B flow shear rate and a rough estimate of the linear ion temperature gradient (ITG) growth rate. The presence of the core barrier region also strongly modifies the other MHD events: crashes on the q = 1.5, 2 surfaces and the disruption.

Flow shear stabilization of a hybrid dissipative trapped electron-ion temperature gradient mode in tokamaks

A simple physical model for toroidal flow shear stabilization of a hybrid dissipative trapped electron-ion temperature gradient mode (namely, the hybrid electron-ion drift mode) is presented. Coupling between the sheared flows and non-adiabatic electrons is proposed as the stabilization mechanism of the hybrid electron-ion drift mode. This implies that the confinement improvement can be achieved not only through the poloidal sheared rotation flow in the edge region of tokamaks for the L-H transition but also through the toroidal sheared rotation in the core region for further confinement improvement associated with the internal transport barrier and negative shear.

Flow-shear stabilization of ion temperature gradient-driven instability in a tokamak: Slab theory

A simple physical model for the flow-shear stabilization of ion temperature gradient (ITG)-driven instability in the presence of dissipative trapped electrons is presented. Reduced fluid equations and magnetic sheared slab geometry are adopted. From analytical analyses and numerical calculations, it was found that the coupling between the sheared flows and non-adiabatic electrons will result in the stabilization of both toroidal sheared flow and poloidal sheared flow on hybrid dissipative trapped electron ITG mode. This implies that the confinement improvement in tokamaks can be obtained not only through the poloidal sheared rotation in the edge region of tokamaks for the H-mode (high-confinement mode), but also through the toroidal sheared rotation in the core region for further confinement improvement associated with internal transport barrier (ITB) and negative shear (or reversed magnetic shear). When the poloidal and toroidal sheared flows are simultaneously considered, it was found that in the presence of poloidal sheared flow, the toroidal sheared flow is a stabilizing or destabilizing effect on hybrid dissipative trapped electron ITG mode according to the relative sign of the poloidal and toroidal sheared flows. However, for sufficiently large value of the toroidal sheared flow, the toroidal sheared flow is always destabilization on the hybrid dissipative electron ITG mode regardless of the relative sign of these sheared flows. These conclusions are consistent with the experimental observations on the Japanese Tokamak-60U (JT-60U) [Y. Koide et al., Phys. Rev. Lett. 72, 3662 (1994)], where large toroidal rotation shear or jump was observed across the surface q=3 (the internal transport barrier location). Toroidal sheared flow stabilization therefore appears to offer favorable prospects for high confinement operation of future fusion reactor.

Calculating magnetohydrodynamic flow spectra

We describe a numerical method for calculating the magnetohydrodynamic (MHD) spectrum of one-dimensional equilibria with flow. Due to a general formulation, the spectrum for two different equilibrium geometries, viz. a plane slab and a cylinder, can be investigated. The linearised equations are discretised with a Finite Element Method. This results in a large non-Hermitian matrix eigenvalue problem, which can be solved using standard techniques. We present test cases for the method and new results on the effect of a sheared poloidal flow and a sheared magnetic field on the MHD spectrum.

Poloidal shear flow effect on toroidal ion temperature gradient mode: A theory and simulation

The effect of poloidal shear flow on the global structure and stability of toroidal ion temperature gradient mode is studied theoretically and also numerically using a toroidal particle simulation code. Reasonable agreements are found between the theoretical and simulation results; both indicating that with increasing shear flow the toroidal ion temperature gradient mode is stabilized in the increase of poloidal asymmetry and in the reduction of radial mode width.

