Toroidal Rotation Velocity Profiles Research Articles

Fast-ion transport and toroidal rotation response to externally applied magnetic perturbations at the ASDEX Upgrade tokamak

This paper studies the effect of 3D magnetic perturbations (MPs) on fast-ion confinement, and its impact on the toroidal rotation velocity profile. Two low collisionality H-mode experiments carried out at the ASDEX Upgrade tokamak have been analysed. The two discharges feature different magnetic field helicity (q 95), and differences in the velocity-space and level of fast-ion losses are observed. A new analysis technique has been developed that sheds light on the dependencies between fast-ion losses and toroidal rotation, providing for the first time correlation patterns resolved in radius and velocity space of the lost fast-ions. The correlation intensifies towards the plasma edge and is strongly dependent on the orbit topology of the lost fast-ions. The ASCOT orbit following code has been used to characterize the fast-ion resonant transport and beam driven torques, using the vacuum approach and including plasma response (PR). The change of the toroidal canonical momentum, which serves as figure of merit for resonant fast-ion transport, has been calculated with ASCOT. The beam geometry and q 95 are found to have a strong impact on the fast-ion transport and losses. The fast-ion transport induced by the MPs affects the beam driven torques. The effect of the changes of the j × B and collisional torques on plasma rotation is analysed using the torques simulated by ASCOT and simple momentum balance calculations. For the low q 95 = 3.8 discharge, which benefits from a resonant amplification, we find excellent agreement with the measured variation of the toroidal velocity. For the high q 95 = 5.5 discharge, the inclusion of the PR improves the comparison with experimental data with respect to the vacuum estimation, but still some differences with experiments are observed. This suggests that other non-resonant effects could play a role for the determination of the toroidal rotation profile.

Two-Gaussian Fitting Method for Charge Exchange Spectroscopy on Measurements of Ion Temperature and Toroidal Plasma Flow Velocity in the KSTAR Tokamak

Charge exchange spectroscopy has been widely used in fusion devices to measure ion temperature, and toroidal and poloidal flow velocities of plasma. For local measurement, especially in the core region of the plasma, the spectrum emitted by the charge exchange reaction between the main plasma ions or impurity ions and the intentionally injected neutral beam should be analyzed so that parameters can be accurately deduced. Since the line-integrated spectrum signal through the line of sight of the diagnostic optics usually contains an unnecessary overlapped spectrum signal, referred to as the background signal, that typically originates from the plasma boundary region, a beam modulation technique is commonly applied to separate the background signal from the measured spectrum. Recently, it has been demonstrated in the KSTAR tokamak that a two-Gaussian fitting (TGF) method can be applied to analyze the spectrum and deduce plasma ion temperature and toroidal rotation velocity profiles of reasonable accuracy without beam modulation. It has been realized that the measurement result by the TGF method can be alternatively used to investigate plasma transport dynamics when beam modulation is prohibited to avoid any possible disturbance inhibiting robust plasma control and stable operation of the neutral beam injection system.

Effects of neoclassical toroidal viscosity induced by the intrinsic error fields and toroidal field ripple on the toroidal rotation in tokamaks

Effects of neoclassical toroidal viscosity (NTV) induced by intrinsic error fields and toroidal field ripple on cocurrent toroidal rotation in H-mode tokamak plasmas are investigated. It is expected that large NTV torque can be localized at the edge region through the 1/ν-regime in the vicinity of Er∼0 in the cocurrent rotating H-mode plasma. Numerical simulation on toroidal rotation demonstrates that the edge localized NTV torque determined by the intrinsic error fields and toroidal field ripples in the level of most tokamaks can damp the toroidal rotation velocity over the whole region while reducing the toroidal rotation pedestal which is clearly observed in Korea Superconducting Tokamak Advanced Research (KSTAR) tokamak. It is found that the NTV torque changes the toroidal rotation gradient in the pedestal region dramatically, but the toroidal rotation profile in the core region responds rigidly without a change in the gradient. On the other hand, it shows that the NTV torque induced by the intrinsic error fields and toroidal field ripple in the level of the KSTAR tokamak, which are expected to be smaller than most tokamaks by at least one order of magnitude, is negligible in determining the toroidal rotation velocity profile. Experimental observation on the toroidal rotation change by the externally applied nonaxisymmetric magnetic fields on KSTAR also suggests that NTV torque arising from nonaxisymmetric magnetic fields can damp the toroidal rotation over the whole region while diminishing the toroidal rotation pedestal.

