Toroidal Rotation Profile Research Articles

ECH effects on toroidal rotation: KSTAR experiments, intrinsic torque modelling and gyrokinetic stability analyses

Toroidal rotation profiles have been investigated in KSTAR H-mode plasma using combined auxiliary heating by co-neutral beam injection (NBI) and electron cyclotron resonance heating (ECH). The ion temperature and toroidal rotation are measured with x-ray imaging crystal spectroscopy and charge exchange recombination spectroscopy. H-mode plasma is achieved using co-current 1.3 MW NBI, and a 0.35 MW ECH pulse is added to the flat-top of H-mode. The core rotation profiles, which are centrally peaked in the pure NBI heating phase, flatten when ECH is injected, while the edge pedestal is unchanged. Dramatic decreases in the core toroidal rotation values (ΔVtor/Vtor ∼ −30%) are observed when on-axis ECH is added to H-mode. The experimental data show that the decrease of core rotation velocity and its gradient are correlated with the increase of core electron temperature and its gradient, and also with the likely steepening of the density gradient. We thus explore the viability of a hypothesized ITG (ITG ion temperature gradient instability) → TEM (trapped electron mode instability) transition as the explanation of the observed counter-current flow induced by ECH. However, the results of linear microstability analyses using inferred profiles suggest that the TEM is excited only in the deep core, so the viability of the hypothesized explanation is not yet clear.

Turbulent momentum transport in core tokamak plasmas and penetration of scrape-off layer flows

The turbulent transport of toroidal angular momentum in the core of a tokamak plasma is investigated in global, full-f gyrokinetic simulations, performed with the GYSELA code in the flux-driven regime. During the initial turbulent phase, a front of positive Reynolds stress propagates radially, generating intrinsic toroidal rotation from a vanishing initial profile. This is also accompanied by a propagating front of turbulent heat flux. In the statistical steady-state regime, turbulent transport exhibits large-scale avalanche-like events which are found to transport both heat and momentum, and similar statistical properties are obtained for both fluxes. The impact of scrape-off layer flows is also investigated by modifying the boundary conditions in the simulations. The observed impact is radially localized for L-mode like poloidal profiles of parallel velocity at the edge, while a constant velocity at the edge can modify the core toroidal rotation profile in a large fraction of the radial domain.

Observation of 1/1 impurity-related ideal internal kink mode locking in the EAST tokamak

m/n = 1/1 pressure gradient driven impurity-related ideal internal kink mode locking is observed in EAST limit-cycle state H-mode plasmas. This 1/1 mode has a radial structure with no inversion around the resonance, which implies that the mode has an ideal internal kink structure. The rotation direction of the 1/1 internal kink mode, as obtained by tomography of a high-resolution multi-array soft x-ray system, is the ion diamagnetic drift velocity direction. Impurities accumulated in the central region play a vital role in mode excitation. Remarkable loss of the yield of neutron rate due to 1/1 mode is also observed. A notch at the location in the vicinity of q = 1 is also observed in the local toroidal rotation profile. Furthermore, the frequency chirping behavior of the 1/1 kink mode is related to the toroidal rotation velocity of the plasma.

Indirect measurement of poloidal rotation using inboard–outboard asymmetry of toroidal rotation and comparison with neoclassical predictions

An alternative experimental spectroscopic measurement of poloidal plasma rotation in toroidally confined plasmas is proven effective in the TCV tokamak. Charge exchange recombination measurements of the toroidal rotation profile over the full mid-plane plasma diameter are used to infer the complete bi-dimensional flow structure of the intrinsic C6+ impurity, which includes its poloidal component. For divergence free flows, the difference between the toroidal rotation frequency ft = ut/R at the inboard and outboard locations on the same flux surface is proportional to the poloidal rotation. This indirect measurement provides increased accuracy as the measured quantity ft,in − ft,out≈4qup/Raxis(q is the local safety factor) is larger than the intrinsic uncertainties of a direct spectroscopic measurement of poloidal velocity. The method is applied in a variety of TCV ohmic and electron cyclotron heated L-mode plasmas in the banana-plateau collisionality regime . In the radial range of normalized poloidal flux ρψ < 0.8, an impurity poloidal velocity of up = 0.5–2.5 km s−1 is observed, always in the electron diamagnetic drift direction. The measurements are compared with neoclassical calculations and they agree in magnitude and sign to within <1 km s−1.

