Theory of Continuum Damping of Toroidal Alfven Eigenmodes in Finite-beta Tokamaks PDF Download
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Author: Liu Chen
Publisher:
ISBN:
Category : Magnetohydrodynamic waves
Languages : en
Pages : 76
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Book Description
Author: Liu Chen
Publisher:
ISBN:
Category : Magnetohydrodynamic waves
Languages : en
Pages : 76
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Book Description
![Theory of Continuum Damping of Toroidal Alfven Eigenmodes in Finite-[beta] Tokamaks PDF](https://books.google.com/books/content/images/frontcover/oRpgAQAACAAJ?fife=w80-h100)
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 77
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Book Description
We have formulated a general theoretical approach for analyzing two-dimensional structures of high-n Toroidal Alfven Eigenmodes (TAE) in large aspect-ratio, finite-[beta] tokamaks. Here, n is the toroidal wave number and [beta] is the ratio between plasma and magnetic pressures. The present approach generalizes the standard ballooning-mode formalism and is capable of treating eigenmodes with extended global radial structures as well as finite coupling between discrete and continuous spectra. Employing the well-known (s, [alpha]) model equilibrium and assuming a linear equilibrium profile, we have applied the present approach and calculated the corresponding resonant continuum damping rate of TAE modes. Here, s and [alpha] denote, respectively, the strengths of magnetic shear and pressure gradients. In particular, it is found that there exists a critical [alpha]{sub c}(s), such that, as [alpha] 2![alpha]{sub c}, the continuum damping rate is significantly enhanced and, thus, could suppress the potential TAE instability.
![Continuum Damping of Toroidal Alfvén Eigenmodes in Finite-[beta] Tokamak Equilibria PDF](https://books.google.com/books/content/images/frontcover/nxt_YgEACAAJ?fife=w80-h100)
Author: Fulvio Zonca
Publisher:
ISBN:
Category :
Languages : en
Pages : 330
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Author: George William Bowden
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
A variety of Alfven wave phenomena are found in toroidal magnetically confined fusion plasmas. Shear Alfven eigenmodes may exist, which can be driven unstable by interaction with energetic particles. The linear stability of such modes depends on damping through several mechanisms. Continuum resonances cause damping of the modes, which occurs even in non-dissipative ideal magnetohydrodynamic (MHD ) theory given appropriate treatment of resulting poles. Additional damping of the modes occurs due to conversion to kinetic Alfven waves and finite parallel electric fields when kinetic extensions to MHD are considered. In this thesis, methods for calculating the damping of Alfven eigenmodes are developed, with particular focus on the continuum damping component. Damping of modes in complicated two- and three-dimensional magnetic geometries characteristic of tokamak and stellarator plasmas is considered.In this work, shear Alfven eigenmodes are analysed based on reduced MHD models. A background is provided, covering relevant theoretical aspects of plasma equilibrium, coordinate systems and linearised MHD waves. A coordinate independent reduced MHD wave equation is derived for Alfven eigenmodes in low beta tokamaks and stellarators. Coupled wave equations in terms of Fourier harmonics of the eigenmode are then derived for large aspect-ratio plasmas.Expressions for continuum damping are derived perturbatively from the coordinate independent and coupled harmonic wave equations. Application of the expressions using Galerkin and shooting methods is described. Damping computed in this manner is compared with values from an accepted method for the benchmark case of a TAE in a large aspect-ratio circular cross-section tokamak. The perturbative technique is shown to produce significant errors, even where continuum damping is small.A novel singular finite element method is developed to compute continuum damping. The Galerkin method adopted employs special basis functions reflecting the asymptotic form of the solution near continuum resonance poles. For particular eigenmodes, the unknown complex eigenvalue and pole location are computed iteratively. The procedure is verified by application to a TAE in a large aspect-ratio circular cross-section tokamak, where well converged and accurate complex eigenvalue and mode structure are obtained.Continuum damping can be computed numerically by solving the ideal MHD eigenvalue problem over a complex contour which circumvents continuum resonance poles according to the causality condition. This calculation is implemented in the ideal MHD eigenvalue code CKA , using analytic continuation of equilibrium quantities. The method is verified through application to a TAE in a tokamak, where the complex eigenvalue computed agrees closely with that found using the accepted resistive method, but converges faster with increasing radial mesh resolution. Continuum damping of shear Alfven eigenmodes is computed for three-dimensional configurations in torsatron, helias and heliac stellarators.Extensions to the ideal MHD wave equations allow non-ideal kinetic effects to be modelled. The damping of a TAE in a tokamak case through these effects is computed using different models for magnetic geometry and kinetic effects. Choice of the former strongly influences results, while choice of.
Author: Linjin Zheng
Publisher: Morgan & Claypool Publishers
ISBN: 1627057072
Category : Science
Languages : en
Pages : 178
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Book Description
This book describes the advanced stability theories for magnetically confined fusion plasmas, especially in tokamaks. As the fusion plasma sciences advance, the gap between the textbooks and cutting-edge researches gradually develops. This book fills in
Author: Kenro Miyamoto
Publisher: Taylor & Francis
ISBN: 1584887109
Category : Science
Languages : en
Pages : 393
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Book Description
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
Author:
Publisher:
ISBN:
Category : Aeronautics
Languages : en
Pages : 1556
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Author: C.Z. Cheng
Publisher:
ISBN:
Category : Alpha rays
Languages : en
Pages : 52
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Book Description
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Ideal and resistive MHD equations for the shear Alfven waves are studied in a low-.beta. toroidal model by employing the high-n ballooning formalism. The ion sound effects are neglected. For an infinite shear slab, the ideal MHD model gives rise to a continuous spectrum of real frequencies and discrete eigenmodes (Alfven-Landau modes) with complex frequencies. With toroidal coupling effects due to nonuniform toroidal magnetic field, the continuum is broken up into small continuum bands and new discrete toroidal eigenmodes can exist inside the continuum gaps. Unstable ballooning eigenmodes are also introduced by the bad curvature when .beta.> .beta./sub c/. The resistivity (n) can be considered perturbatively for the ideal modes. In addition, four branches of resistive modes are induced by the resistivity: (1) Resistive entropy modes which are stable (.delta.' 0) with frequencies approaching zero as n35, (3) Resistive periodic shear Alfven waves which approach the finite frequency end points of the continuum bands and n12, and (4) Resistive ballooning modes which are purely growing with growth rate proportional to eta13.beta.23 as eta .--. O and .beta. .-->. O.
Author: Linjin Zheng
Publisher: BoD – Books on Demand
ISBN: 9535102117
Category : Science
Languages : en
Pages : 224
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Book Description
To understand plasma physics intuitively one need to master the MHD behaviors. As sciences advance, gap between published textbooks and cutting-edge researches gradually develops. Connection from textbook knowledge to up-to-dated research results can often be tough. Review articles can help. This book contains eight topical review papers on MHD. For magnetically confined fusion one can find toroidal MHD theory for tokamaks, magnetic relaxation process in spheromaks, and the formation and stability of field-reversed configuration. In space plasma physics one can get solar spicules and X-ray jets physics, as well as general sub-fluid theory. For numerical methods one can find the implicit numerical methods for resistive MHD and the boundary control formalism. For low temperature plasma physics one can read theory for Newtonian and non-Newtonian fluids etc.
