The early time evolution of helical plasma perturbations can be described by expanding the velocity field V(x,t) in a time series, the coefficients of which can be calculated by using the ideal MHD equations as an algorithm. The authors study the stabilizing effect that a longitudinal magnetic field has on such perturbations and derive a short-time criterion valid for both Z-pinches and cylindrical tokamaks. It is found that even if the divergence of the perturbation is equal to zero, the system is not marginally stable. In particular, if the helicity of the unperturbed magnetic field is opposite to the helicity of the plasma perturbation, one obtains the conditions q<1 approximately unstable and q<1 approximately stable, whereas, if the two helicities are of the same direction, the system is stable. The modification of the above criterion due to para- or diamagnetic poloidal currents is also discussed.
Linear frequency response of reconnecting perturbations