Effect of ion orbit loss on the structure in the H-mode tokamak edge pedestal profiles of rotation velocity, radial electric field, density, and temperature

An investigation of the effect of ion orbit loss of thermal ions and the compensating return ion current directly on the radial ion flux flowing in the plasma, and thereby indirectly on the toroidal and poloidal rotation velocity profiles, the radial electric field, density, and temperature profiles, and the interpretation of diffusive and non-diffusive transport coefficients in the plasma edge, is described. Illustrative calculations for a high-confinement H-mode DIII-D [J. Luxon, Nucl. Fusion 42, 614 (2002)] plasma are presented and compared with experimental results. Taking into account, ion orbit loss of thermal ions and the compensating return ion current is found to have a significant effect on the structure of the radial profiles of these quantities in the edge plasma, indicating the necessity of taking ion orbit loss effects into account in interpreting or predicting these quantities.

Profile Measurement of Ion Temperature and Toroidal Rotation Velocity with Charge Exchange Recombination Spectroscopy Diagnostics in the HL-2A Tokamak

This paper deals with the profile measurement of impurity ion temperature and toroidal rotation velocity that can be achieved by using the charge exchange recombination spectrum (CXRS) diagnostics tool built on the HL-2A tokamak. By using CXRS, an accurate impurity ion temperature and toroidal plasma rotation velocity profile can be achieved under the condition of neutral beam injection (NBI) heating. Considering the edge effect of the line of CVI 529.06 nm (n = 8∼7), which contains three lines (active exciting spectral line (ACX), passivity exciting spectral line (PCX) and electron exciting spectral line (ICE)), and using three Gaussian fitted curves, we obtain the following experimental results: the core ion temperature of HL-2A device is nearly thousands of eV, and the plasma rotation velocity reaches about 104 m · s−1. At the end of paper, some explanations are presented for the relationship between the curves and the inner physical mechanism.

Development of a spatially resolving x-ray crystal spectrometer for measurement of ion-temperature (Ti) and rotation-velocity (v) profiles in ITER

Imaging x-ray crystal spectrometer (XCS) arrays are being developed as a US-ITER activity for Doppler measurement of T(i) and v profiles of impurities (W, Kr, and Fe) with ∼7 cm (a/30) and 10-100 ms resolution in ITER. The imaging XCS, modeled after a prototype instrument on Alcator C-Mod, uses a spherically bent crystal and 2D x-ray detectors to achieve high spectral resolving power (E/dE>6000) horizontally and spatial imaging vertically. Two arrays will measure T(i) and both poloidal and toroidal rotation velocity profiles. The measurement of many spatial chords permits tomographic inversion for the inference of local parameters. The instrument design, predictions of performance, and results from C-Mod are presented.

The ITER core imaging x-ray spectrometer

The core imaging x-ray spectrometer (CIXS) is one of several ITER diagnostic systems planned for measurements of the central ion and electron temperature profiles and of the toroidal and poloidal rotation velocity profiles, Ti, Te, vϕ, and vθ respectively. The diagnostic is based on precision determinations of the Doppler broadening and centroid shift of the lines of highly ionized heavy impurities using a curved Bragg crystal spectral disperser and imager. In a departure from earlier designs, the CIXS employs a novel imaging geometry utilizing spherically bent crystals operating at a Bragg angle near 45°, which spatially and spectrally resolves the x-ray emission from the plasma. In addition, the working radiation will be the L-shell emission of highly charged tungsten ions. Particular emphasis is placed on the strong 3d5/2 → 2p3/2 electric dipole transition in neon-like tungsten W64 +. Here we present the conceptual design of the instrument, which may include an x-ray calorimeter, and discuss the spectral features used in future measurements.