Evidence of Neoclassical Toroidal Viscosity on the Neoclassical Tearing Modes in TCV tokamak

The interplay between the plasma toroidal rotation and the onset of magnetohydrodynamics instabilities, such as the Neoclassical Tearing Modes (NTMs), is an important issue for tokamak performance. An interesting mechanism characterizing this interaction is the breaking of axisymmetry due to the NTM helical structure, which is the source of a magnetic viscous drag parallel to the toroidal field. This effect, known as Neoclassical Toroidal Viscosity (NTV) depends on magnetic island width, and is responsible of the nearly global slowing down of the toroidal velocity across the profile. In the TCV tokamak the spontaneous plasma toroidal rotation profile, observed even in absence of other external momentum sources [1], can be modified by nearly central electron cyclotron heating (ECH) with a slight poloidal asymmetry and current drive (ECCD) [1,2,3]. The evidence of NTV effect on the plasma toroidal velocity profile of TCV is apparent as a pronounced flattening at the onset of m/n=3/2 and 2/1 tearing instabilities in the neoclassical regime in TCV discharges (Ip~150 kA, ne_av~2 1019 m−3 Te~3 keV) with 1.5 MW EC ramp up/down phases. Comparison of the measured and calculated toroidal plasma velocity is performed using the NTV formulation [4,5] applicable in the collisionless regimes. The different aspects of the NTM onset associated both with the ECH-coECCD effect on the current profile and with NTV observed in several TCV discharges are discussed, in the frame of classical and neoclassical tearing modes theory applied to 3/2 and 2/1 modes.

Intrinsic Toroidal Rotation, Density Peaking, and Turbulence Regimes in the Core of Tokamak Plasmas

Observations in the ASDEX Upgrade tokamak show a correlation between the gradient of the intrinsic toroidal rotation profile and the logarithmic gradient of the electron density profile. The intrinsic toroidal rotation in the center of the plasma reverses from co- to countercurrent when the logarithmic density gradients are large, and the turbulence is either dominated by trapped electron modes or is at the transition between ion temperature gradient and trapped electron modes. A study based on local gyrokinetic calculations suggests that the dominant trend in the observations can be explained by the combination of residual stresses produced by E × B and profile shearing mechanisms.

Modelling of Small Size Divertor Tokamak Plasma Edge in the Higher Confinement Regime

A version of the B2SOLPS0.5.2D fluid transport code is the new version of B2SOLPS fluid transport code, which is suited technique to simulate the edge plasma of small size divertor tokamak in the H- regime. The results of simulation provide the following: (1) the radial electric field inside the transport barrier is consistent with the neoclassical nature of the radial electric field. (2) The absolute value of the radial electric field shear at inner side of internal transport barrier is small and consistent with the value of shear before the L–H transition, while the value of shear at barrier is significantly large. (3) As a result of strong radial electric field shear and strong barrier formation the diffusion coefficient reduced by factor ~3 with respect to L-mode while ion heat conductivity reduced by factor ~22 with respect to L-mode inside the barrier. (4) The toroidal (Parallel) flux is directed along co-current direction as L-mode but at inner side of barrier is significantly large in absolute value. (5) The radial profile of toroidal rotation in vicinity of transition layer is determined by the parameter δ (width of the transition layer) depending on the collisionality and anomalous diffusion coefficient.

