S. Novo, M. Núñez and J. Rojo
A fast numerical method for the Alfvén spectrum of ideal magnetohydrodynamics
Phys. Fluids B, 3 (11) (1991), pp. 2967-2972

A numerical method is developed to find the Alfvén spectrum of axisymmetric toroidal equilibria. It involves the numerical integration of ordinary differential equations only and is therefore faster than finite element algorithms; moreover, the Alfvén frequencies of every flux surface may be calculated independently from the rest. The method is applied to the Shafranov-Solov'ev equilibrium for the first Fourier modes, and the results are compared to those obtained with the geometrical optics approximation. This comparison shows which of the parameters of the equilibrium are relevant on each branch of spectral points. Other features observed in the graphics obtained by this algorithm are also analyzed.
AMS(MOS) subject classification: 76W05, 34E05 

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