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Notes: Gyrocenter-gauge kinetic theory is developed as an extension of the existing gyrokinetic theories. In essence, the formalism introduced here is a kinetic description of magnetized plasmas in the gyrocenter coordinates which is fully equivalent to the Vlasov–Maxwell system in the particle coordinates. In particular, provided the gyroradius is smaller than the scale-length of the magnetic field, it can treat high-frequency range as well as the usual low-frequency range normally associated with gyrokinetic approaches. A significant advantage of this formalism is that it enables the direct particle-in-cell simulations of compressional Alfvén waves for magnetohydrodynamic (MHD) applications and of rf (radio frequency) waves relevant to plasma heating in space and laboratory plasmas. The gyrocenter-gauge kinetic susceptibility for arbitrary wavelength and arbitrary frequency electromagnetic perturbations in a homogeneous magnetized plasma is shown to recover exactly the classical result obtained by integrating the Vlasov–Maxwell system in the particle coordinates. This demonstrates that all the waves supported by the Vlasov–Maxwell system can be studied using the gyrocenter-gauge kinetic model in the gyrocenter coordinates. This theoretical approach is so named to distinguish it from the existing gyrokinetic theory, which has been successfully developed and applied to many important low-frequency and long parallel wavelength problems, where the conventional meaning of "gyrokinetic" has been standardized. Besides the usual gyrokinetic distribution function, the gyrocenter-gauge kinetic theory emphasizes as well the gyrocenter-gauge distribution function, which sometimes contains all the physics of the problems being studied, and whose importance has not been realized previously. The gyrocenter-gauge distribution function enters Maxwell's equations through the pull-back transformation of the gyrocenter transformation, which depends on the perturbed fields. The efficacy of the gyrocenter-gauge kinetic approach is largely due to the fact that it directly decouples particle's gyromotion from its gyrocenter motion in the gyrocenter coordinates. As in the case of kinetic theories using guiding center coordinates, obtaining solutions for this kinetic system involves only following particles along their gyrocenter orbits. However, an added advantage here is that unlike the guiding center formalism, the gyrocenter coordinates used in this theory involves both the equilibrium and the perturbed components of the electromagnetic field. In terms of solving the kinetic system using particle simulation methods, the gyrocenter-gauge kinetic approach enables the reduction of computational complexity without the loss of important physical content. © 2000 American Institute of Physics.

Notes: Theory of E×B shear suppression of turbulence in toroidal geometry [Phys. Plasmas 2, 1648 (1995)] is extended to include fast time variations of the E×B flows often observed in nonlinear simulations of tokamak turbulence. It is shown that the quickly time varying components of the E×B flows, while they typically contribute significantly to the instantaneous E×B shearing rate, are less effective than the slowly time varying components in suppressing turbulence. This is because the shear flow pattern changes before eddies get distorted enough. The effective E×B shearing rate capturing this important physics is analytically derived and estimated from zonal flow statistics of gyrofluid simulation. This provides new insights into understanding recent gyrofluid and gyrokinetic simulations that yield a reduced, but not completely quenched, level of turbulence in the presence of turbulence-driven zonal flows. © 1999 American Institute of Physics.

Notes: A fully three-dimensional gyrokinetic particle code using magnetic coordinates for general geometry has been developed and applied to the investigation of zonal flows dynamics in toroidal ion-temperature-gradient turbulence. Full torus simulation results support the important conclusion that turbulence-driven zonal flows significantly reduce the turbulent transport. Linear collisionless simulations for damping of an initial poloidal flow perturbation exhibit an asymptotic residual flow. The collisional damping of this residual causes the dependence of ion thermal transport on the ion–ion collision frequency, even in regimes where the instabilities are collisionless. © 2000 American Institute of Physics.

Notes: 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 (TFTR) [D. J. Grove and D. M. Meade, Nucl. Fusion 25, 1167 (1985)], 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. © 1998 American Institute of Physics.

Notes: A high-n stability code, HINST, has been developed to study the stability of TAE (toroidicity induced Alfvén eigenmodes) in large tokamaks such as the International Thermonuclear Experimental Reactor (ITER) [D. E. Post, Plasma Physics and Controlled Nuclear Fusion Research (International Atomic Energy Agency, Vienna, 1991), Vol. 3, p. 239] where the spectrum of unstable TAE modes is shifted toward medium to high-n modes. The code solves the two-dimensional (2-D) eigenmode problem by expanding the eigenfunction in terms of basis functions. Based on the Fourier-ballooning formalism the eigenmode problem is reduced to a system of coupled one-dimensional equations, which is solved numerically by using the finite element method. The numerical method allows one to include nonperturbatively nonideal effects such as: finite ion Larmor radius, trapped electron collisional damping, etc. The 2-D numerical results of TAE and resonance TAE (RTAE) modes are compared with those from local ballooning calculations and the global magnetohydrodynamic nonvariational code NOVA [C. Z. Cheng and M. S. Chance, J. Comput. Phys. 71, 124 (1987)]. The results show that for ITER-like plasma parameters, TAE and RTAE modes can be driven unstable by alpha particles for n=10–20. The growth rate for the most unstable mode is within the range γ/ωA(similar, equals)0.3%–1.5%. The most unstable modes are localized near r/a(similar, equals)0.5 and have a broad radial mode envelope width. © 1998 American Institute of Physics.

