Abstract:
The nonlinear Fourier method of Callebaut consists in concentrating on the family of higher order terms
of a single Fourier term of the linearized analysis. Thus we have obtained the higher order terms of plasma
perturbations, gravitational ones, etc. In the simplest case of cold plasma this resulted in obtaining an analytical
expression for the higher order terms. This allowed to investigate the convergence of the series, which in this
case limits the first order amplitude to 1/e of the equilibrium density. For the cases without an analytical
expression we developed a numerical-graphical method to obtain the convergence limit. Near this limit the
total amplitude of the wave becomes very large. The convergence limit decreases with increasing pressure.
Thus a wave with moderate first order amplitude may carry a very large energy due to the higher orders.
Moreover, this energy is concentrated in a very narrow interval of the phase interval (0, 2π). This may be
relevant in many situations. E.g. in the case of ball lightning a tremendous energy may be accumulated while
the glowing is still restricted. The triggering of solar flares or coronal mass ejections may thus be caused. Again,
when these eruptions reach the Earth the influence of a first order term may be far too small to cause electric
power plants to break down; however, the total of all terms may be much more powerful. Cf. March 1989 when
the whole state of Quebec, Canada, was a day without electricity due to a solar storm. This is an alternative
mechanism from the one proposed by Callebaut and Tsintsadze based on soliton envelope formation, although
there the accent was on the heating of the plasma.
