Abstract
We present an analytical model of the self-consistent equilibrium of a magnetic flux rope, which is obtained in cylindrical geometry. The equilibrium quantities, namely, the azimuthal magnetic field and plasma pressure, are determined in a self-consistent way through the current density, which is derived as a solution of a nonlinear equation. By minimizing the energy functional, it was shown that the constrained equilibrium state is stable. The obtained results are also applicable to the cylindrical tokamak magnetic configurations. It is shown that the analytically predicted radial profiles of equilibrium quantities are in good agreement with the experimental data.
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