Locating Schumann Resonant Frequencies on a Single Particle Radiation
Patterns Using Golden Ratio Spiral

- Yucemoz Mert

## Abstract

Although lightning discharge is not the only source or only physical
phenomenon that affects the Schumann resonances, they have the highest
contribution to the Schumann resonances oscillating between the ground
the ionosphere. Schumann resonances are predicted through several
different numerical models such as the transmission-line matrix model or
partially uniform knee model. Here we report a 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. This prediction allows the
physical understanding of where Schumann resonances originate from
radiation emitted by a particle that involves many frequencies that are
not related to Schumann resonances. In addition, this method allows to
predict the wave propagation direction of each frequency value in the
Schumann frequency spectrum. Particles accelerated by lightning leader
tip electric fields are capable of contributing most of the Schumann
resonances. The radiation pattern of a single particle consists of many
frequencies that there are only specific ones within this pattern that
contribute to the Schumann radiation. Vast majority of Schumann
resonances distribute quite nicely obeying the Golden ratio interval.
This property used in conjunction with the full single-particle
radiation patterns also revealed that high-frequency forward-backward
peaking radiation patterns as well as low-frequency radiation patterns
can contribute to Schumann resonances. Moreover, this also allows to
locate them on the full radiation pattern. Furthermore, theoretical
analysis using Golden ratio spiral predicts that there are more Schumann
resonances in high frequency forward-backward peaking radiation pattern
of relativistic particle than low frequency dipole radiation pattern.