Velocity shear effect on Rayleigh–Taylor vortices in nonuniform magnetized plasmas

In this paper, the effect of velocity shear on Rayleigh–Taylor vortices has been demonstrated. An inhomogeneous plasma is considered with a density profile such that the diamagnetic drift velocity Vn=(cTe/eB)dn0/dx is a constant and includes the effect of an ambient poloidal shear flow Veq(x)=V⊥0′(x−x0)y. The final equation describing the stationary Rayleigh–Taylor vortex is shown to have the structure of a nonlinear Poisson equation, where the nonlinearity arises essentially because of the velocity shear term. This equation has been solved numerically and it has been shown that qualitatively new two-dimensional monopole vortex solutions may be obtained in the appropriate parameter space. Therefore, a new important nonlinear effect related to equilibrium shear flow has been identified in the calculations of Rayleigh–Taylor vortices which results in monopole-like solutions in plasmas.

Self-Consistent Flow Shear Induced by Drift-Thermal Turbulence

The self-consistent poloidal flow shear induced by turbulence driven by impurity radiation has been studied analytically. A set of reduced equations is obtained. In our system, three equilibrium states exist. The first is the zero flow shear state, which is relevant to the behavior such as L mode; the second is the positive flow shear state, which is relevant to the behavior such as dithering H mode; and the third is the negative flow shear state, which is relevant to the behavior such as edge-localized modes.

Theory of self-organized critical transport in tokamak plasmas

A theoretical and computational study of the ion temperature gradient (ITG) and ηi instabilities in tokamak plasmas has been carried out. In a toroidal geometry the modes have a radially extended structure and their eigenfrequencies are constant over many rational surfaces that are coupled through toroidicity. These nonlocal properties of the ITG modes impose a strong constraint on the drift mode fluctuations and the associated transport, showing self-organized criticality. As any significant deviation away from marginal stability causes rapid temperature relaxation and intermittent bursts, the modes hover near marginality and exhibit strong kinetic characteristics. As a result of this, the temperature relaxation is self-similar and nonlocal, leading to radially increasing heat diffusivity. The nonlocal transport leads to Bohm-like diffusion scaling. Heat input regulates the deviation of the temperature gradient away from marginality. We present a critical gradient transport model that describes such a self-organized relaxed state. Some of the important aspects in tokamak transport like Bohm diffusion, near marginal stability, radially increasing fluctuation energy and heat diffusivity, intermittency of the wave excitation, and resilient tendency of the plasma profile can be described by this model, and these prominent features are found to belong to one physical category that originates from the radially extended nonlocal drift modes. The obtained transport properties and scalings are globally consistent with experimental observations of low confinement mode (L-mode) discharges. The nonlocal modes can be disintegrated into smaller radial islands by a poloidal shear flow, suggesting that the transport changes from Bohm-like to near gyro-Bohm.

Theory of Resistivity-Gradient-Driven Turbulence in the Presence of Flow

The resistivity-gradient-driven turbulence is investigated in the presence of both poloidal and parallel/toroidal flows. At saturation, the poloidal flow shear reduces fluctuations at the edge of plasmas, the parallel flow and its shear both reduce fluctuations in the core of plasmas. This indicates that the mechanism for a high confinement regime (H mode) may be the turbulence suppression due to the poloidal flow shear at the edge of plasmas, and the mechanism for a very high confinement (VH mode) may be the turbulence suppression due to the toroidal flow and its shear in the core of plasmas.

Toroidal gyrokinetic particle simulations of core fluctuations and transport

The generation of low frequency electrostatic fluctuations and the formation of anomalous particle and heat diffusion in the core region of tokamak plasmas is investigated using gyrokinetic particle-in-cell simulations in toroidal geometry. We consider the case of H-mode tokamak plasmas characterized by nearly flat core density profiles. The principle source of fluctuations include ion temperature gradient (ITG)-driven instabilities and ITG-dissipative trapped electron modes. We compare the evolution of both branches of instability and find that the electron diffusivity can be larger than the ion thermal diffusivity in the latter case. An externally imposed radial electric field, which gives rise to sheared poloidal flows, is demonstrated to reduce the radial correlation length of the turbulent transport and hence reduce the anomalous thermal flux.