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# Attractors and frozen-in invariants in turbulent plasma

Institute of Applied Chemical Physics, Russian Research Centre ‘Kurchatov Institute’, pl. Kurchatova 1, Moscow, 123182, Russian Federation

Work on turbulent equipartitions in a plasma (i. e., attractors characterized by Lagrangian invariants) is reviewed. Although such attractors also exist in the convective zone of the Sun and in atmospheres, the primary emphasis is on turbulent transport in tokamaks. By extending the hydrodynamic concept of freezing-in to Vlasov’s equation, it is explained why the magnetic field topology in a collisionless plasma is conserved even though the conventional hydrodynamic description breaks down. Arguments are presented to support the conjecture that the canonical profiles of tokamak plasma are due to an attractor with a plasma frozen into the poloidal magnetic field. In fact, the exclusion from the conventional set of frozen-in integrals of the one for the toroidal magnetic field is all what is needed. The reason for the break-down of this invariant is the poloidal noninvariancy of the magnetic field, an effect to which trapped particles are particularly sensitive. The predictions of the attractor and of two attraction basin boundaries (H- mode and transport suppression by the reversed shear) are confirmed experimentally to a reasonable accuracy.

 Text can be downloaded in Russian. English translation is available on IOP Science.
PACS: 52.30.−q, 52.35.Ra, 52.55.Fa (all)
DOI: 10.1070/PU1997v040n05ABEH000235
URL: https://ufn.ru/en/articles/1997/5/b/
Citation: Yan’kov V V "Attractors and frozen-in invariants in turbulent plasma" Phys. Usp. 40 477–493 (1997)
 BibTexBibNote ® (generic)BibNote ® (RIS)Medline RefWorks RT Journal T1 Attractors and frozen-in invariants in turbulent plasma A1 Yan’kov,V.V. PB Physics-Uspekhi PY 1997 FD 10 May, 1997 JF Physics-Uspekhi JO Phys. Usp. VO 40 IS 5 SP 477-493 DO 10.1070/PU1997v040n05ABEH000235 LK https://ufn.ru/en/articles/1997/5/b/

Îðèãèíàë: ßíüêîâ Â Â «Aòòðàêòîðû è èíâàðèàíòû âìîðîæåííîñòè â òóðáóëåíòíîé ïëàçìå» ÓÔÍ 167 499–516 (1997); DOI: 10.3367/UFNr.0167.199705b.0499

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