Nonlinear Stability of an Ideal Plasma
The functional series for the first integrals of helicity are used for the derivation of the sufficient stability conditions of ideal plasma in the sense of Lyapunov. The Euler equations for the Lyapunov functional imply the Grad-Shafranov equation with pressure profile determined by the toroidal field. The calculations were carried out both for cylindrical and toroidal configurations. In the considered example the magnetic field is mostly created by currents in plasma. The safety factor is less than one and decreases in the direction of the plasma boundary. The toroidal field behaves similarly: decreasing but not turning to zero. The pressure and density of helicity and their gradients, however, turn to zero at the boundary.
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