Rotation Drive and Momentum Transport with Electron Cyclotron Heating in Tokamak Plasmas

The role of electron cyclotron resonance heating (ECRH) on the toroidal rotation velocity profile has been investigated in the JT-60U tokamak device by separating the effects of the change in momentum transport, the intrinsic rotation by pressure gradient, and the intrinsic rotation by ECRH. It is found that ECRH increases the toroidal momentum diffusivity and the convection velocity. It is also found that ECRH drives the codirection (co) intrinsic rotation inside the EC deposition radius and the counterdirection (ctr) intrinsic rotation outside the EC deposition radius. This ctr rotation starts from the EC deposition radius and propagates to the edge region.

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.

Momentum transport and plasma rotation profile in toroidal direction in JT-60U L-mode plasmas

The characteristics of momentum transport and plasma rotation in the toroidal direction are studied, using near-perpendicular neutral beam injection (PERP-NBI), co tangential and counter (CTR) tangential NBI in JT-60U. Diffusive and non-diffusive terms of momentum transport are evaluated from the transient analysis by using the momentum source modulation. Fast ion losses due to the toroidal field ripple, which locally induces the edge CTR rotation, are used as a novel momentum source. Parameter dependence of these transport coefficients i.e. the toroidal momentum diffusivity (χϕ) and the convection velocity (Vconv), and the relation between momentum and heat diffusivities (χi) are investigated in L-mode plasmas systematically. The toroidal momentum diffusivity increases with increasing heating power and decreases with increasing plasma current. The relation of χϕ and χi to some non-dimensional parameters is investigated. A clear dependence of χϕ/χi on normalized plasma pressure (βN) is observed. It is also found that toroidal rotation velocity profiles in the case with and without external torque input can be almost reproduced by χϕ and Vconv estimated from the transient momentum transport analysis at low β (βN < 0.4).

Certain considerations concerning the nature of radial electric field and toroidal rotation velocity profile in tokamak plasma

A new and simple approach aimed at understanding the nature of the radial electric field in some types of tokamak plasmas is presented. It is shown that the radial electric field at some point on a magnetic surface in a tokamak plasma can be divided physically into two parts. The first part is related to a very small difference between densities of electrons and ions of two component plasmas on a magnetic surface in the corotating frame. The second part is related to toroidal rotations of current layers on magnetic surfaces. A new integral equation is calculated. The efficiency of this approach is shown by means of an illustrative example of a Tore-Supra experiment.

Effects of ripple loss of fast ions on toroidal rotation in JT-60U

The driving mechanism of toroidal rotation and the momentum transport are studied on JT-60U in relation to the toroidal rotation in the direction antiparallel to the plasma current, i.e. counter (CTR) direction, with near-perpendicular neutral beam (PERP-NB) injection. Fast ion losses due to the toroidal field ripple induce CTR rotation in the peripheral region, and the magnitude of CTR rotation with PERP-NBs reduces by installing the ferritic steel tiles as a consequence of the reduction in the ripple losses. It is also found that toroidal rotation velocity profiles in the core region can be explained by momentum transport considering diffusivity and convective velocity estimated from transient momentum transport analysis in L-mode plasmas.

Toroidal rotation and momentum transport in Alcator C-Mod plasmas with no momentum input

The time evolution of toroidal rotation velocity profiles has been measured in Alcator C-Mod [Hutchinson et al., Phys. Plasmas 1, 1511 (1994)] plasmas using a tangentially viewing x-ray spectrometer array. The strong co-current toroidal rotation in enhanced Dα (EDA) high confinement mode (H-mode) plasmas is observed to propagate in from the edge on a time scale similar to the energy confinement time. The ensuing steady state rotation velocity profiles in both Ohmic and ion cyclotron range of frequencies (ICRF) heated EDA H modes, which are generated in the absence of any external momentum input, are found to be relatively flat. These profiles may be simulated by a simple diffusion model with the boundary condition of an edge rotation, which appears during the H-mode period. The observed profiles are well matched by the simulations using a momentum diffusivity of ∼0.1 m2/s, which is much larger than the calculated neo-classical value, and the momentum transport may be regarded as anomalous. The Alcator C-Mod rotation observations have been compared in detail with the calculations of neo-classical and sub-neo-classical theory, to the predictions from modeling of ICRF wave induced energetic ion orbit shifts, and to estimates from turbulence driven mechanisms. The magnitude and scalings of the observed rotation results are in accord with neo-classical and sub-neo-classical calculations, but the measured momentum diffusivity is higher than the predictions by a large factor. The prediction of rotation reversal with a high magnetic field side resonance location for ICRF wave induced ion orbit shifts has not been observed in the experiments. While the turbulence driven rotation calculations are mostly qualitative, they represent some of the observed features.

