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Magnetic island structure in a tokamak in the vacuum field approximation

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dc.contributor.author Mahlangu SV en
dc.date.accessioned 2016-09-22T11:18:18Z
dc.date.available 2016-09-22T11:18:18Z
dc.date.submitted 1999 en
dc.identifier.uri http://hdl.handle.net/20.500.11892/109633
dc.description.abstract Perturbed Hamiltonian dynamics is characterized by a dense set of islands in phase space [1, 13]. Typically each island has an unstable separatrix [18] where chaotic behaviour is borne. For small perturbations, these islands are separated from each other by regular KAM surfaces [2, 13, 18], but as the perturbation grows the islands may overlap, and large-scale chaotic regions develop. This is just the situation for magnetic confinement devices such as tokamaks (Russian acronym for a toroidal chamber for plasma confinement), and is important as overlap of magnetic islands short-circuits the interior of the system to boundaries and loss of confinement ensues [3, 9] . Equilibrium configurations are integrable and non-chaotic for ideal tokamaks without magnetic islands. However whenever pertubing magnetic field is applied to the plasma, the configuration becomes non-integrable and islands appears. Approximation techniques must now be employed. We shall model the perturbed magnetic field structure in a tokamak in the vacuum field approximation, that is, by ignoring the inductive response of the plasma to the field [3]. Magnetic islands and chaos are thereby introduced. The equations of motion of magnetic field lines are solved numerically and resonance widths for different modes of primary resonances [13, 18] are measured. In addition, we obtain analytic estimates for island size to first order in the aspect ratio [9], ε, and compare them with the numerical results. The coupling strength (δ/ε)* at which two primary resonances overlap [7] is estimated and the calcu- lated values are compared with numerical results. We will work through various models with levels of complexity increasing from a simple "straight tokamak" to a full toroidally shaped plasma. Various physical effects such as Shafranov shift, toroidicity, offset and triangularity [9, 16, 20] are introduced as the model is developed. Their effects on the resonance width are discussed. We find that the island width formula, adapted to include these physical effects, agrees reasonably well with numerical computations for the tokamak with Shafranov shift and so may be of use in engineering design of tokamaks in this case. The overlap criteria agrees quite accurately since overlap leads to global stochasticity and loss of confinement. This is a very important criteria and so the formula gives a quick reasonable estimate for this dangerous effect. The above physical effects in general enhance island size and in this sense are a threat to plasma confinement. en
dc.language English en
dc.subject Physics en
dc.title Magnetic island structure in a tokamak in the vacuum field approximation en
dc.type Masters degree en
dc.description.degree MSc en

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