Effect Of Toroidal Rotation Research Articles

High-resolution tangential absolute extreme ultraviolet arrays for radiated power density measurements on NSTX-U

The radiated-power-density diagnostic on the equatorial midplane for the NSTX-U tokamak will be upgraded to measure the radial structure of the photon emissivity profile with an improved radial resolution. This diagnostic will enhance the characterization and studies of power balance, impurity transport, and MHD. The layout and response expected of the new system is shown for different plasma conditions and impurity concentrations. The effect of toroidal rotation driving poloidal asymmetries in the core radiation from high-Z impurities is also addressed.

Effects of centrifugal modification of magnetohydrodynamic equilibrium on resistive wall mode stability

Toroidal rotation effects are self-consistently taken into account not only in the linear magnetohydrodynamic (MHD) stability analysis but also in the equilibrium calculation. The MHD equilibrium computation is affected by centrifugal force due to the toroidal rotation. To study the toroidal rotation effects on resistive wall modes (RWMs), a new code has been developed. The RWMaC modules, which solve the electromagnetic dynamics in vacuum and the resistive wall, have been implemented in the MINERVA code, which solves the Frieman–Rotenberg equation that describes the linear ideal MHD dynamics in a rotating plasma. It is shown that modification of MHD equilibrium by the centrifugal force significantly reduces growth rates of RWMs with fast rotation in the order of M2 = 0.1 where M is the Mach number. Moreover, it can open a stable window which does not exist under the assumption that the rotation affects only the linear dynamics. The rotation modifies the equilibrium pressure gradient and current density profiles, which results in the change of potential energy including rotational effects.

Effect of toroidal rotation on the geodesic acoustic mode in magnetohydrodynamics

Theoretical research on the geodesic acoustic mode (GAM) induced by equilibrium toroidal rotation flow in the tokamak plasmas is approached by using ideal magnetohydrodynamic model. The dispersion relation of the GAM is presented by taking into account magnetic field perturbations. It is shown that β can decrease the frequency of the GAM.

Stability of localized modes in rotating tokamak plasmas

The ideal magnetohydrodynamic stability is investigated of localized interchange modes in a large-aspect ratio tokamak plasma. The resulting stability criterion includes the effects of toroidal rotation and rotation shear and contains various well-known limiting cases. The analysis allows for a general adiabatic index, resulting in a stabilizing contribution from the convective effect. A further stabilizing effect from rotation exists when the angular frequency squared decreases radially more rapidly than the density. Flow shear, however, also decreases the stabilizing effect of magnetic shear through the Kelvin–Helmholtz mechanism. Numerical simulations reveal the merits and limitations of the performed local analysis.

Impact of plasma poloidal rotation on resistive wall mode instability in toroidally rotating plasmas

Stability of resistive wall mode (RWM) is investigated in a cylindrical plasma and an axisymmetric toroidal plasma by taking into account not only toroidal rotation but also poloidal rotation. Since the Doppler shifted frequency is responsible for the RWM stability, the modification of this Doppler shifted frequency by poloidal rotation affects the rotation effect on RWM. When a poloidal rotation frequency is not so large, the effect of poloidal rotation on the RWM stability can be approximately treated with the modified toroidal rotation frequency. In a toroidal plasma, this modified frequency is determined by subtracting a toroidal component of the rotation parallel to the magnetic field from the toroidal rotation frequency. The poloidal rotation that counteracts the effect of the Doppler shift strongly reduces the stabilizing effect of toroidal rotation, but by changing the rotational direction, the poloidal rotation enhances this stabilizing effect. This trend is confirmed in not only a cylindrical plasma but also a toroidal plasma. This result indicates that poloidal rotation produces the dependence of the critical toroidal rotation frequency for stabilizing RWM on the rotational direction of toroidal rotation in the same magnetic configuration.

