Advanced transport modelling in tokamak plasmas (original) (raw)
Related papers
Toroidal rotation in tokamak plasmas
Nuclear Fusion, 2009
A comprehensive transport equation for the evolution of toroidal rotation in tokamak plasmas is developed from the two-fluid momentum equations taking account of the constraints imposed by faster time scale processes. In addition to the usual collision-induced and microturbulence-induced transport processes, the plasma toroidal rotation equation includes the effects of non-axisymmetric field errors produced by external fields and MHD-type instabilities in the plasma. Non-resonant field errors produce a toroidal torque throughout the plasma that relaxes the toroidal flow to an "intrinsic" ion-temperature-gradient diamagnetic-type flow in the direction counter to the plasma current. A resonant field error causes a toroidal torque localized near its rational surface. The combination of resonant and non-resonant field errors is found to predict scalings for error field penetration and mode locking thresholds that are in closer agreement with empirical data from tokamak plasmas.
Canonical profiles and transport model for the toroidal rotation in tokamaks
Plasma Physics and Controlled Fusion, 2011
The equilibrium equation for a rotating plasma is constructed supposing the thermal Mach number is much less than unity. The canonical profile of angular rotation velocity is defined as the profile which minimizes the total plasma energy while conserving toroidal current and obeying the equilibrium condition. The transport model based on this canonical profile, with stiffness calibrated by JET data, reasonably describes the velocity of the forced toroidal rotation. The RMS deviations of the calculated rotation profiles from the experimental ones do not exceed 10-15%. The developed model is also applied to the modeling of MAST rotation.
Transport equations in tokamak plasmas
Physics of Plasmas, 2010
Tokamak plasma transport equations are usually obtained by flux surface averaging the collisional Braginskii equations. However, tokamak plasmas are not in collisional regimes. Also, ad hoc terms are added for: neoclassical effects on the parallel Ohm's law; fluctuation-induced transport; heating, current-drive and flow sources and sinks; small magnetic field non-axisymmetries; magnetic field transients etc. A set of self-consistent second order in gyroradius fluid-moment-based transport equations for nearly axisymmetric tokamak plasmas has been developed using a kinetic-based approach. The derivation uses neoclassical-based parallel viscous force closures, and includes all the effects noted above. Plasma processes on successive time scales and constraints they impose are considered sequentially: compressional Alfvén waves (Grad-Shafranov equilibrium, ion radial force balance); sound waves (pressure constant along field lines, incompressible flows within a flux surface); and collisions (electrons, parallel Ohm's law; ions, damping of poloidal flow). Radial particle fluxes are driven by the many second order in gyroradius toroidal angular torques on a plasma species: 7 ambipolar collision-based ones (classical, neoclassical etc.) and 8 non-ambipolar ones (fluctuation-induced, polarization flows from toroidal rotation transients etc.). The plasma toroidal rotation equation results from setting to zero the net radial current induced by the non-ambipolar fluxes. The radial particle flux consists of the collision-based intrinsically ambipolar fluxes plus the non-ambipolar fluxes evaluated at the ambipolarity-enforcing toroidal plasma rotation (radial electric field). The energy transport equations do not involve an ambipolar constraint and hence are more directly obtained. The "mean field" effects of microturbulence on the parallel Ohm's law, poloidal ion flow, particle fluxes, and toroidal momentum and energy transport are all included selfconsistently. The final equations describe radial transport of plasma toroidal rotation, and poloidal and toroidal magnetic fluxes, as well as the usual particle and energy transport.
Turbulent transport in tokamak plasmas with rotational shear
Nonlinear gyrokinetic simulations have been conducted to investigate turbulent transport in tokamak plasmas with rotational shear. At sufficiently large flow shears, linear instabilities are suppressed, but transiently growing modes drive subcritical turbulence whose amplitude increases with flow shear. This leads to a local minimum in the heat flux, indicating an optimal E × B shear value for plasma confinement. Local maxima in the momentum fluxes are also observed, allowing for the possibility of bifurcations in the E × B shear. The sensitive dependence of heat flux on temperature gradient is relaxed for large flow shear values, with the critical temperature gradient increasing at lower flow shear values. The turbulent Prandtl number is found to be largely independent of temperature and flow gradients, with a value close to unity.
Multi-mode modeling of toroidal momentum confinement in tokamaks
It is important to predict the plasma toroidal rotation in tokamaks because of the large impact of rotation on plasma confinement, fusion power production, and large scale instabilities such as resistive wall modes and neoclassical tearing modes. In tokamak discharges driven with a sufficiently large neutral beam torque, the gradient in toroidal plasma rotation produces a dominant contribution to flow shear, which reduces turbulent transport and increases confinement . It is believed that most of flux of momentum observed in tokamaks [2] is driven by ion temperature gradient (ITG) or trapped electron modes (TEM).