Destabilization mechanism of edge localized MHD mode by a toroidal rotation in tokamaks

Effects of toroidal rotation and density profiles on the stability of an edge localized MHD mode are investigated numerically. From the numerical results we show that both the density gradient and the sheared rotation profile can destabilize the edge ballooning mode and the peeling–ballooning mode, and particularly, the sheared rotation can destabilize these modes effectively. To clarify the mechanisms of these destabilizing effects of density gradient and sheared rotation, we define some energies and distinguish them by physics. By comparing these energies, we clarify that the destabilization by the density gradient can be explained as the destabilizing effect of the centrifugal instability, and that by the sheared toroidal rotation is induced mainly by the difference between the eigenmode frequency and the toroidal rotation frequency of the plasma. Although the strong rotation shear also has a stabilizing effect on the MHD modes by changing the mode structure, the edge MHD mode first becomes unstable due to the appearance of the destabilizing effect before changing the mode structure.

Lower hybrid heating and current drive on the Alcator C-Mod tokamak

On the Alcator C-Mod tokamak, lower hybrid current drive (LHCD) is being used to modify the current profile with the aim of obtaining advanced tokamak (AT) performance in plasmas with parameters similar to those that would be required on ITER. To date, power levels in excess of 1 MW at a frequency of 4.6 GHz have been coupled into a variety of plasmas. Experiments have established that LHCD on C-Mod behaves globally as predicted by theory. Bulk current drive efficiencies, n20IlhR/Plh ∼ 0.25, inferred from magnetics and MSE are in line with theory. Quantitative comparisons between local measurements, MSE, ECE and hard x-ray bremsstrahlung, and theory/simulation using the GENRAY, TORIC-LH CQL3D and TSC-LSC codes have been performed. These comparisons have demonstrated the off-axis localization of the current drive, its magnitude and location dependence on the launched n∥ spectrum, and the use of LHCD during the current ramp to save volt-seconds and delay the peaking of the current profile. Broadening of the x-ray emission profile during ICRF heating indicates that the current drive location can be controlled by the electron temperature, as expected. In addition, an alteration in the plasma toroidal rotation profile during LHCD has been observed with a significant rotation in the counter-current direction. Notably, the rotation is accompanied by peaking of the density and temperature profiles on a current diffusion time scale inside of the half radius where the LH absorption is taking place.

Comparisons of predicted plasma performance in ITER H-mode plasmas with various mixes of external heating

Performance in H-mode DT plasmas in ITER with various choices of heating systems are predicted and compared. Combinations of external heating by negative ion neutral beam injection (NNBI), ion cyclotron range of frequencies and electron cyclotron heating are assumed. Scans with a range of physics assumptions about boundary temperatures in the edge pedestal, alpha ash transport and toroidal momentum transport are used to indicate effects of uncertainties. Time-dependent integrated modelling with the PTRANSP code is used to predict profiles of heating, beam torque and plasma profiles. The GLF23 model is used to predict temperature profiles. Either GLF23 or the assumption of a constant ratio for χϕ/χi is used to predict toroidal rotation profiles driven by the beam torques. Large differences for the core temperatures are predicted with different mixes of the external heating during the density and current ramp-up phase, but the profiles are similar during the flat-top phase. With χϕ/χi = 0.5, the predicted toroidal rotation is relatively slow and the flow shear implied by the pressure, toroidal rotation and neoclassical poloidal rotation are not sufficient to cause significant changes in the energy transport or steady state temperature profiles. The GLF23-predicted toroidal rotation is faster by a factor of six, and significant flow shear effects are predicted. Heating mixes with more NNBI power are predicted to have up to 20% higher fusion power during steady state phases. This advantage is decisive in some cases where the physics assumptions are close to marginal or critical values. L-mode plasmas are predicted having QDT ≃ 2–4.