Simulation of Toroidal Rotation Effect on Heat Flux Transport in the Edge Plasma of Small Size Divertor Tokamak

The effect of toroidal rotation on heat flux transport in the edge plasma of small size divertor was simulated by B2SOLP0.5.2D transport code. The main results of simulation shows that, the following: (1) the radial heat flux is strongly influenced by toroidal rotation. (2) The amplification of conduction part of radial heat flux imposes nonresilient profile of ion temperature, under which the effect of toroidal rotation on ion temperature profile is strong. (3) The ion distribution and its gradients are lower for counter-injection neutral beam than for co-injection neutral beam. (4) Reversal of toroidal rotation during using neutral beam injection result in reverses of radial electric field and E × B drift velocity. (5) The toroidal rotation strong influence on the ion temperature scale length of the ion temperature gradient (ITG). (6) Switch on and off all drifts leads to higher change in the ion density distribution in edge plasma of small size divertor tokamak when the unbalance neutral beam injection are considered (7) the comparison between radial heat flux at different momentum input shows that, the radial ion heat flux with larger ion temperature scale length in the case of co-injection neutral beam is larger than the ion heat flux with smaller ion temperature scale length in the case of counter-injection neutral beam.

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.

Fast dynamics of type I and grassy ELMs in JT-60U

In order to understand the physics of the ELM trigger and determine the ELM size, the fast ELM dynamics of type I and grassy ELMs have been studied in JT-60U, using new fast diagnostics with high spatial and temporal resolutions such as a lithium beam probe (Δt ∼ 0.5 ms) and a charge exchange recombination spectroscopy (Δt ∼ 2.5 ms), which can measure the electron density and the ion temperature, respectively. The evolution of the ion pressure profile in the pedestal region has been evaluated for the first time by detailed edge profile measurements. Then, the dynamics of the density, the ion temperature and the ion pressure in the ELM cycle has been investigated. The co-rotating plasmas are compared with the counter (ctr)-rotating plasmas for the understanding of the toroidal rotation effects. Type I ELMs observed in co-rotating plasmas exhibit a larger and wider ELM affected area (Δnped/nped ∼ 30%, radial extent >15 cm) than ctr-rotating plasmas (Δnped/nped ∼ 20%, radial extent ∼10 cm). Just before a type I ELM crash, the pedestal ion pressure and its maximum gradient in co-rotating plasmas are 20% and 12% higher than those in ctr-rotating plasmas, respectively. It is found that the radial extent of the ion pressure gradient at the pedestal region in co-rotating plasmas is 14% wider than that in ctr-rotating plasmas. The experimental results suggest that the ELM size is connected with the structure of the plasma pressure in the whole pedestal region. As for the dynamics of grassy ELMs, the collapse of density pedestal is smaller (<20%) and narrower (∼5 cm) than those of type I ELMs, as observed in the collapse of the electron temperature pedestal. Thus, it is confirmed that both conductive and convective losses due to grassy ELMs are small.

MINERVA: Ideal MHD stability code for toroidally rotating tokamak plasmas

A new linear MHD stability code MINERVA is developed for investigating a toroidal rotation effect on the stability of ideal MHD modes in tokamak plasmas. This code solves the Frieman–Rotenberg equation as not only the generalized eigenvalue problem but also the initial value problem. The parallel computing method used in this code realizes the stability analysis of both long and short wavelength MHD modes in short time. The results of some benchmarking tests show the validity of this MINERVA code. The numerical study with MINERVA about the toroidal rotation effect on the edge MHD stability shows that the rotation shear destabilizes the intermediate wavelength modes but stabilizes the short wavelength edge localized MHD modes, though the rotation frequency destabilizes both the long and the short wavelength MHD modes.

Geodesic Acoustic Mode Induced by Toroidal Rotation in Tokamaks

The effect of toroidal rotation on the geodesic acoustic mode (GAM) in a tokamak is studied. It is shown that, in addition to a small frequency upshift of the ordinary GAM, another GAM, with much lower frequency, is induced by the rotation. The new GAM appears as a consequence of the nonuniform plasma density and pressure created by the centrifugal force on the magnetic surfaces. Both GAMs in a rotating plasma are shown to exist both as continuum modes with finite mode numbers m and n at the rational surfaces q=m/n as well as in the form of axisymmetric modes with m=n=0.

