ALBERT

Notes: Using a Fourier–Bessel representation for the fluctuating (turbulent) electrostatic potential, an equation governing the sheared-flow modes in toroidal geometry is derived from the gyrokinetic Poisson equation, where both the adiabatic and nonadiabatic responses of the electrons are taken into account. It is shown that the principal geometrical effect on sheared-flow modes of the electrostatic potential is due to the flux-surface average of 1/B, where B is the magnetic field strength. © 2000 American Institute of Physics.

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: An efficient numerical method for treating electrons in magnetized plasmas has been developed. The scheme, which is based on the perturbative (δf) gyrokinetic particle simulation, splits the particle electron responses into adiabatic and nonadiabatic parts. The former is incorporated into the gyrokinetic Poisson's equation, while the latter is calculated dynamically with the aid of the charge conservation equation. The new scheme affords us the possibility of suppressing unwanted high-frequency oscillations and, in the meantime, relaxing the Courant condition for the thermal particles moving in the parallel direction. It is most useful for studying low-frequency phenomena in plasmas. As an example, one-dimensional drift wave simulation has been carried out using the scheme and the results are presented in this paper. This methodology can easily be generalized to problems in three-dimensional toroidal geometry, as well as those in unmagnetized plasmas. © 2000 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: 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: Internal disruption in a tokamak has been simulated using a three-dimensional magneto-inductive gyrokinetic particle code. The code operates in both the standard gyrokinetic mode (total-f code) and the fully nonlinear characteristic mode (δf code). The latter is a quiet low noise algorithm. The computational model represents a straight tokamak with periodic boundary conditions in the toroidal direction and a square cross section with perfectly conducting walls in the poloidal direction. The linear mode structure of an unstable m=1 (poloidal) and n=1 (toroidal) kinetic internal kink mode is clearly observed, especially in the δf code. The width of the current layer around the x-point, where magnetic reconnection occurs, is found to be close to the collisionless electron skin depth, indicating the importance of electron inertia. Both codes give very similar nonlinear results, in which full reconnection in the Alfvén time scale is observed along with the electrostatic potential structures created during this phase. The resulting E×B drift from the potential dominates the nonlinear phase after the full reconnection. © 1995 American Institute of Physics.

Notes: A time varying weighting (δf ) scheme for gyrokinetic particle simulation is applied to a steady-state, multispecies simulation of neoclassical transport. Accurate collision operators conserving momentum and energy are developed and implemented. Simulation results using these operators are found to agree very well with neoclassical theory. For example, it is dynamically demonstrated that like-particle collisions produce no particle flux and that the neoclassical fluxes are ambipolar for an ion–electron plasma. An important physics feature of the present scheme is the introduction of toroidal flow to the simulations. Simulation results are in agreement with the existing analytical neoclassical theory. The poloidal electric field associated with toroidal mass flow is found to enhance density gradient-driven electron particle flux and the bootstrap current while reducing temperature gradient-driven flux and current. Finally, neoclassical theory in steep gradient profile relevant to the edge regime is examined by taking into account finite banana width effects. In general, in the present work a valuable new capability for studying important aspects of neoclassical transport inaccessible by conventional analytical calculation processes is demonstrated. © 1995 American Institute of Physics.

Notes: Gyrokinetic perpendicular dynamics, an important component not systematically considered in previous gyrokinetic theories, is identified and developed. A "distribution function" S and its governing gyrokinetic equation are introduced to describe the gyrokinetic perpendicular dynamics. The complete treatment of the perpendicular current rendered by the gyrokinetic perpendicular dynamics enables one to recover the compressional Alfvén wave from the gyrokinetic model. From the viewpoint of gyrokinetic theory, the physics of the compressional Alfvén wave is the polarization current at second order. Therefore, in a low frequency gyrokinetic system, the compressional Alfvén wave is naturally decoupled from the shear Alfvén wave and drift wave. In the gyrocenter coordinates, the gyrophase dependent parts of the distribution function S and f˜ are decoupled from the gyrophase independent part f¯. Introducing the gyrokinetic perpendicular dynamics also extends the gyrokinetic model to arbitrary frequency modes. As an example, the Bernstein wave is recovered from the gyrokinetic model. The gyrokinetic perpendicular dynamics uncovered here emphasizes that the spirit of gyrokinetic reduction is to decouple the gyromotion from the particle's gyrocenter orbit motion, instead of averaging out the gyromotion. © 1999 American Institute of Physics.

Notes: A three-dimensional (3-D) global gyrokinetic particle code in toroidal geometry has been used for investigating the transport properties of ion temperature gradient (ITG) drift instabilities in tokamak plasmas. Using the isotopes of hydrogen (H+), deuterium (D+) and tritium (T+), it is found that, under otherwise identical conditions, there exists a trend for favorable isotope scaling for the ion thermal diffusivity, i.e., χi decreases with mass. Such a trend, which exists both at the saturation of the instability and also at the fully nonlinear stage, can be understood from the resulting wave number and frequency spectra. © 1997 American Institute of Physics.