Advances in understanding the generation and evolution of the toroidal rotation profile on DIII-D

Recent experiments using DIII-D's capability to vary the injected torque at constant power have focused on developing the physics basis for understanding rotation through the detailed study of momentum sources, sinks and transport. Non-resonant magnetic braking has generally been considered a sink of momentum; however, recent results from DIII-D suggest that it may also act as a source. The torque applied by the field depends on the rotation relative to a non-zero ‘offset’ rotation. Therefore, at low initial rotation, the application of non-resonant magnetic fields can actually result in a spin-up of the plasma. Direct evidence of the effect of reverse shear Alfvén eigenmodes on plasma rotation has been observed, which has been explained through a redistribution of the fast ions and subsequent modification to the neutral beam torque profile. An effective momentum source has been identified by varying the input torque from neutral beam injection at fixed βN, until the plasma rotation across the entire profile is essentially zero. This torque profile is largest near the edge, but is still non-negligible in the core, qualitatively consistent with models for a so-called ‘residual stress’. Perturbative studies of the rotation using combinations of co- and counter-neutral beams have uncovered the existence of a momentum pinch in DIII-D H-mode plasmas, which is quantitatively similar to theoretical predictions resulting from consideration of low-k turbulence.

Toroidal rotation in RF heated JET plasmas

Observations of bulk plasma rotation in radio frequency (RF) heated JET discharges are reported. This study is concentrated on RF heated L-mode plasmas. In particular, the toroidal rotation profiles in plasmas heated by ion cyclotron resonance frequency (ICRF) waves and lower hybrid (LH) waves have been analysed. It is the first time that rotation profiles in JET plasmas with LH waves have been measured in dedicated discharges. It is found that the toroidal plasma rotation in the outer region of the plasmas is in the co-current direction irrespective of the heating scenario. An interesting feature is that the toroidal rotation profile appears to be hollow in many discharges at low plasma current, but a low current in itself does not seem to be a sufficient condition for finding such profiles. Fast ion transport and finite orbit width effects are mechanisms that could explain hollow rotation profiles. This possibility has been investigated by numerical simulations of the torque on the bulk plasma due to fast ICRF accelerated ions. The obtained torque is used in a transport equation for the toroidal momentum density to estimate the effect on the thermal bulk plasma rotation profile.

Observation of Self-Generated Flows in Tokamak Plasmas with Lower-Hybrid-Driven Current

In Alcator C-Mod discharges lower hybrid waves have been shown to induce a countercurrent change in toroidal rotation of up to 60 km/s in the central region of the plasma (r/a approximately <0.4). This modification of the toroidal rotation profile develops on a time scale comparable to the current redistribution time (approximately 100 ms) but longer than the energy and momentum confinement times (approximately 20 ms). A comparison of the co- and countercurrent injected waves indicates that current drive (as opposed to heating) is responsible for the rotation profile modifications. Furthermore, the changes in central rotation velocity induced by lower hybrid current drive (LHCD) are well correlated with changes in normalized internal inductance. The application of LHCD has been shown to generate sheared rotation profiles and a negative increment in the radial electric field profile consistent with a fast electron pinch.

