A time-dependent explicit finite-difference code is developed for computing growth rates of gross magnetohydrodynamic modes in helically symmetric high-β, ℓ = 1 equilibria. The effect of numerical dispersion on current- and pressure-driven modes and the convergence of the growth rate with the grid size for modes in screw-pinch, θ-pinch, and helical equilibria are discussed. In the case of diffuse MHD equilibria with a long helical period length, the eigenvalues computed by this code are in agreement with those of a δW-analysis and of experiments and are a factor of about two smaller than predicted by the surface current theory. The growth rates o f m ≥ 2 modes are given as functions of the helical periodicity number, the helical amplitude of the magnetic axis, beta, and the longitudinal wave number k.
The ideal MHD stability of time-dependent Z-pinch equilibria