Ballooning mode spectrum in general toroidal systems

Dewar, R. L.

doi:10.1063/1.864028

Cited by 287 publications

(273 citation statements)

References 18 publications

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“…Key early works are Connor, Hastie, and Taylor (1979) and ; more recent developments are found in Romanelli and Zonca (1993), Kim and Wakatani (1994), and . A three-dimensional ballooning theory was developed by Dewar and Glasser (1983).…”

Section: Drift-wave Eigenmodes In Toroidal Geometrymentioning

confidence: 99%

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Drift waves and transport

1999

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Drift waves occur universally in magnetized plasmas producing the dominant mechanism for the transport of particles, energy and momentum across magnetic field lines. A wealth of information obtained from quasistationary laboratory experiments for plasma confinement is reviewed for drift waves driven unstable by density gradients, temperature gradients and trapped particle effects. The modern understanding of Bohm transport and the role of sheared flows and magnetic shear in reducing the transport to the gyro-Bohm rate are explained and illustrated with large scale computer simulations. The types of mixed wave and vortex turbulence spontaneously generated in nonuniform plasmas are derived with reduced magnetized fluid descriptions. The types of theoretical descriptions reviewed include weak turbulence theory, Kolmogorov anisotropic spectral indices, and the mixing length. A number of standard turbulent diffusivity formulas are given for the various space-time scales of the drift-wave turbulent mixing. [S0034-6861(99)00803-X] CONTENTS

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Section: Drift-wave Eigenmodes In Toroidal Geometrymentioning

confidence: 99%

“…The free parameter 0 is the Floquet exponent of the wave function and determines the radial orientation of the convective cells. More globally, q 0 should be thought of as an approximation to the eikonal ͐ k dq (Dewar and Glasser, 1983).…”

Section: B Single Helicity and Ballooning Eigenmodesmentioning

confidence: 99%

Drift waves and transport

1999

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“…However, it has been known for many years [7] that the ray-tracing problem in strongly three-dimensional systems is singular because, in the absence of an adiabatic invariant, the phase-space motion is not bounded-the rays escape to infinity in the wavevector sector. Dewar and Glasser [7] argued that this gives rise to a continuous unstable spectrum, with correspondingly singular generalized eigenfunctions.…”

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confidence: 99%

“…Dewar and Glasser [7] argued that this gives rise to a continuous unstable spectrum, with correspondingly singular generalized eigenfunctions. (A more rigorous treatment involves the concept of the essential spectrum and Weyl sequences [13,14].…”

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Strong “Quantum” Chaos in the Global Ballooning Mode Spectrum of Three-Dimensional Plasmas

2001

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The spectrum of ideal magnetohydrodynamic (MHD) pressure-driven (ballooning) modes in strongly nonaxisymmetric toroidal systems is difficult to analyze numerically owing to the singular nature of ideal MHD caused by lack of an inherent scale length. In this paper, ideal MHD is regularized by using a k-space cutoff, making the ray tracing for the WKB ballooning formalism a chaotic Hamiltonian billiard problem. The minimum width of the toroidal Fourier spectrum needed for resolving toroidally localized ballooning modes with a global eigenvalue code is estimated from the Weyl formula. This phase-space-volume estimation method is applied to two stellarator cases.PACS numbers: 52.35. Py, 52.55.Hc, 05.45.Mt In design studies for new magnetic confinement devices for fusion plasma experiments (e.g. investigations [1,2] leading to the proposed National Compact Stellarator Experiment, NCSX [3]), the maximum pressure that can stably be confined in any proposed magnetic field configuration is routinely estimated by treating the plasma as an ideal magnetohydrodynamic (MHD) fluid. One linearizes about a sequence of equilibrium states with increasing pressure, and studies the spectrum of normal modes (frequency ω) to determine when there is a component with Im ω > 0, signifying instability.Even with the simplification obtained by using the ideal MHD model, the computational task of determining the theoretical stability of a three-dimensional (i.e. nonaxisymmetric) device, such as NCSX or the four currently operating helical axis stellators [4], remains a challenging one.The problem can be posed as a Lagrangian field theory, with the potential term being the energy functional δW [5]. For a static equilibrium, the kinetic energy is quadratic in ω, so that ω 2 is real. Thus instability occurs when ω 2 < 0. There are two main approaches to analyzing the spectrum-local and global. * Permanent address: Research School of Physical Sciences & Engineering, The Australian National University. E-mail: robert.dewar@anu.edu.au.In the local approach, which is used for analytical simplification, one orders the scale length of variation of the eigenfunction across the magnetic field lines to be short compared with equilibrium scale lengths [6]. Both interchange and ballooning stability can be treated by solving the general ballooning equations [7], a system of ordinary differential equations defined on a given magnetic field line.The global (Galerkin) approach is to expand the plasma displacement field in a finite basis set, inserting this ansatz in the Lagrangian to find a matrix eigenvalue representation of the spectral problem. This approach has been implemented for ideal MHD in threedimensional plasmas in two codes, TERPSICHORE [8] and CAS3D [9].Although the Galerkin approach is potentially exact, if one could use a complete, infinite basis set, it is in practice computationally challenging due to the large number of basis functions required to resolve localized instabilities. This leads to very large matrices which must be diagonalize...

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On the essential spectrum of ideal magnetohydrodynamics. Dedicated to harold grad on the occasion of his sixtieth birthday

Hameiri

1985

Comm Pure Appl Math

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The essential spectrum of magnetohydrodynamics (MHD) is shown to arise from waves propagating one-dimensionally along magnetic field lines. Different polarizations of these waves give rise to the "Alfven" and "ballooning" spectra. The essential spectrum of an axisymmetric equilibrium when a single azimuthal mode number is considered consists of the Alfven spectrum only, while the ballooning modes appear as intervals of accumulation of discrete eigenvalues with different mode numbers. We derive some necessary and one sufficient conditions for stability and show some examples where the criteria coincide to yield a simple condition for stability.

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Ballooning mode spectrum in general toroidal systems

Cited by 287 publications

References 18 publications

Drift waves and transport

Drift waves and transport

Strong “Quantum” Chaos in the Global Ballooning Mode Spectrum of Three-Dimensional Plasmas

On the essential spectrum of ideal magnetohydrodynamics. Dedicated to harold grad on the occasion of his sixtieth birthday

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