Energetically resolved multiple-fluid equilibria of tokamak plasmas

In many magnetically confined fusion experiments, a significant fraction of the stored energy of the plasma resides in energetic, or non-thermal, particle populations. Despite this, most equilibrium treatments are based on MHD: a single fluid treatment which assumes a Maxwell–Boltzmann distribution function. Detailed magnetic reconstruction based on this treatment ignore the energetic complexity of the plasma and can result in model-data inconsistencies, such as thermal pressure profiles which are inconsistent with the total stored kinetic energy of the plasma. Alternatively, ad hoc corrections to the pressure profile, such as summing the energetic and thermal pressures, have poor theoretical justification. Motivated by this omission, we generalize ideal MHD one step further: we consider multiple quasi-neutral fluids, each in thermal equilibrium and each thermally insulated from each other—no population mixing occurs. Kinetically, such a model may be able to describe the ion or electron distribution function in regions of velocity phase space with a large number of particles, at the expense of more weakly populated phase space, which may have uncharacteristically high temperature and hence pressure. As magnetic equilibrium effects increase with the increase in pressure, our work constitutes an upper limit to the effect of energetic particles. When implemented into an existing solver, FLOW (Guazzotto et al 2004 Phys. Plasmas 11, 604–14), it becomes possible to qualitatively explore the impact of resolving the energetic populations on plasma equilibrium configurations in realistic geometry. Deploying the modified code, FLOW-M, on a high performance spherical torus configuration, we find that the effect of variations of the pressure, poloidal flow and toroidal flow of the energetic populations is qualitatively similar to variations in the background plasma. We also study the robustness of the equilibrium to uncertainties in the current profile and the energetic toroidal rotation or energetic pressure profile. For constant toroidal current and stored energy, the change in the poloidal flux with changes in the current profile is similar irrespective of whether the toroidal rotation or pressure was changed, indicating insensitivity to whether uncertainties lie in the pressure or toroidal rotation profiles. We conclude that to a first approximation, lumping the energetic and thermal fluids together, as is done for many equilibrium solvers, qualitatively produces correct results.

Observations of counter-current toroidal rotation in Alcator C-Mod LHCD plasmas

Following the application of lower hybrid current drive (LHCD) power, the core toroidal rotation in Alcator C-Mod L- and H-mode plasmas is found to increment in the counter-current direction, in conjunction with a decrease in the plasma internal inductance, li. Along with the drops in li and the core rotation velocity, there is peaking of the electron and impurity density profiles, as well as of the ion and electron temperature profiles. The mechanism generating the counter-current rotation is unknown, but it is consistent in sign with an inward shift of energetic electron orbits, giving rise to a negative core radial electric field. The peaking in the density, toroidal rotation (in the counter-current direction) and temperature profiles occurs over a time scale similar to the current relaxation time but slow compared with the energy and momentum confinement times. Most of these discharges exhibit sawtooth oscillations throughout, with the inversion radius shifting inward during the LHCD and profile evolution. The magnitudes of the changes in the internal inductance and the central rotation velocity are strongly correlated and found to increase with increasing LHCD power and decreasing electron density. The maximum effect is obtained with a waveguide phasing of 60° (a launched parallel index of refraction n‖ ∼ 1.5), with a significantly smaller magnitude at 120° (n‖ ∼ 3.1), and with no effect for negative or heating (180°) phasing. Regardless of the plasma parameters and launched n‖ of the waves, there is a strong correlation between the rotation velocity and li changes, possibly providing a clue for the underlying mechanism.

Physics Mechanisms of Toroidal Rotation Profile and Properties of Momentum Transport in JT-60U

The roles of momentum transport on the toroidal rotation velocity (Vt) profile and the properties of transport coefficients are found by transient momentum transport analysis. The perturbation technique enables us to evaluate the momentum diffusivity (χφ) and the convection velocity (Vconv), and to calculate Vt profiles driven by external torque input by neutral beams (NBs). The measured Vt profiles with and without the external torque input are almost reproduced by χφ and Vconv in low-β (βN < 0.4) plasmas. At higher β, the local pressure gradient plays a role in determining the local value of intrinsic rotation velocity. Concerning the momentum transport, χφ increases with increasing heating power, and decreases with increasing plasma current (Ip). In H-mode plasmas, χφ is smaller than that in L-mode plasmas under similar experimental conditions. It is found that χφ, which is separated from the non-diffusive term increases with increasing heat diffusivity (χi), χφ/χi ∼ 1-3, and -Vconv increases with increasing χφ, Vconv/χφ ∼ -2.5 to -0.7 m-1 , in H-mode plasmas.