H-mode pedestal structure in the variation of toroidal rotation and toroidal field ripple in JT-60U

The effects of toroidal rotation and toroidal field (TF) ripple on the edge pedestal structure and edge-localized-modes (ELMs) were examined in JT-60U. The amplitude of the TF ripple was changed by the installation of ferritic steel tiles (FSTs). The profile of toroidal rotation VT became less counter with FSTs, particularly in the case where co-NBI was used in a large volume configuration. In this case, the plasma pressure was raised across the whole profile of the plasma. At the plasma edge, higher pedestal temperature was obtained with the growth of pedestal width. However, the effect of FSTs became less significant in a small volume configuration. As the VT became less counter at the pedestal, ELM frequency fELM was reduced and ELM energy loss ΔWELM was increased at fixed power crossing the separatrix Psep. The observed larger ELM energy drop at VT in a relatively co-direction involves the ELM perturbations of the electron temperature profile across an ELM that extends radially more inward. In addition, the inter-ELM transport loss is reduced and the pedestal pressure pped is weakly raised. The effect of FSTs appeared clearly in the large volume configuration where pped is raised even at a given VT at the pedestal while pped is not changed by FSTs at the small volume configuration. This suggests that the reduction of the TF ripple, the magnitude of which can affect the VT profile, plays a role in the increasing of pped. For increased pped due to the use of co-NBI and the reduction of TF ripple, the spatial width of the pedestal ion temperature became greater.

The effect of toroidal plasma rotation on sawteeth in MAST

Results from MAST concerning the effect of toroidal rotation driven by neutral beam injection (NBI) on sawteeth are presented. The sawtooth period is shown to increase as the co-NBI power, and thus the toroidal plasma rotation, is increased. As the counter-NBI power is increased, the sawtooth period decreases to a minimum that is shorter than in Ohmically heated plasmas, before lengthening at high toroidal flows. The sawtooth period reaches a minimum when the sawtooth precursor changes the direction of rotation. This can be interpreted as the counter-NBI inducing a toroidal flow which balances the intrinsic ion diamagnetic rotation of the plasma, at which point the mode precursor changes direction. Magnetohydrodynamic stability analyses of the ideal n = 1 internal kink mode with respect to toroidal rotation at finite ion diamagnetic frequency show good accordance with the experimental results. When MAST discharges are modelled at the experimental ion diamagnetic frequency, , the ideal n = 1 internal kink mode is stabilized completely by co-rotation approaching the ion sound speed. When the rotation is oriented in the counter- direction, the mode is initially driven more unstable, before being stabilized by high toroidal flows. Experimentally, the radial extent of the sawtooth crash, and hence the q = 1 surface, varies with respect to the sawtooth period. Stability analyses show that the marginally stable radial location of the q = 1 surface reaches a minimum at approximately the same counter-toroidal rotation as that which minimizes the sawtooth period experimentally. The magnitude of the toroidal rotation at the q = 1 surface determines the stabilizing effect of the toroidal flow upon the ideal n = 1 internal kink mode.

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

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

Steady state operation research in JT-60U with extended pulse length

Recent experimental results for steady state operation research in JT-60U are presented with emphasis on extension of sustained duration of high performance. The duration of heating has been extended from 10 to 30 s, and plasma properties and dynamics have been investigated in a long time scale exceeding the current diffusion time and close to the wall saturation time on ELMy H-mode, high βp H-mode and reversed shear H-mode regimes. The duration of sustainment of high beta and/or a large fraction of bootstrap current has been extended. The particle control with the saturated wall has been studied. Development of real-time control of q profile and effects of toroidal rotation on ELMs and the QH-mode are also discussed.

Stabilization of the quasi-interchange instability in low-shear tokamak plasmas by toroidal rotation

The effect of toroidal rotation on the ideal magnetohydrodynamic stability of the internal kink, or quasi-interchange, mode in tokamak plasmas with the safety factor, q, close to unity within a wide region in the plasma core is analysed. For equilibria with a large aspect ratio and circular cross section it is shown that rigid, toroidal rotation stabilizes the quasi-interchange mode if the rotation frequency, Ω, exceeds a critical frequency, Ωcrit, and a simple expression for Ωcrit is derived. Unless the plasma pressure and the radial extent of the low-shear region are both rather large, rotation frequencies of the order of a few per cent of the Alfvén frequency are found to be sufficient to stabilize the quasi-interchange mode. The stabilization is caused by the nonuniform plasma density and the associated Brunt–Väisälä (BV) frequency created by the centrifugal force. When Ω exceeds Ωcrit, the quasi-interchange instability transforms into a stable oscillation with a frequency close to the lowest BV-frequency in the low-shear region of the plasma.

