Analytical stability boundaries for ideal kink modes in tokamaks with large edge currents

The ideal magnetohydrodynamic stability analysis of the m≥2 external kink modes in cylindrical tokamaks is reconsidered. Except for very small edge currents, the instability bands of these models are found to be accurately described by m-(m+1)Im/I0<nqa<m, where the quantities Im are defined as ∫0aJ(r)(r/a)2m2πr dr and J(r) is the current density in the plasma. This result may help to clarify the role played by the bootstrap current for the edge localized modes observed in high-confinement tokamak discharges