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Notes: Recent developments in gyrokinetic-magnetohydrodynamics (MHD) theory and in electromagnetic gyrokinetic particle simulations raise the question of consistency between the gyrokinetic model and the fluid model. Due to the special characteristics of the guiding center coordinates, it is a nontrivial exercise to show this consistency. In this paper it is shown, in a very general setting, that the gyrokinetic theory and the fluid equations do give an equivalent description of plasma equilibrium (∂/∂t=0). The fluid continuity equation and momentum equation for equilibrium plasmas are recovered entirely from the gyrokinetic theory. However, it was Spitzer who first realized the importance of consistency between guiding-center motion and fluid equations. In particular, he studied the "apparent paradoxical result" regarding the difference between perpendicular particle flow and guiding-center flow, which will be referred to as the Spitzer paradox in this paper. By recovering the fluid equations from the gyrokinetic theory, we automatically resolve the Spitzer paradox, whose essence is how the perpendicular current and flow are microscopically generated from particles' guiding-center motion. The mathematical construction in the gyrokinetic theory which relates observable quantities in the laboratory frame to the distribution function in the guiding-center coordinates is consistent with Spitzer's original physical picture, while today's gyrokinetic-MHD theory covers a much wider range of problems in a much more general and quantitative way. © 2000 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: 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: A two-dimensional (2D) numerical solution method is developed for the recently derived linear gyrokinetic system which describes arbitrary wavelength electromagnetic perturbations in tokamak plasmas. The system consists of the gyrokinetic equation, the gyrokinetic Poisson equation, and the gyrokinetic moment equation. Since familiar magnetohydrodynamic (MHD) results can be recovered entirely from this gyrokinetic model, and all interesting kinetic effects are intrinsically included, this gyrokinetic system offers an approach for kinetic MHD phenomena which is more rigorous, self-consistent, and comprehensive than the previous hybrid models. Meanwhile, drift type microinstabilities can be also investigated systematically in this theoretical framework. The linear gyrokinetic equation is solved for the distribution function in terms of the perturbed fields by integrating along unperturbed particle orbits. The solution is substituted back into the gyrokinetic moment equation and the gyrokinetic Poisson equation. When the boundary conditions are incorporated, an eigenvalue problem is formed. The resulting numerical code, KIN-2DEM, is applied to kinetic ballooning modes, internal kink modes, and toroidal Alfvén eigenmodes (TAEs). The numerical results are benchmarked against the well-established FULL code [G. Rewoldt, W. M. Tang, and M. S. Chance, Phys. Fluids 25, 480 (1982)], the PEST code [J. Manickam, Nucl. Fusion 24, 595 (1984)], and the NOVA-K code [C. Z. Cheng, Phys. Rep. 211, No. 1 (1992)]. More importantly, kinetic effects on MHD modes can be investigated nonperturbatively. In particular, the kinetic effects of the background plasma on internal kink modes and the hot particle destabilization of TAEs are studied numerically. © 1999 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: An analytic solution is obtained for free-boundary, high-beta equilibria in large aspect ratio tokamaks with a nearly circular plasma boundary. In the absence of surface currents at the plasma-vacuum interface, the free-boundary equilibrium solution introduces constraints arising from the need to couple to an external vacuum field which is physically realizable with a reasonable set of external field coils. This places a strong constraint on the pressure profiles that are consistent with a given boundary shape at high εβp. The equilibrium solution also provides information on the flux surface topology. The plasma is bounded by a separatrix. Increasing the plasma pressure at fixed total current causes the plasma aperture to decrease in a manner that is described. © 1997 American Institute of Physics.

Notes: An existing microwave interferometer system is modified to add the capability of polarimetry in the CDX-U tokamak. Though this interferometer system can scan vertically and radially, only the vertical view channel is modified to accomodate Faraday rotation measurements, with its radial scanning capability preserved. For our relatively long microwave wavelength, the signal amplitude variation due to refraction is more important than effects due to vibration. An amplitude independent design of Faraday rotation diagnostics has been developed. By using a linearly polarized beam as input and putting a rotating polarizer in the beam after the plasma, birefringency effects are minimized. A digital phase detection technique has been developed for better resolution of the Faraday rotation angle. © 1995 American Institute of Physics.

Notes: Good ferroelectric properties have previously been reported for both the (1−x)SrBi2Ti2O9–xBi3TiNbO9 bulk ceramics and thin films. In this work, x-ray diffraction and Raman scattering were used to investigate the effect of the incorporation of Bi3TiNbO9 into SrBi2Ta2O9 bulk ceramics and thin films. A better crystallization, larger grain size and larger displacement of the Ta–O(4) or Ta–O(5) ions are the origin for the good ferroelectric properties of (1−x)SrBi2Ta2O9–xBi3TiNbO9 with x=0.3–0.4. © 2001 American Institute of Physics.

Notes: [Auszug] Oral administration of protein can induce antigen-specific immune hyporesponsiveness1. However, the utility of oral tolerance to autoantigens in the treatment of autoimmune diseases may be limited when candidate autoantigens cannot be produced by conventional systems in quantities sufficient for ...