Observations of anomalous momentum transport in Alcator C-Mod plasmas with no momentum input

Anomalous momentum transport has been observed in Alcator C-Mod tokamak plasmas. The time evolution of core impurity toroidal rotation velocity profiles has been measured with a tangentially viewing crystal x-ray spectrometer array. Following the L-mode to EDA (enhanced Dα) H-mode transition in both Ohmic and ion cyclotron range of frequencies heated discharges, the ensuing co-current toroidal rotation velocity, which is generated in the absence of any external momentum source, is observed to propagate in from the edge plasma to the core with a timescale of the order of the observed energy confinement time, but much less than the neo-classical momentum confinement time. The ensuing steady state toroidal rotation velocity profiles in EDA H-mode plasmas are relatively flat, with Vϕ ∼ 50 km s−1, and the momentum transport can be simulated using a simple diffusion model. Assuming that the L–H transition produces an instantaneous edge source of toroidal torque (which disappears at the H- to L-mode transition), the momentum transport may be characterized by a diffusivity, with values of ∼0.07 m2 s−1 during EDA H-mode and ∼0.2 m2 s−1 in L-mode. These values are large compared to the calculated neo-classical momentum diffusivities, which are of the order of 0.003 m2 s−1. Velocity profiles of ELM-free H-mode plasmas are centrally peaked (with Vϕ(0) exceeding 100 km s−1 in some cases), which suggests the presence of an inward momentum pinch; the observed profiles are consistent with simulations including an edge inward convection velocity of ∼10 m s−1. In EDA H-mode discharges which develop internal transport barriers, the velocity profiles become hollow in the centre, indicating the presence of a negative radial electric field well in the vicinity of the barrier foot. Upper single null diverted and inner wall limited L-mode discharges exhibit strong counter-current rotation (with Vϕ(0)∼−60 km s−1 in some cases), which may be related to the observed higher H-mode power threshold in these configurations. For plasmas with locked modes, the toroidal rotation is observed to cease (Vϕ ⩽ 5 km s−1).

Observation of anomalous momentum transport in tokamak plasmas with no momentum input.

Anomalous momentum transport has been observed in Alcator C-Mod tokamak plasmas through analysis of the time evolution of core impurity toroidal rotation velocity profiles. Following the L-mode to EDA (enhanced D(alpha)) H-mode transition, the ensuing cocurrent toroidal rotation velocity, which is generated in the absence of any external momentum source, is observed to propagate in from the edge plasma to the core. The steady state toroidal rotation velocity profiles are relatively flat and the momentum transport can be simulated with a simple diffusion model. Velocity profiles during edge localized mode free (ELM-free) H-modes are centrally peaked, which suggests the addition of inward momentum convection. In all operating regimes the observed momentum diffusivities are much larger than the neoclassical values.

Pressure profile modification of internal transport barrier plasmas in Alcator C-Mod

Internal transport barrier (ITB) plasmas with peak pressures of 0.25 MPa and pressure gradients as large as 2.5 MPa m−1 have been produced in Alcator C-Mod using off-axis ion cyclotron range of frequencies (ICRF) heating. The onset of the ITBs is apparent when the pressure gradient exceeds 1.0 MPa m−1, which is similar to the JET criterion of ρ⋆s/L⩾0.014. Concommitant with the peaking of the core pressure as the ITB develops is a drop of the toroidal rotation velocity profile inside of the barrier foot; the maximum of the velocity gradient coincides with the peak in the pressure gradient. The quasi-coherent (QC) mode, associated with the enhanced Dα (EDA) H-mode plasmas which evolve the ITBs, breaks up and disappears as the barriers develop, even though the measured edge pedestal parameters remain fixed. The position of the ITB foot has been moved over a range of (1/3) of the plasma minor radius by varying the toroidal magnetic field. The peak in the calculated bootstrap current density profile has correspondingly been regulated over a similar range in plasma minor radius. The location of the density profile foot is found to expand as the toroidal magnetic field is reduced and the ICRF frequency is lowered. The density foot radius is relatively independent of q95, however, in a scan of the plasma current at fixed BT and wave frequency.

