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Variational problems for the canonical profiles

  • Tokamaks
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Abstract

A noncontradictory formulation of the variational problem for a canonical profile is proposed that refines the problem posed by B.B. Kadomtsev for a circular plasma cylinder. The results are generalized to a toroidal plasma with an arbitrary cross section. For the problem in toroidal geometry, boundary conditions are proposed with which to single out the Kadomtsev-like solution (the canonical profile) from the solutions to the Euler equation. Canonical profiles for the L-and H-modes are constructed. For a number of interesting examples, it is numerically shown that the second variation of the magnetic energy functional is positive. The canonical profile transport model is outlined, and the relationship between the canonical, numerical, and experimental profiles in tokamaks is briefly discussed.

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Authors and Affiliations

  1. Nuclear Fusion Institute, Russian Research Centre Kurchatov Institute, pl. Kurchatova 1, Moscow, 123182, Russia

    Yu. N. Dnestrovskij, A. Yu. Dnestrovskij, A. V. Danilov, S. E. Lysenko & S. V. Cherkasov

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  1. Yu. N. Dnestrovskij
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  2. A. Yu. Dnestrovskij
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  3. A. V. Danilov
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  4. S. E. Lysenko
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  5. S. V. Cherkasov
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Additional information

Original Russian Text © Yu.N. Dnestrovskij, A.Yu. Dnestrovskij, A.V. Danilov, S.E. Lysenko, S.V. Cherkasov, 2008, published in Fizika Plazmy, 2008, Vol. 34, No. 1, pp. 3–19.

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Dnestrovskij, Y.N., Dnestrovskij, A.Y., Danilov, A.V. et al. Variational problems for the canonical profiles. Plasma Phys. Rep. 34, 1–17 (2008). https://doi.org/10.1134/S1063780X08010017

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  • DOI: https://doi.org/10.1134/S1063780X08010017

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