T. Rafiq

Physics basis of Multi-Mode anomalous transport module

The derivation of Multi-Mode anomalous transport module version 8.1 (MMM8.1) is presented. The MMM8.1 module is advanced, relative to MMM7.1, by the inclusion of peeling modes, dependence of turbulence correlation length on flow shear, electromagnetic effects in the toroidal momentum diffusivity, and the option to compute poloidal momentum diffusivity. The MMM8.1 model includes a model for ion temperature gradient, trapped electron, kinetic ballooning, peeling, collisionless and collision dominated magnetohydrodynamics modes as well as model for electron temperature gradient modes, and a model for drift resistive inertial ballooning modes. In the derivation of the MMM8.1 module, effects of collisions, fast ion and impurity dilution, non-circular flux surfaces, finite beta, and Shafranov shift are included. The MMM8.1 is used to compute thermal, particle, toroidal, and poloidal angular momentum transports. The fluid approach which underlies the derivation of MMM8.1 is expected to reliably predict, on an energy transport time scale, the evolution of temperature, density, and momentum profiles in plasma discharges for a wide range of plasma conditions.

Development of drift-resistive-inertial ballooning transport model for tokamak edge plasmas

A new model is developed for transport driven by drift-resistive-inertial ballooning modes (DRIBMs) in axisymmetric tokamak plasmas. The model is derived using two-fluid reduced Braginskii equations in a generalized s−α geometry. The unified theory includes diamagnetic effects, parallel electron and ion dynamics, electron inertia, magnetic perturbations, transverse particle diffusion, gyroviscous stress terms, electron and ion equilibrium temperature gradients, and temperature perturbations. A mixing length approximation is used to compute electron and ion thermal transport as well as particle fluxes from eigenvalues and eigenvectors of the linearized equations. The prediction for the saturation level is obtained by balancing the DRIBM growth rate against the nonlinear E×B convection. The parametric dependence of DRIBMs is investigated in systematic scans over density gradient, electron and ion temperature gradients, magnetic-q, collision frequency, magnetic shear, and Larmor radius. The DRIBM threshold ...

Integrated modelling for prediction of optimized ITER performance

ITER hybrid and target steady-state fusion burn scenarios are simulated using the PTRANSP integrated modelling code together with input from the TSC code. In the hybrid scenarios, the majority of the current is driven inductively; whereas, for the target steady-state scenarios, approximately 22% of the current (at 1000 s) is driven inductively with the remaining current driven by the bootstrap, neutral beam and radio frequency sources. Predictive simulations are carried out using either the new Multi-Mode or the GLF23 anomalous transport model. Momentum transport is used to compute the toroidal angular frequency profile which, in turn, is used to compute the self-consistent flow shear suppression of anomalous transport. The simulations of the hybrid scenario indicate that the fusion power production at 1000 s will be approximately 500 MW corresponding to a fusion Q = 9.4. The fusion power predicted in the simulations of the target steady-state scenarios is found to depend on the time dependence of the input heating and associated current drive. It is found that turning off some components of auxiliary heating causes the fusion power production to increase. The fusion power obtained in the target steady-state scenarios, depending on the transport model and input injected power, ranges from 168 MW up to 226 MW, corresponding to a fusion Q ranging from 2.0 to 6.8.

Local magnetic shear and drift waves in stellarators

A study of the effect of local magnetic shear on the drift wave stability is presented. The eigenvalue problem for the drift wave equation is solved numerically in fully three-dimensional stellarator plasma using the ballooning mode formalism. It is found that negative local magnetic shear has a stabilizing effect on the drift wave instability and positive local shear is destabilizing. This is in agreement with the effect of negative global magnetic shear in tokamaks and also agrees with the simple estimates. As a consequence the highly unstable modes found on a specific magnetic surface are localized in the region of positive local magnetic shear.

A comparison of drift wave stability in stellarator and tokamak geometry

The influence of plasma geometry on the linear stability of electrostatic ion-temperature-gradient driven drift modes (ITG modes) is investigated. An advanced fluid model is used for the ions together with Boltzmann distributed electrons. The derived eigenvalue equation is solved numerically. A comparison is made between an H – 1NF [Fusion Technol. 17, 123 (1990)] like stellarator equilibrium, a numerical tokamak equilibrium and the analytical s - alpha equilibrium. The numerical and the analytical tokamak are found to be in good agreement in the low inverse aspect ratio limit. The growth rates of the tokamak and stellarator are comparable whereas the modulus of the real frequency is substantially larger in the stellarator. The threshold in Ln/LT for the stellarator is found to be somewhat larger. In addition, a stronger stabilization of the ITG mode growth is found for large L n / R in the stellarator case.

