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Lectures Year : 2023

Magnetic coordinates and equilibrium magnetic field


This note addresses some properties of confining magnetic configurations. In a first step, it is shown that confinement is ensured if the field lines lie on surfaces, called magnetic (or flux) surfaces. These surfaces have to be tori in accordance with the hairy ball theorem. The existence of magnetic flux surfaces is granted when the configuration is axisymmetric. When it is not, flux surfaces can still exist under some reasonable conditions. A set of curvilinear flux coordinates can then be built, that reflect the structure of the magnetic field. The second step consists in calculating the force exerted on the plasma. The condition of force balance leads to a constraint on the magnetic field called the Grad-Shafranov equation. The equation prescribes the magnetic field, for given pressure and current profiles. Examples of solutions of the Grad-Shafranov are given. It is also shown that a vertical magnetic field is needed to ensure an equilibrium. Warning: hasty readers may skip sections with a star.
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hal-03974960 , version 1 (06-02-2023)


Attribution - NonCommercial - NoDerivatives


  • HAL Id : hal-03974960 , version 1


Xavier Garbet. Magnetic coordinates and equilibrium magnetic field. Doctoral. France. 2023. ⟨hal-03974960⟩
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