Energetic Consistency and Momentum Conservation in the Gyrokinetic Description of Tokamak Plasmas

Gyrokinetic field theory is addressed in the context of a general Hamiltonian. The background magnetic geometry is static and axisymmetric, and all dependence of the Lagrangian upon dynamical variables is in the Hamiltonian or in free field terms. Equations for the fields are given by functional derivatives. The symmetry through the Hamiltonian with time and toroidal angle invariance of the geometry lead to energy and toroidal momentum conservation. In various levels of ordering against fluctuation amplitude, energetic consistency is exact. The role of this in underpinning of conservation laws is emphasised. Local transport equations for the vorticity, toroidal momentum, and energy are derived. In particular, the momentum equation is shown for any form of Hamiltonian to be well behaved and to relax to its magnetohydrodynamic (MHD) form when long wavelength approximations are taken in the Hamiltonian. Several currently used forms, those which form the basis of most global simulations, are shown to be well defined within the gyrokinetic field theory and energetic consistency.Comment: RevTeX 4, 47 pages, no figures, revised version updated following referee comments (discussion more strictly correct/consistent, 4 references added, results unchanged as they depend on consistency of the theory), resubmitted to Physics of Plasma

High-m Kink/Tearing Modes in Cylindrical Geometry

The global ideal kink equation, for cylindrical geometry and zero beta, is simplified in the high poloidal mode number limit and used to determine the tearing stability parameter, $\Delta^\prime$. In the presence of a steep monotonic current gradient, $\Delta^\prime$ becomes a function of a parameter, $\sigma_0$, characterising the ratio of the maximum current gradient to magnetic shear, and $x_s$, characterising the separation of the resonant surface from the maximum of the current gradient. In equilibria containing a current "spike", so that there is a non-monotonic current profile, $\Delta^\prime$ also depends on two parameters: $\kappa$, related to the ratio of the curvature of the current density at its maximum to the magnetic shear, and $x_s$, which now represents the separation of the resonance from the point of maximum current density. The relation of our results to earlier studies of tearing modes and to recent gyro-kinetic calculations of current driven instabilities, is discussed, together with potential implications for the stability of the tokamak pedestal.Comment: To appear in Plasma Physics and Controlled Fusio

Modelling granular soil behaviour using a physics engine

A physics engine is a software library used in the film and computer games industries to realistically animate a physical system. In this paper it is shown that particulate media can be faithfully modelled using a rigid body physics engine, thereby providing a viable alternative to the discrete element method codes currently used in the field of geomechanics. An overview of the simulation method implemented in the widely used Box2D physics engine is provided, and it is shown that this tool can successfully capture the critical state response of granular media, using particles modelled as randomly shaped polygons

Intrinsic rotation with gyrokinetic models

The generation of intrinsic rotation by turbulence and neoclassical effects in tokamaks is considered. To obtain the complex dependences observed in experiments, it is necessary to have a model of the radial flux of momentum that redistributes the momentum within the tokamak in the absence of a preexisting velocity. When the lowest order gyrokinetic formulation is used, a symmetry of the model precludes this possibility, making small effects in the gyroradius over scale length expansion necessary. These effects that are usually small become important for momentum transport because the symmetry of the lowest order gyrokinetic formulation leads to the cancellation of the lowest order momentum flux. The accuracy to which the gyrokinetic equation needs to be obtained to retain all the physically relevant effects is discussed

Reduction and approximation in gyrokinetics

The gyrokinetics formulation of plasmas in strong magnetic fields aims at the elimination of the angle associated with the Larmor rotation of charged particles around the magnetic field lines. In a perturbative treatment or as a time-averaging procedure, gyrokinetics is in general an approximation to the true dynamics. Here we discuss the conditions under which gyrokinetics is either an approximation or an exact operation in the framework of reduction of dynamical systems with symmetryComment: 15 pages late

Should we perform multiparametric magnetic resonance imaging of the bladder before transurethral resection of bladder? Time to reconsider the rules

We would like to congratulate Ueno and colleagues [1] on their paper on diagnostic accuracy and interobserver agreement for the new Vesical Imaging-Reporting and Data System (VI-RADS) [2] for muscle-invasive bladder cancer (MIBC) in this issue of European Urology. Their report on 74 patients who underwent multiparametric magnetic resonance imaging (mpMRI) before transurethral resection of bladder tumor (TURBT) raises great interest in the RADS (Reporting and Data Systems) era. They address the questions of reproducibility and diagnostic performance of mpMRI in the setting of bladder ca (BC), in which potential applications of this imaging technique have seen constant growth in the past decades without a definitive role having been identified

Taxa de natalidade no rebanho bovino no Pantanal: nutrição, sanidade e genética.

No século XVIII com a decadência das lavras auríferas de Cuiabá, a população local passou a desenvolver a agricultura no vale do Guaporé e a pecuária na planície pantaneira, região salubre e com pastagens nativas de melhor qualidade para a criação de gado. No sentido norte-sul, todo o Pantanal foi ocupado pela pecuária de corte extensiva promovendo até as primeiras décadas do último século a indústria do charque e de outros subprodutos como crina, couro e extratos. A criação de gado floresceu tanto que na década de 40 representava 6% do rebanho nacional e 90% do então estado de Mato Grosso. Com o desenvolvimento da pecuária no Triângulo Mineiro e noroeste de São Paulo, o gado do Pantanal passou a ser comercializado "em pé" para aquelas regiões impulsionado, posteriormente, com a construção da estrada de ferro Noroeste do Brasil. A taxa de natalidade no rebanho nelorado em pastagens nativas no Pantanal está em torno de 55%, mas varia de 40% a 60% em função da proporção de fitofisionomias e do grau de propensão à inundação das invernadas. Períodos de seca melhoram o índice de natalidade em todo o Pantanal pela disponibilização de mais pastagens de melhor qualidade nas áreas baixas sujeitas a inundação. Outra característica da região é a idade tardia na primeira cria com aproximadamente quatro anos (Tullio, 1986; Pott et al., 1987a; Abreu et al., 2000). O objetivo deste trabalho é revisar os trabalhos publicados sobre o assunto.bitstream/item/79415/1/COT29.pd