Integrated Modeling Simulations of Toroidal Momentum Transport in Tokamaks
2008
Simulations of JET H-mode and hybrid discharges are carried out using the PTRANSP predictive integrated modeling code to compute the time evolution of the plasma toroidal rotation frequency profile as well as the temperature and current density profiles. Momentum and thermal transport coefficients are computed using the recently advanced Weiland model together with a model for transport driven by electron temperature gradient (ETG) modes as well as neoclassical transport. Corresponding simulations are also carried out using the GLF23 transport model together with neoclassical transport. The new version of the Weiland transport model includes inward convection of momentum driven by the drift mode turbulence. Under appropriate conditions, additional momentum transport is driven by convection of ions. In neutral beam injected discharges, the source of torque in the plasma core is computed using the NUBEAM module. Results of predictive simulations are compared with experimental data for H-mode and hybrid tokamak discharges over a wide range of injected torque per particle.
Transport bifurcation induced by sheared toroidal flow in tokamak plasmas
Physics of Plasmas, 2011
Abstract: First-principles numerical simulations are used to describe a transport bifurcation in a differentially rotating tokamak plasma. Such a bifurcation is more probable in a region of zero magnetic shear than one of finite magnetic shear because in the former case the component of the sheared toroidal flow that is perpendicular to the magnetic field has the strongest suppressing effect on the turbulence. In the zero-magnetic-shear regime, there are no growing linear eigenmodes at any finite value of flow shear. However, subcritical ...
Simulations of ITB H-Mode Tokamak Plasmas with Predictive Toroidal Velocity Model
2010
A model for predicting toroidal velocity in H-mode tokamak plasma after neutral beam heating is turned on is implemented in an integrated predictive modelling code BALDUR in order to self-consistently simulate the time-evolution of plasma current, temperature, and density profiles in tokamaks. In this model, the toroidal velocity is developed according to a theory of electromagnetism in which the toroidal velocity can be obtained from a current density flow in toroidal direction. The core transport model used in these simulations is a combination of a neoclassical transport model called NCLASS, and an anomalous transport model, semi-empirical Mixed Bohm/gyro-Bohm (Mixed B/gB) that includes ITB effects. The boundary condition of the plasma is assumed to be at the top of the pedestal. The pedestal temperature is calculated using a theory-based pedestal model which is based on a combination of magnetic and flow shear stabilization pedestal width scaling and an infinite-n ballooning pre...
Physics of Plasmas, 1998
Sheared rotation dynamics are widely believed to have significant influence on experimentally-observed confinement transitions in advanced operating modes in major tokamak experiments, such as the Tokamak Fusion Test Reactor ͑TFTR͒ ͓D. J. Grove and D. M. Meade, Nucl. Fusion 25, 1167 ͑1985͔͒, with reversed magnetic shear regions in the plasma interior. The high-n toroidal drift modes destabilized by the combined effects of ion temperature gradients and trapped particles in toroidal geometry can be strongly affected by radially-sheared toroidal and poloidal plasma rotation. In previous work with the FULL linear microinstability code, a simplified rotation model including only toroidal rotation was employed, and results were obtained. Here, a more complete rotation model, which includes contributions from toroidal and poloidal rotation and the ion pressure gradient to the total radial electric field, is used for a proper self-consistent treatment of this key problem. Relevant advanced operating mode cases for TFTR are presented. In addition, the complementary problem of the dynamics of fluctuation-driven E؋B flow is investigated by an integrated program of gyrokinetic simulation in annulus geometry and gyrofluid simulation in flux tube geometry.
Transport and Turbulence with Innovative Plasma Shapes in the TCV Tokamak
2010
We present recent results on turbulence measurements in TCV L-mode plasmas. It has been shown that the heat transport is reduced by a factor of two for a plasma at negative triangularity compared with a plasma at positive triangularity. This transport reduction is reflected in the reduction of the temperature fluctuation level, in the low frequency part of the spectrum (20-150 kHz), measured by correlation ECE in the outer equatorial plane. Moreover, the radial correlation length of the turbulence is typically reduced by a factor of two at negative triangularity compared with positive triangularity. Nonlinear gyrokinetic simulations predict that the TEM turbulence might be dominant for these TCV plasmas. The TEM induced transport is shown to decrease with decreasing triangularity and increasing collisionality. Both dependences are in fairly good agreement with experimental observations. We also report on an innovative divertor magnetic configuration: the snowflake (SF) divertor whose properties are expected to affect the local heat load to the divertor plates in particular during ELMs when compared with the classical single-null (SN) divertor. In L-mode plasmas, the intermittent particle and heat transport in the SOL is associated with the presence of "blobs" propagating in the radial direction. Intermittency is compared between SN and SF configurations by looking at the statistical properties of the ion saturation current J sat measured with Langmuir probes (LPs) in the LFS scrape-off layer. For ELMy H-mode SF plasmas, the time evolution of J sat during ELMs is estimated with LPs covering the strikepoints target zones.