Abstract
This Chapter is devoted to the variational formulation for the “canonical profiles” of the plasma temperature and pressure. The basis for the variational description is the functional for the magnetic energy associated with the plasma current together with the conditions for the conservation of the total plasma current and total magnetic flux. The variation of this functional leads to the Euler equation that defines the canonical profile. We start with a cylindrical plasma with circular cross section and then generalize to a toroidal plasma with arbitrary cross section. We also derive the variational formulation for the canonical profile of the toroidal rotation.
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