Search

We introduce the anti-symmetric representation of the extended magnetohydrodynamic (MHD) equations. In this representation, the use of the anti-symmetric flux operator ( ∇ · v + v · ∇ ) results in conservation theorems with discrete analogs. Inherently robust numerical applications are achieved with little effort, and conservation to machine precision is possible with simple numerical schemes. Starting from the two-fluid equations, we construct a single-fluid MHD model based on generalized center-of-mass variables for the mass ( ρ), momentum ( ρ v), and pressure ( p). This model is shown to possess identical conservation properties to the two-fluid system, with the only restriction being the use of a single temperature. Common approximations to the Braginskii heat fluxes and to the gyroviscous stress tensor are cast into our representation for convenience. The discrete conservation properties are verified using the classic Orszag–Tang vortex problem. In addition to the favorable mass, momentum, and energy conservation properties, the time reversibility of the simulations is demonstrated.

We derive a set of fluid moment equations with inherent consistency and numerical stability, conceived by exploiting the anti-symmetric nature of the plasma flow operator (∇·v+v·∇). The obtained equations can be interpreted as an alternative to the traditional Eulerian and Lagrangian representations—one in which plasma flows generate infinitesimal rotations of generalized fluid moments n, nv, and p. The continuous model has a discrete analog with exact mass, momentum, and energy conservation, which is achieved by construction through vanishing integrals of the anti-symmetric flow terms. Positivity preservation is obtained through the use of the generalized moment quantities. The conservation properties of the approach are illustrated in simulations of seeded blob propagation, where we verify numerical conservation to machine accuracy.

Ion temperature has been measured to be of the same order, or higher, than the electron temperature in the scrape-off layer (SOL) of tokamak machines, questioning its importance in determining the SOL turbulent dynamics. Here, we present a detailed analysis of finite ion temperature effects on the linear SOL instabilities, such as the resistive and inertial branches of drift waves and ballooning modes, and a discussion of the properties of the ion temperature gradient (ITG) instability in the SOL, identifying the gi 1⁄4 Ln=LTi threshold necessary to drive the mode unstable. The non-linear analysis of the SOL turbulent regimes by means of the gradient removal theory is performed, revealing that the ITG plays a negligible role in limited SOL discharges, since the ion temperature gradient is generally below the threshold for driving the mode unstable. It follows that the resistive ballooning mode is the prevailing turbulence regime for typical limited SOL parameters. The theoretical estimates are confirmed by non-linear flux-driven simulations of SOL plasma dynamics.

The propagation of blobs structures of localized enhanced plasma pressure is studied in global three dimensional simulations of a simple magnetized torus. In particular we carry out single seeded blob simulations to explore the dependence of the blob velocity with respect to its size. It is found that the velocity scaling for two dimensional blobs is satisfied in the parameter space where polarization currents are the dominant damping mechanism. On the other hand three dimensional blobs propagate faster than their two dimensional counterparts in the parallel current damping regime. A detailed analysis of the charge and current balance reveals that in fact the difference in speed is due to an overestimation of the strength of the sheath current term in the two dimensional model compared to the self consistent three dimensional model. © 2014 Euratom.

The proper boundary conditions at the magnetic presheath entrance for plasma fluid turbulence models based on the drift approximation are derived, focusing on a weakly collisional plasma sheath with Ti≪Te and a magnetic field oblique to a totally absorbing wall. First, the location of the magnetic presheath entrance is rigorously derived. Then boundary conditions at the magnetic presheath entrance are analytically deduced for v||i, v||e, n, ϕ, Te, and for the vorticity ω = ∇⊥2ϕ. The effects of E × B and diamagnetic drifts on the boundary conditions are also investigated. Kinetic simulations are performed that confirm the analytical results. Finally, the new set of boundary conditions is implemented in a three-dimensional global fluid code for the simulation of plasma turbulence and, as an example, the results of a tokamak scrape-off layer simulation are discussed. The framework presented can be generalized to obtain boundary conditions at the magnetic presheath entrance in more complex scenarios.

The cycling dynamics of the internal kink mode, which drives sawtooth oscillations in tokamak plasmas, is studied using the three dimensional, non-linear magnetohydrodynamic (MHD) code XTOR-2F [H. Lütjens and J.-F. Luciani, J. Comput. Phys. 229, 8130 (2010)]. It is found that sawtooth cycling, which is characterized by quiescent ramps and fast crashes in the experiment, can be recovered in two-fluid MHD provided that a criterion of diamagnetic stabilization is fulfilled. The simulation results indicate that diamagnetic effects alone may be sufficient to drive sawteeth with complete magnetic reconnection in high temperature Ohmic plasmas.

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...

Predictive simulations of ITER [R. Aymar et al., Plasma Phys. Control. Fusion 44, 519 (2002)], discharges are carried out for the 15MA high confinement mode (H-mode) scenario using PTRANSP, the predictive version of the TRANSP code. The thermal and toroidal momentum transport equations are evolved using turbulent and neoclassical transport models. A predictive model is used to compute the temperature and width of the H-mode pedestal. The ITER simulations are carried out for neutral beam injection (NBI) heated plasmas, for ion cyclotron resonant frequency (ICRF) heated plasmas, and for plasmas heated with a mix of NBI and ICRF. It is shown that neutral beam injection drives toroidal rotation that improves the confinement and fusion power production in ITER. The scaling of fusion power with respect to the input power and to the pedestal temperature is studied. It is observed that, in simulations carried out using the momentum transport diffusivity computed using the GLF23 model [R. Waltz et al., Phys. Plasm...

A comparison is made between two versions of the Weiland model for computing anomalous transport driven by drift modes such as the ion temperature gradient (ITG) and trapped electron mode (TEM) in tokamak plasmas. Both are quasilinear fluid models that include physical effects resulting from finite β, magnetic shear, electron-ion collisions, impurities, and fast ions. An outline of the derivation is presented for the newer Weiland19 model, which includes a more accurate description of the effects of finite β, low and negative magnetic shear, plasma elongation, varying correlation lengths, particle pinch, and momentum transport. It is shown that the two models produce nearly the same ion thermal diffusivity as a function of normalized temperature gradient in a circular plasma with moderate magnetic shear, low β, and moderately low density gradient. The models differ significantly at low magnetic shear and in elongated plasmas with high β. In addition, the two models differ significantly in the behavior of ...

A revised version of the ISLAND module [C. N. Nguyen et al., Phys. Plasmas 11, 3604 (2004)] is used in the BALDUR code [C. E. Singer et al., Comput. Phys. Commun. 49, 275 (1988)] to carry out integrated modeling simulations of DIII-D [J. Luxon, Nucl. Fusion 42, 614 (2002)], Joint European Torus (JET) [P. H. Rebut et al., Nucl. Fusion 25, 1011 (1985)], and ITER [R. Aymar et al., Plasma Phys. Control. Fusion 44, 519 (2002)] tokamak discharges in order to investigate the adverse effects of multiple saturated magnetic islands driven by neoclassical tearing modes (NTMs). Simulations are carried out with a predictive model for the temperature and density pedestal at the edge of the high confinement mode (H-mode) plasma and with core transport described using the Multi-Mode model. The ISLAND module, which is used to compute magnetic island widths, includes the effects of an arbitrary aspect ratio and plasma cross sectional shape, the effect of the neoclassical bootstrap current, and the effect of the distortion ...