Download or read book Gyrokinetic Neoclassical Study of the Bootstrap Current in the Tokamak Edge Pedestal with Fully Non linear Coulomb Collisions written by and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: As a follow-up on the drift-kinetic study of the non-local bootstrap current in the steep edge pedestal of tokamak plasma by Koh et al. [Phys. Plasmas 19, 072505 (2012)], a gyrokinetic neoclassical study is performed with gyrokinetic ions and drift-kinetic electrons. Besides the gyrokinetic improvement of ion physics from the drift-kinetic treatment, a fully non-linear Fokker-Planck collision operator--that conserves mass, momentum, and energy--is used instead of Koh et al.'s linearized collision operator in consideration of the possibility that the ion distribution function is non-Maxwellian in the steep pedestal. An inaccuracy in Koh et al.'s result is found in the steep edge pedestal that originated from a small error in the collisional momentum conservation. The present study concludes that (1) the bootstrap current in the steep edge pedestal is generally smaller than what has been predicted from the small banana-width (local) approximation [e.g., Sauter et al., Phys. Plasmas 6, 2834 (1999) and Belli et al., Plasma Phys. Controlled Fusion 50, 095010 (2008)], (2) the plasma flow evaluated from the local approximation can significantly deviate from the non-local results, and (3) the bootstrap current in the edge pedestal, where the passing particle region is small, can be dominantly carried by the trapped particles in a broad trapped boundary layer. In conclusion, a new analytic formula based on numerous gyrokinetic simulations using various magnetic equilibria and plasma profiles with self-consistent Grad-Shafranov solutions is constructed.
Download or read book Neoclassical Simulation of Tokamak Plasmas Using Continuum Gyrokinetc Code TEMPEST written by and published by . This book was released on 2007 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present gyrokinetic neoclassical simulations of tokamak plasmas with self-consistent electric field for the first time using a fully nonlinear (full-f) continuum code TEMPEST in a circular geometry. A set of gyrokinetic equations are discretized on a five dimensional computational grid in phase space. The present implementation is a Method of Lines approach where the phase-space derivatives are discretized with finite differences and implicit backwards differencing formulas are used to advance the system in time. The fully nonlinear Boltzmann model is used for electrons. The neoclassical electric field is obtained by solving gyrokinetic Poisson equation with self-consistent poloidal variation. With our 4D ([psi], [theta], [epsilon], [mu]) version of the TEMPEST code we compute radial particle and heat flux, the Geodesic-Acoustic Mode (GAM), and the development of neoclassical electric field, which we compare with neoclassical theory with a Lorentz collision model. The present work provides a numerical scheme and a new capability for self-consistently studying important aspects of neoclassical transport and rotations in toroidal magnetic fusion devices.
Download or read book Fully Electromagnetic Nonlinear Gyrokinetic Equations for Tokamak Edge Turbulence written by and published by . This book was released on 2008 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: An energy conserving set of the fully electromagnetic nonlinear gyrokinetic Vlasov equation and Maxwell's equations, which is applicable to both L-mode turbulence with large amplitude and H-mode turbulence in the presence of high E [Chi] B shear has been derived. The phase-space action variational Lie perturbation method ensures the preservation of the conservation laws of the underlying Vlasov-Maxwell system. Our generalized ordering takes [rho]i“[rho][theta]¡ ~ LE ~ Lp “R (here [rho]i is the thermal ion Larmor radius and [rho][theta]¡ = B/B[theta]] [rho]i), as typically observed in the tokamak H-mode edge, with LE and Lp being the radial electric field and pressure gradient lengths. We take [kappa] perpendicular to [rho]i ~ 1 for generality, and keep the relative fluctuation amplitudes e[delta][phi] /[Tau]i ~ [delta][Beta] / [Beta] up to the second order. Extending the electrostatic theory in the presence of high E [Chi] B shear [Hahm, Phys. Plasmas 3, 4658 (1996)], contributions of electromagnetic fluctuations to the particle charge density and current are explicitly evaluated via pull-back transformation from the gyrocenter distribution function in the gyrokinetic Maxwell's equation.
