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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.

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...

The linear stability of coupled collisionless trapped electron (TE) and ion temperature gradient (ITG) modes is investigated in an International Thermonuclear Experimental Reactor [C. Gormezano , Nucl. Fusion 47, S285 (2007)]-like magnetic field configuration. An advanced fluid model in the electrostatic limit and the ballooning mode formalism are used to derive an eigenvalue equation. The growth rates and real frequencies of the most unstable modes and their eigenfunctions are calculated. The coexistence of unstable ITG and TE modes and their relative strengths with respect to the fraction of trapped electrons, wave vector, and local plasma parameters, such as density gradient, electron/ion temperature gradient, and ion to electron temperature ratio are analyzed. The influence of geometrical factors, such as local/global magnetic shear and magnetic field curvature on both ITG and TE modes is also discussed.

Geometrical effects on linear stability of electrostatic resistive edge modes are investigated in the three-dimensional Wendelstein 7-X stellarator [G. Grieger et al., Plasma Physics and Controlled Nuclear Fusion Research 1990 (International Atomic Energy Agency, Vienna, 1991), Vol. 3, p. 525] and the International Thermonuclear Experimental Reactor [Progress in the ITER Physics Basis, Nucl. Fusion 7, S1, S285 (2007)]-like equilibria. An advanced fluid model is used for the ions together with the reduced Braghinskii equations for the electrons. Using the ballooning mode representation, the drift wave problem is set as an eigenvalue equation along a field line and is solved numerically using a standard shooting technique. A significantly larger magnetic shear and a less unfavorable normal curvature in the tokamak equilibrium are found to give a stronger finite-Larmor radius stabilization and a more narrow mode spectrum than in the stellarator. The effect of negative global magnetic shear in the tokamak is ...

The linear electrostatic dissipative trapped-electron mode is investigated in a quasihelically symmetric (QHS) stellarator and a configuration whose symmetry is spoiled by the addition of a mirror contribution to the magnetic spectrum. The effect of the trapped electrons is accounted for using the drift kinetic equation with an energy-dependent Krook collision operator and an effective collision frequency giving the rate of detrapping. The ballooning mode formalism and Wentzel-Kramers-Brillouin type boundary conditions are used to solve an eigenvalue problem for a drift wave equation with nearly adiabatic electrons in a fully three-dimensional magnetohydrodynamic equilibria. The trapped-electron growth rate is calulated using a perturbative approach. Multiple classes of helically localized and toroidally localized eigenfunctions in the ballooning space are calculated. The results of the QHS configuration is compared and contrasted with the results of the mirror configuration. The helically trapped modes a...

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 ...

A set of coupled nonlinear differential equations governing the dynamics of low-frequency electromagnetic waves in the presence of equilibrium sheared flow for inhomogeneous collisional magnetized plasma has been derived. In the linear limit of a uniform density plasma, it is shown that equilibrium sheared plasma flows can cause an instability of resistive Alfven-like waves. Furthermore, a quasi-stationary solution of the mode coupling equations can be represented in the form of localized vortex structures. On the other hand, the temporal behavior of the mode coupling equations is governed by six coupled equations, which are a generalization of the Lorenz-Stenflo equations and which admit chaotic trajectories.

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 illustrated. In the simulations carried out using the MMM7.1 model it is found that: The drift-resistive-inertial ballooning modes contribute to the anomalous transport primarily near the edge of the plasma; transport associated with the ion temperature gradient and trapped electron modes contribute in the core region but decrease in the region of the plasma boundary; and neoclassical ion thermal transport contributes mainly near the center of the discharge.