Kink instability of a cylindrical tokamak with an arbitrary current distribution

A new method to analyze the MHD kink instability in the cylindrical approximation is presented. Using the nonlinear equilibrium equation with the helical perturbation method, an expression for the growth rate of instability of a perturbation is obtained. For m=1 mode, the growth rate and the stability-instability criterion, q(a)=1, are calculated analytically for an arbitrary current distribution. The growth rate is also calculated in the case of a uniform current. (auth.)