High-n ballooning instabilities in toroidally rotating tokamaks

High-n ballooning instabilities are studied with an initial-value code for toroidally rotating tokamaks, where n is a toroidal mode number. The effects of toroidal rotation are classified into two parts: (i) increase of effective pressure gradient due to the centrifugal force of the toroidal flow, and (ii) averaging of local magnetic equilibrium configuration over a period of poloidal angle in the case of finite flow-velocity shear. With the increase of effective pressure gradient in the rigid-rotation case, the growth rate of ballooning mode increases in the low-pressure regime as the toroidal flow velocity is increased, whereas it decreases in the high-pressure regime. The flow-velocity shear generally reduces the growth rate of the high-n ballooning mode by the averaging of the local equilibrium magnetic configuration. However, it is found that the ballooning mode becomes unstable by increasing the flow-velocity shear in a low-aspect-ratio tokamak. This is understood by the change of the local magnetic configuration, and by the changes of both the mode structure and the potential function in the ballooning space.

Effect of toroidal rotation on the localized modes in low beta circular tokamaks

Effects of finite toroidal rotation on the stability of radially localized ideal magnetohydrodynamic (MHD) modes are investigated analytically for low-beta, large aspect-ratio circular tokamaks. Specifically, it is found that, for the Mercier interchange mode, a finite rotation shear is generally stabilizing. For the double internal kink mode, however, finite toroidal rotation shear further enhances the ballooning destabilizing effect.

Rotating toroidal equilibria of quasi-neutral and non-neutral plasmas

Starting from the fundamental ion and electron fluid equations, a “master” equilibrium equation set is constructed for axisymmetric toroidal plasmas. These equations retain the effects of different ion and electron densities, temperatures, sheared rotation, and electric forces. The master equation is then examined in various limits including the non-neutral plasma limit. An ordering is assumed which makes the effects of the Reynolds stress, pressure, magnetic stress, and electric field stress all comparable emphasizing the natural transition from the non-neutral case to the quasi-neutral one. For sub-relativistic flows, charge separation effects are only significant for nearly force-free plasmas. A set of equilibrium equations are derived for three different cases: (A) ni≈ne, (B) ni≠ne≠0, and (C) ni=0 and ne≠0. In the pure electron plasma case, the resulting equilibrium equation includes the effects of toroidal rotation, poloidal magnetic field, and electron pressure extending the equation of Daugherty and Levy [Phys. Fluids 10, 155 (1967)].

Toroidal rotation effect on the ballooning modes of low frequency under gyrokinetic description

Gyrokinetic theory for ballooning modes with frequency lower than the thermal ion bounce frequency is presented. Due to a vast difference of the centrifugal and the Coriolis forces experienced by ions and electrons, the parallel electric field effect is found to be excited even in this low frequency case. Nevertheless, it is proved that, under suitable ordering assumptions, the magnetohydrodynamic (MHD)-structure-like ballooning mode equation can still be obtained. The kinetic effects are found to appear in three aspects: enlarging the magnitude of the apparent inertia, resulting in a real shift of the marginal frequency, and contributing a stabilizing term.

Self-consistent analysis of steady state Tokamaks sustained by beam-driven and bootstrap currents

Beam-driven steady state Tokamaks of moderate size (R0=4.55 m) are analyzed by an optimizing beam current drive analysis code, which consistently includes MHD equilibrium, kink and ballooning stability analysis, bootstrap current, global power balance and toroidal momentum balance calculations. The maximum Q values attained are Q=7-9 with fusion powers of Pf=500-800 MW. L-mode confinement given by Kaye-Goldston scaling is sufficient to sustain steady state conditions. The Q value is nearly doubled due to the bootstrap current and the Ti>Te feature of beam-driven Tokamaks. The optimum beam energy is 1.0-1.2 MeV and the toroidal rotation effects are negligible.