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A kinetic theory for magnetic islands in a low collision frequency tokamak plasma is presented. Self-consistent equations for the islands’ width, w, and propagation frequency, ω, are derived. These include contributions from the perturbed bootstrap current and the toroidally enhanced ion polarization drift. The bootstrap current is independent of the island propagation frequency and provides a drive for the island in tokamak plasmas when the pressure decreases with an increasing safety factor. The polarization drift is frequency dependent, and therefore its effect on the island stability cannot be deduced unless ω is known. This frequency is determined by the dominant dissipation mechanism, which for low effective collision frequency, νeff=ν/ε<ω, is governed by the electrons close to the trapped/passing boundary. The islands are found to propagate in the electron diamagnetic direction in which case the polarization drift is stabilizing and results in a threshold width for island growth, which is of the order of the ion banana width. At larger island widths the polarization current term becomes small and the island evolution is determined by the bootstrap current drive and Δ′ alone, where Δ′ is a measure of the magnetic free energy.

After a general discussion of the experimental characteristics of the L-H transition and consideration of basic theoretical principles underlying models for it, this paper reviews the various theories of the L-H transition available in the literature, providing some background information on each theory and expressing the transition criteria in forms suitable for comparison with experiment. Some conclusions on the relevance of these models for explaining the experimental data on the transition are drawn.

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