Download or read book The Macro and Micro instabilities in the Pedestal Region of the Tokamak written by Jingfei Ma and published by . This book was released on 2015 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we present the theoretical and numerical studies of the linear characteristics and nonlinear transport features of the instabilities driven by the steep profile gradient and edge current in the pedestal region of the tokamak. Two important instabilities, the peeling-ballooning (P-B) modes (macro-instability) and the drift-Alfven modes (micro-instability), are studied using the fluid analysis and the BOUT++ codes. In particular, the edge-localized modes (ELMs), which appear to be the energy burst in the nonlinear stage of the peeling-ballooning mode, are numerically studied and the results are compared with the experimental measurement. In addition, the features of the impurity transport in the edge region of the tokamak are theoretically analyzed. Firstly, we explore the fundamental characteristics of the P-B modes and the ELM bursts numerically using the three-field reduced MHD model under the BOUT++ framework, in the shifted-circular geometry, i.e. the limiter tokamak geometry. In the linear simulations, the growth rate and real frequency and the mode structure versus the toroidal mode number (n) are shown. The features of the ELM bursts are shown in the nonlinear simulations, including the time evolution of the relative energy loss (ELM size) and the pedestal profile. Secondly, two original research projects related to the P-B modes and the ELM burst are described. One is the study of the scaling law between the relative energy loss of ELMs and the edge collisionality. We generate a sequence of shifted-circular equilibria with different edge collisionality varying over four orders of magnitude using EFIT. The simulation results are in good agreement with the multi-tokamak experimental data. Another is the study of the differences of the linear behaviors of the P-B modes between the standard and snowflake divertor configurations. Using DIII-D H-mode ElMing equilibria, we found that the differences are due to the local magnetic shear change at the outboard midplane, which is the result of the realization of the snowflake configuration. Finally, the micro-instability, the drift-Alfven instability in the pedestal region of the DIII-D tokamak is studied. A modified six-field Landau fluid model under BOUT++ framework is used to study the linear characteristics and transport features of the drift-Alfven modes. Based on the DIII-D H-mode discharge, a sequence of divertor tokamak equilibria with different pedestal height is generated by the 'VARYPED' tool for our studies. Qualitative agreement is obtained between theoretical analysis and the simulation results in the linear regime. Moreover, the heat transport induced by the drift-Alfven turbulence is explored and the convection level is estimated for both ions and electrons.
Download or read book Observation of Non classical Radial Current Diffusion in a Fully Bootstrap Current Driven Tokamak written by Y. S. Hwang and published by . This book was released on 1996 with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Gyrokinetic Simulation of Global Turbulent Transport Properties in Tokamak Experiments written by and published by . This book was released on 2006 with total page 92505 pages. Available in PDF, EPUB and Kindle. Book excerpt: A general geometry gyro-kinetic model for particle simulation of plasma turbulence in tokamak experiments is described. It incorporates the comprehensive influence of noncircular cross section, realistic plasma profiles, plasma rotation, neoclassical (equilibrium) electric fields, and Coulomb collisions. An interesting result of global turbulence development in a shaped tokamak plasma is presented with regard to nonlinear turbulence spreading into the linearly stable region. The mutual interaction between turbulence and zonal flows in collisionless plasmas is studied with a focus on identifying possible nonlinear saturation mechanisms for zonal flows. A bursting temporal behavior with a period longer than the geodesic acoustic oscillation period is observed even in a collisionless system. Our simulation results suggest that the zonal flows can drive turbulence. However, this process is too weak to be an effective zonal flow saturation mechanism.
Download or read book Observation of Non classical Radial Current Diffusion in a Fully Bootstrap Current Driven Tokamak written by Y. S. Hwang and published by . This book was released on 1996 with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book RF Effects on Neoclassical Theory and the Bootstrap Current in Tokamaks written by S. D. Schultz and published by . This book was released on 1997 with total page 4 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Bootstrap Currents in Radio frequency driven Tokamak Equilibria written by and published by . This book was released on 1988 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Interest in the bootstrap current arising from neoclassical transport in tokamaks has increased recently in view of certain experimental observations. In this study, the bootstrap current is calculated for a number of rf current-driven tokamaks. Two-dimensional, self-consistent, steady-state tokamak MHD equilibria are obtained by including both the transport-driven bootstrap current and the externally driven rf current. The self-consistency is acomplished by iterating between two-dimensional MHD equilibrium calculations and the current calculations (including bootstrap and rf ray-tracing). Calculations for other reactor parameters of interest are also carried out. It is found that for reactor-grade plasmas, the bootstrap current contribution to the toroidal current is, in general, important. An approxiamte scaling law for GAMMA, based on parametric survey performed, is also obtained. 16 refs., 8 figs., 1 tab.