Theoretical interpretation of the toroidal rotation velocityobserved in Alcator C-Mod Ohmic H-mode discharges

It is shown that neoclassical theory explains quite well the origin of the co-current toroidal rotation velocity measured in the core of stationary Alcator C-Mod edge localized mode (ELM)-free Ohmic high confinement (H)-mode discharges. Both edge and core toroidal rotation velocity profiles are determined to a good approximation by the edge ion temperature and density pedestals, where the gradients are large and the plasma is in the high collisionality regime. Under these conditions, the predicted radial electric field profile is similar to those measured in the DIII-D tokamak whereas the usual expression for the poloidal velocity is modified by finite Larmor radius (FLR) effects. Over the entire plasma cross section, the expression of the toroidal velocity can approximately be cast as the product of a dimensionless non-local functional of the pedestal normalized profiles Ti(r)/Ti(rinf) and Ni(r)/Ni(rinf) with powers of the plasma density, temperature, safety factor and magnetic field at the pedestal inflexion point rinf provided the FLR related corrections are independent of the latter parameters. The collapse of the core toroidal rotation velocity when either an internal transport barrier forms (that leads to impurity accumulation), or the plasma experiences a transition from the H- to the low confinement (L)-mode, or ELMs appear, and the spin up at the L-H transition are also explained. In the edge region, power balance is consistent with the prediction from sub-neoclassical ion energy transport theory at high collisionality. The role of charge exchange neutrals is discussed and the critical density above which they are expected to noticeably slow down the rotation is estimated. The toroidal velocity gradient predicted by theory at the edge of the ELM-free Ohmic H-mode discharge mainly under study (qs = 3.4) is near the onset value for the Kelvin-Helmholtz (K-H) parallel velocity shear (PVS) instability; this result is very interesting since a transition from ELM-free to enhanced Dα (EDA) H-modes occurs at q≅3.5-4; the PVS K-H instability appears to have the characteristics of the `quasi-coherent' mode that is present in all EDA plasmas, but not in ELM-free H-modes.

Progress in internal transport barrier plasmas with lower hybrid current drive and heating in JET (Joint European Torus)

In optimized shear plasmas in the Joint European Torus [P. H. Rebut and B. E. Keen, Fusion Technol. 11, 13 (1987)], safety factor (q) profiles with negative magnetic shear are produced by applying lower hybrid (LH) waves during the plasma current ramp-up phase. These plasmas produce a barrier to the electron energy transport. The radius at which the barrier is located increases with the LH wave power. When heated with high power from ion cyclotron resonance heating and neutral beam injection, they can additionally produce transient internal transport barriers (ITBs) seen on the ion temperature, electron density, and toroidal rotation velocity profiles. Due to recent improvements in coupling, q profile control with LH current drive in ITB plasmas with strong combined heating can be explored. These new experiments have led to ITBs sustained for several seconds by the LH wave. Simulations show that the current driven by the LH waves peaks at the ITB location, indicating that it can act in the region of low magnetic shear.

Evidence for a toroidal-momentum-transport nondiffusive term from the JFT-2M tokamak.

Toroidal rotation velocity profiles are measured by multichord charge-exchange spectroscopy for discharges where the direction of the neutral beams is changed from parallel to the plasma current to antiparallel. Analysis of the transport of toroidal momentum in the transient phase suggests the existence of a nondiffusive term in the transport matrix. This nondiffusive term results in a spontaneous source of toroidal momentum in the direction antiparallel to the plasma current.

Improvement of angular momentum confinement with density peaking on ASDEX

Toroidal rotation velocity profiles during neutral beam injection on ASDEX have been investigated by means of charge exchange recombination spectroscopy. For both co- and counter-injection of neutral beams the ratio of the injected power and the line averaged electron density is found to be an essential experimental, parameter for the central rotation speed. With counter-injection, a continuous rise of rotation velocity and density is observed, indicating strong improvement of angular momentum confinement. This improvement is found to be strongly correlated with the peakedness of the density profile. Simple model calculations of momentum transport indicate that the increase of momentum confinement with density peaking can be partly attributed to the variation of torque deposition with the shape of the density profile.