Notes: A linear gyrokinetic system for arbitrary wavelength electromagnetic modes is developed. A wide range of modes in inhomogeneous plasmas, such as the internal kink modes, the toroidal Alfvén eigenmode (TAE) modes, and the drift modes, can be recovered from this system. The inclusion of most of the interesting physical factors into a single framework enables one to look at many familiar modes simultaneously, and thus to study the modifications of and the interactions between them in a systematic way. Especially, it is possible to investigate self-consistently the kinetic magnetohydrodynamics (MHD) phenomena entirely from the kinetic side. Phase space Lagrangian Lie perturbation methods and a newly developed computer algebra package for vector analysis in general coordinate system are utilized in the analytical derivation. In tokamak geometries, a two-dimensional finite element code has been developed and tested. In this paper, the basic theoretical formalism and some of the preliminary results are presented. © 1998 American Institute of Physics.

Notes: The role of E×B flow shear on confinement enhancement in the DIII-D tokamak [Plasma Physics and Controlled Nuclear Fusion Research, 1986 (International Atomic Energy Agency, Vienna, 1987), Vol. 1, p. 159] high internal inductance discharges with high-confinement edge is investigated experimentally using a nonaxisymmetric poloidal magnetic-field perturbation from an external coil to drag down the plasma toroidal rotation. At similar values of internal inductance, discharges which rotate faster and have a stronger E×B flow shear have better confinement. These results indicate that E×B flow shear likely plays an important role in the confinement enhancement of these discharges. © 1998 American Institute of Physics.

Notes: Neoclassical transport in the presence of large ion orbits is investigated. The study is motivated by the recent experimental results that ion thermal transport levels in enhanced confinement tokamak plasmas fall below the "irreducible minimum level" predicted by standard neoclassical theory. This apparent contradiction is resolved in the present analysis by relaxing the basic neoclassical assumption that the ions orbital excursions are much smaller than the local toroidal minor radius and the equilibrium scale lengths of the system. Analytical and simulation results are in agreement with trends from experiments. The development of a general formalism for neoclassical transport theory with finite orbit width is also discussed. © 1997 American Institute of Physics.

Notes: Advanced tokamak configurations can have improved stability properties for high-n microinstabilities such as the toroidal drift mode (trapped-electron-ηi mode) and the kinetically-calculated magnetohydrodynamic (MHD) ballooning mode. A promising means to achieve this end involves employing tokamak configurations with very small aspect ratio, as in the proposed National Spherical Tokamak Experiment (NSTX) [M. Ono et al., Bull. Am. Phys. Soc. 40, 1655 (1995)] or the existing Small Tight Aspect Ratio Tokamak (START) experiment [R. J. Colchin et al., Phys. Fluids B 5, 2481 (1993)]. Kinetic instabilities are analyzed here using a comprehensive toroidal eigenvalue code with realistic equilibria for cases based on NSTX and START along with artificial cases to study parametric sensitivities. It is found that, as the aspect ratio decreases, the amount of "bad'' magnetic curvature decreases, causing stabilization of both electrostatic and electromagnetic high-n instabilities at sufficiently small aspect ratio. © 1996 American Institute of Physics.

Notes: The kinetic stability properties in a number of high performance discharges from the DIII-D tokamak [R. D. Stambaugh for the DIII-D Team, Plasma Physics and Controlled Nuclear Fusion Research, 1994 (International Atomic Energy Agency, Vienna, 1995), Vol. 1, p. 83] have been analyzed utilizing a comprehensive kinetic eigenvalue code. The instability considered is the toroidal drift mode [trapped-electron-ion temperature gradient (ηi) mode]. This code has been interfaced with equilibria specific to DIII-D plasmas. Experimentally measured kinetic profile data, along with motional stark effect data and external magnetic data, was used, and the corresponding magnetohydrodynamic (MHD) equilibria were computed numerically. In particular, a low confinement mode (L-mode) case, a high-li high confinement mode (H-mode) case, a very high confinement mode (VH-mode) case, and a high plasma pressure/poloidal magnetic pressure (βp) case have been analyzed. For the L-mode case, a wide region of instability was found, while for the H-mode and VH-mode and high-βp cases, only relatively narrow regions of instability were found. An assessment of the influence of velocity-shear flow on these instabilities has also been made, as well as of changes in the electron and ion temperature gradients and density gradients. While the experimental values of the sheared toroidal flow velocity are not sufficient to stabilize the instability, an increase by a factor of two to four in the flow velocity could completely stabilize this mode. © 1996 American Institute of Physics.