Download or read book Collisions in Global Gyrokinetic Simulations of Tokamak Plasmas Using the Delta f Particle in cell Approach written by Thibaut Vernay and published by . This book was released on 2013 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nonlinear Gyrokinetic Tokamak Physics written by Alain Jean Brizard and published by Ann Arbor, Mich. : University Microfilms International. This book was released on 1990 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nonlinear Gyrokinetic Simulations of Intrinsic Rotation in Up down Asymmetric Tokamaks written by Justin Richard Ball and published by . This book was released on 2013 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: Experiments and theory show that tokamak plasmas with strong toroidal rotation and rotation shear can suppress turbulent energy transport as well as allow violation of the Troyon [beta] limit. However, using external neutral beams to inject toroidal momentum, as is done in many current experiments, would require a prohibitive amount of energy in larger, reactor-sized devices. The most promising alternative to achieve significant mean plasma flow that scales to large devices is intrinsic rotation, the rotation that is observed in the absence of external momentum injection. Intrinsic rotation is observed in current experiments, but is generated by effects that are formally small in [pi]* =- [pi]i / a, the ratio of the ion gyroradius to the tokamak minor radius. These effects are insufficient in anticipated reactors because [pi]*, will be significantly smaller. Recent theoretical work concludes that up-down asymmetry in the poloidal crosssection of tokamaks can drive intrinsic rotation to lowest order in [pi]*, [1, 2]. In this thesis, we extend GS2, a local [delta] f gyrokinetic code that self-consistently calculates momentum transport, to permit up-down asymmetric configurations. MHD analysis shows that ellipticity is most effective at introducing up-down asymmetry throughout the plasma. Accordingly, tokamaks with tilted elliptical poloidal cross-sections were simulated in GS2 to determine nonlinear momentum transport. The results suggest that the current experimentally measured rotation levels can be generated in reactorsized devices using up-down asymmetry. Surprisingly, linear and nonlinear gyrokinetic simulations also suggest that tilted elliptical flux surfaces may naturally suppress turbulent energy transport. Using cyclone base case parameters [3] (except for an elongation K = 2), a 40% reduction in the linear turbulent growth rate was observed by tilting the flux surface [pi]/4 from vertical. However, this reduction of energy transport was not observed when the background temperature gradient was increased by 50%.
Download or read book Computational Modeling of Neoclassical and Resistive MHD Tearing Modes in Tokamaks written by and published by . This book was released on 1996 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Theory Of Toroidally Confined Plasmas The Third Edition written by Roscoe B White and published by World Scientific Publishing Company. This book was released on 2013-11-18 with total page 527 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate level textbook develops the theory of magnetically confined plasma, with the aim of bringing the reader to the level of current research in the field of thermonuclear fusion. It begins with the basic concepts of magnetic field description, plasma equilibria and stability, and goes on to derive the equations for guiding center particle motion in an equilibrium field. Topics include linear and nonlinear ideal and resistive modes and particle transport. It is of use to workers in the field of fusion both for its wide-ranging account of tokamak physics and as a kind of handbook or formulary.This edition has been extended in a number of ways. The material on mode-particle interactions has been reformulated and much new information added, including methodology for Monte Carlo implementation of mode destabilization. These results give explicit means of carrying out mode destabilization analysis, in particular for the dangerous fishbone mode. A new chapter on cyclotron motion in toroidal geometry has been added, with comparisons of the analysis of resonances using guiding center results. A new chapter on the use of lithium lined walls has been added, a promising means of lowering the complexity and cost of full scale fusion reactors. A section on nonlocal transport has been added, including an analysis of Levy flight simulations of ion transport in the reversed field pinch in Padova, RFX.
Download or read book The Plasma Boundary of Magnetic Fusion Devices written by P.C Stangeby and published by CRC Press. This book was released on 2000-01-01 with total page 738 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Plasma Boundary of Magnetic Fusion Devices introduces the physics of the plasma boundary region, including plasma-surface interactions, with an emphasis on those occurring in magnetically confined fusion plasmas. The book covers plasma-surface interaction, Debye sheaths, sputtering, scrape-off layers, plasma impurities, recycling and control, 1D and 2D fluid and kinetic modeling of particle transport, plasma properties at the edge, diverter and limiter physics, and control of the plasma boundary. Divided into three parts, the book begins with Part 1, an introduction to the plasma boundary. The derivations are heuristic and worked problems help crystallize physical intuition, which is emphasized throughout. Part 2 provides an introduction to methods of modeling the plasma edge region and for interpreting computer code results. Part 3 presents a collection of essays on currently active research hot topics. With an extensive bibliography and index, this book is an invaluable first port-of-call for researchers interested in plasma-surface interactions.
Download or read book Theory of Fusion Plasmas written by Olivier Sauter and published by American Institute of Physics. This book was released on 2008-12-02 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Joint Varenna-Lausanne International Workshop on Theory of Fusion Plasmas takes place every other year in a place particularly favorable for informal and in depth discussions. Invited and contributed papers present state-of-the art researches in theoretical plasma physics, covering all domains relevant to fusion plasmas. This workshop always allows a fruitful mix of experienced researchers and students, to allow for a better understanding of the key theoretical physics models and applications, such as: Theoretical issues related to burning plasmas; Anomalous Transport (Turbulence, Coherent Structures, Microinstabilities) RF Heating and Current Drive; Macroinstabilities; Plasma-Edge Physics and Divertors; Fast particles instabilities.
Download or read book Controlled Fusion and Plasma Physics written by Kenro Miyamoto and published by Taylor & Francis. This book was released on 2006-10-23 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: Resulting from ongoing, international research into fusion processes, the International Tokamak Experimental Reactor (ITER) is a major step in the quest for a new energy source.The first graduate-level text to cover the details of ITER, Controlled Fusion and Plasma Physics introduces various aspects and issues of recent fusion research activ
