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2001
Confinement phenomenology characteristic of magnetically confined plasmas emerges naturally from a simple sandpile algorithm when the parameter controlling redistribution scale length is varied. Close analogs are found for enhanced confinement, edge pedestals, and edge localized modes (ELMs), and for the qualitative correlations between them. These…
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2001
The linear and nonlinear dynamics of zonal flows and their interactions with drift wave turbulence is considered in the simple but illuminating generalized Charney–Hasegawa–Mima model due to Smolyakov et al. [Phys. Plasmas 7 , 1349 (2000)]. Two positive definite, exact, integral invariants associated with the full generalized Charney–Hasegawa…
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2001
An avalanche or ‘‘sandpile’’ model is discussed that generalizes the original self-organized criticality avalanche model of Bak, Tang, and Wiesenfeld [Phys. Rev. Lett. 59 , 381 (1987)] to include spatially extended local redistribution. A single control parameter specifies the spatial extent of local redistribution when the critical gradien…
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2001
A cylindrical model with an equilibrium surface current and a uniform equilibrium plasma flow velocity parallel to the axis of the cylinder is used to investigate resistive wall instability. This system can be unstable to the ideal, external kink mode, which can be stabilized by the presence of a perfectly conducting wall. This is the classic condi…
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2001
An approximation to the relativistic broadening of an electron cyclotron resonance is obtained by including only the effect of the momentum parallel to the magnetic field. This approximation is then applied to the calculation of the absorption of the electromagnetic X-mode and compared to the full relativistic analysis with which it agrees very wel…
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2000
Electron Bernstein waves are analyzed as possible candidates for heating spherical tokamaks. An inhomogeneous plane slab model of the plasma with a sheared magnetic field is used to calculate the linear conversion of the ordinary mode (O-mode) to the extraordinary mode (X-mode). A formula for the fraction of the incident O-mode energy which is conv…
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1999
Ion cyclotron emission (ICE) excited by collective instability of fusion a particles has been observed during deuterium-tritium experiments with radio-frequency heating and neutral beam injection (NBI) in the Joint European Torus. A model based on classical a-particle confinement is broadly consistent with this data. ICE spectra from discharges wit…
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1999
There is increasing evidence that the Earth’s magnetosphere, like other macroscopic confined plasma systems (magnetic fusion plasmas, astrophysical accretion discs), displays sandpile-type phenomenology so that energy dissipation is by means of avalanches which do not have an intrinsic scale. This may in turn imply that these systems evolve via s…
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1999
A uniform compressible plasma with a uniform flow along the magnetic field in the presence of a resistive wall is shown to be subject to two instabilities. For the first instability, the flow velocity is required to exceed the Alfve´n speed, whereas for the second it need only exceed the sound speed. For a sufficiently high ion temperature, ion La…
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1999
A simple one-dimensional sandpile model is constructed which possesses exact analytical solvability while displaying both scale-free behavior and fractal properties. The sandpile grows by avalanching on all scales, yet its shape and energy content are described by a simple, continuous (but nowhere differentiable) analytical formula. The avalanche e…
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