Eigenfrequency of a Schumann Resonance

There are different numerical models, such as the transmission-line
matrix model or partially uniform knee model used to predict Schumann
radiation. This report introduces a new idea, and reasoning to the
previously stated idea of locating Schumann resonances on a single
particle’s radiation pattern using a Golden ratio and their Octave,
triad relationship. In addition, this different prediction method for
Schumann resonances derived from the first principle fundamental physics
combining both particle radiation patterns and the mathematical concept
of the golden ratio spiral that expands at the rate of the golden ratio.
The idea of golden ratio spiral allows locating Schumann resonant
frequencies on particle’s radiation patterns. The Octaves allows us to
predict the magnitude of other Schumann resonances on the radiation
pattern of a single accelerated charged particle conveniently by knowing
the value of the initial Schumann resonant frequency. In addition, it
also allows us to find and match Schumann resonances that are on the
same radiation lobe. Furthermore, it is important to find Schumann
octaves as they propagate in the same direction and have a higher
likelihood of wave interference. Method of Triads together with Octaves
helps to predict magnitude and direction of Schumann resonant points
without needing to refer to a radiation pattern plot. As the golden
ratio seems to be part of the Schumann resonances, it is helpful in
understanding to know why this is the case. The main method used in the
reasoning of the existence of golden ratio in Schumann resonances is the
eigenfrequency modes, $ \sqrt{n(n+1)} $ in the
spherical harmonic model. It has been found that eigenfrequency modes
have two a start off points, $ n_0 = 0 $ or $ n_0 =
\frac{\sqrt{5}-1}{2} $ where the
non-zero one is exactly the golden ratio. This allows to extend the
existing eigenfrequency modes to $
\sqrt{(n_0+n)^2+(n_o+n)} $ in order to explain
why golden ratio exist within Schumann resonances.