Dependence of heat transport on toroidal rotation in conventional H-modes in JT-60U

The relation between heat transport in the plasma core and the toroidal rotation profile was examined in conventional ELMy H-mode plasmas in JT-60U. Heat transport in the plasma core is not strongly influenced locally by toroidal rotation. The large increase in heat conduction imposes a resilient profile of ion temperature, under which the local effect of the toroidal rotation profile on scale length of the ion temperature gradient is very weak. Energy confinement improvement is observed with toroidal rotation which increases in the co-direction with respect to the plasma current. In this case, the increase in the ion temperature in both the plasma core and the pedestal region is observed. However, heat transport in the plasma core varies while maintaining self-similar temperature profiles as the toroidal rotation profile is varied. Pressure at the H-mode pedestal becomes slightly larger with the toroidal rotation in the co-direction. Thus, energy confinement enhanced with co-toroidal rotation is determined by increased pedestal height and reduced transport brought on by profile resilience. When pedestal temperature was fixed between the cases of co- and counter-NBI by adjusting the plasma density, identical temperature profiles were obtained in spite of totally different toroidal rotation profiles.

Investigation of resistive wall mode stabilization physics in high-beta plasmas using applied non-axisymmetric fields in NSTX**Supported by US DOE Contracts DE-FG02-99ER54524 and DE-AC0276CH03073.

The National Spherical Torus Experiment (NSTX) offers an operational space characterized by high-beta (βt = 39%, βN > 7, ) and low aspect ratio (A > 1.27) to leverage the plasma parameter dependences of RWM stabilization and plasma rotation damping physics giving greater confidence for extrapolation to ITER. Significant new capability for RWM research has been added to the device with the commissioning of a set of six non-axisymmetric magnetic field coils, allowing generation of fields with dominant toroidal mode number, n, of 1–3. These coils have been used to study the dependence of resonant field amplification on applied field frequency and RWM stabilization physics by reducing the toroidal rotation profile below its steady-state value through non-resonant magnetic braking. Modification of plasma rotation profiles shows that rotation outside q = 2.5 is not required for passive RWM stability and there is large variation in the RWM critical rotation at the q = 2 surface, both of which are consistent with distributed dissipation models.

Transport with reversed shear in the National Spherical Torus Experiment

In the National Spherical Torus Experiment (NSTX) [M. Ono et al., Nucl. Fusion 40, 557 (2000)], plasmas with strongly reversed magnetic shear, s≡(r∕q)(dq∕dr)&amp;lt;0, in the plasma core exhibit a marked improvement in electron confinement compared to otherwise similar plasmas with positive or only weakly reversed magnetic shear. The q profile itself is determined by the early evolution of the plasma current, the plasma cross section, and the neutral-beam heating power. In the region of shear reversal, the electron thermal diffusivity can be significantly reduced. Detailed experimental investigation of this phenomenon has been made possible by the successful development of a motional Stark effect (MSE) polarimetry diagnostic suitable for the low magnetic field in NSTX, typically 0.35–0.55T. Measurements of the electron and ion temperature, density, and plasma toroidal rotation profiles are also available with high spatial and temporal resolution for analysis of the plasma transport properties.

Plasma rotation and momentum transport studies at JET

An experimental study in plasma rotation and momentum transport was carried out at JET. The toroidal rotation profile was found to scale approximately with that of the ion temperature. However, significant deviations from this were found in high density ELMy H-mode discharges, which had broader rotation profiles. A rotation database analysis showed the variation of the dimensionless Mach number with respect to the plasma scenario. For predominantly NBI heated discharges the Mach number was found to be in the range of 0.3–0.45. Larger Mach numbers were observed in type I ELMy H-modes, while scenarios exhibiting type III ELMs or L-mode had lower Mach numbers. Advanced scenarios often showed a significant increase in the central Mach number when an internal transport barrier formed. A detailed study was done to investigate the Prandtl number, P r , defined as the ratio between momentum and ion heat diffusivity. Generally the Prandtl number was found to be significantly below unity, e.g. 0.18 < P r < 0.35. Although it is often predicted that momentum and heat diffusivity are equal in ITG dominated plasma, also for high density ELMy H-mode discharges with temperature profiles close and above the ITG threshold, the Prandtl number was P r ∼ 0.3.