Integrated modeling of temperature profiles in L-mode tokamak discharges

Simulations of doublet III-D, the joint European tokamak, and the tokamak fusion test reactor L-mode tokamak plasmas are carried out using the PTRANSP predictive integrated modeling code. The simulation and experimental temperature profiles are compared. The time evolved temperature profiles are computed utilizing the Multi-Mode anomalous transport model version 7.1 (MMM7.1) which includes transport associated with drift-resistive-inertial ballooning modes (the DRIBM model [T. Rafiq et al., Phys. Plasmas 17, 082511 (2010)]). The tokamak discharges considered involved a broad range of conditions including scans over gyroradius, ITER like current ramp-up, with and without neon impurity injection, collisionality, and low and high plasma current. The comparison of simulation and experimental temperature profiles for the discharges considered is shown for the radial range from the magnetic axis to the last closed flux surface. The regions where various modes in the Multi-Mode model contribute to transport are ...

Ion-temperature-gradient modes in stellarator geometry

The ion-temperature-gradient (ITG)-driven drift mode is studied in three-dimensional stellarator geometry using a two-fluid reactive model in the electrostatic limit. The model includes first-order FLR effect in the presence of parallel ion dynamics and using the Boltzmann distribution for the electrons. The resulting eigenvalue is solved numerically using the ballooning mode theory. The results are contrasted with the corresponding tokamak results with positive shear. In stellarators, the level of the maximum growth rate of the ITG mode is found to be smaller and the threshold (ηi2.2) is somewhat higher. The effects of small and large temperature ratios and density gradients are found to be stabilizing on electrostatic ITG modes in stellarators.

Simulation of electron thermal transport in H-mode discharges

Electron thermal transport in DIII-D H-mode tokamak plasmas [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] is investigated by comparing predictive simulation results for the evolution of electron temperature profiles with experimental data. The comparison includes the entire profile from the magnetic axis to the bottom of the pedestal. In the simulations, carried out using the automated system for transport analysis (ASTRA) integrated modeling code, different combinations of electron thermal transport models are considered. The combinations include models for electron temperature gradient (ETG) anomalous transport and trapped electron mode (TEM) anomalous transport, as well as a model for paleoclassical transport [J. D. Callen, Nucl. Fusion 45, 1120 (2005)]. It is found that the electromagnetic limit of the Horton ETG model [W. Horton et al., Phys. Fluids 31, 2971 (1988)] provides an important contribution near the magnetic axis, which is a region where the ETG mode in the GLF23 model [R. E. Waltz et al., Phy...

Unified theory of resistive and inertial ballooning modes in three-dimensional configurations

Analytic results for the stability of resistive ballooning modes (RBMs) and electron inertial ballooning modes are obtained using a two-scale analysis. This work generalizes previous calculations used for axisymmetric s−α geometry [R. H. Hastie, J. J. Ramos, and F. Porcelli, Phys. Plasmas 10, 4405 (2003)] to general three-dimensional geometry. A unified theory is developed for RBMs and inertial ballooning modes, in which the effects of both ideal magnetohydrodynamic free energy (as measured by the asymptotic matching parameter Δ′) and geodesic curvature drives in the nonideal layer are included in the dispersion relation. This unified theory can be applied to determine the stability of drift-resistive-inertial ballooning modes in the low temperature edge regions of tokamak and stellarator plasmas where steep density gradients exist.

Drift wavs in helically symmetric stellarators

The local linear stability of electron drift waves and ion temperature gradient modes (ITG) is investigated in a quasihelically symmetric (QHS) stellarator and a conventional asymmetric (Mirror) stellarator. The geometric details of the different equilibria are emphasized. Eigenvalue equations for the models are derived using the ballooning mode formalism and solved numerically using a standard shooting technique in a fully three-dimensional stellarator configuration. While the eigenfunctions have a similar shape in both magnetic geometries, they are slightly more localized along the field line in the QHS case. The most unstable electron drift modes are strongly localized at the symmetry points (where stellarator symmetry is present) and in the regions where normal curvature is unfavorable and magnitude of the local magnetic shear and magnetic field is minimum. The presence of a large positive local magnetic shear in the bad curvature region is found to be destabilizing. Electron drift modes are found to ...