Energy principle and kink instability in a toroidal plasma with strong magnetic field

In the first part of the present work an equation is obtained for an energy principle in which the kinetic and potential energies are functionals of only one function. This can be done by expanding the exact equation in inverse powers of the strong toroidal magnetic field. This simplified energy principle is accurate within terms of the order of the square of the curvature.In the second part of the report, the equation is applied to studies of the kink instability in a toroidal plasma. It is shown that branch splitting and forbidden zones in the spectrum of unstable Alfven oscillations arise from toroidal curvature. The appearance of these zones shows clearly how plasma stability deteriorates as plasma pressure increases. This effect is proportional to curvature and plasma pressure and may explain confinement pressure limits discovered by recent computations of the stability of a high-β tokamak (for free plasma boundary).