Previously the radiation patterns of combined parallel and perpendicular motions from the accelerated relativistic particle at low and high frequencies of the bremsstrahlung process with an external lightning electric field were explained. The primary outcome was that radiation patterns have four relative maxima with two forward peaking and two backward peaking lobes. The asymmetry of the radiation pattern, i.e., the different intensities of forwarding and backward peaking lobes, is caused by the Doppler effect. A novel outcome is that bremsstrahlung has an asymmetry of the four maxima around the velocity vector caused by the curvature of the particle’s trajectory as it emits radiation. Previously stated bremsstrahlung asymmetry, R was an asymmetry in the radiation lobe pairs about particles velocity vector. Bremsstrahlung asymmetry used to occur at the same level in both forward radiation lobe pairs and backward radiation lobe pairs. However, in high-density mediums where the emitted wave can lag behind the speed of the particle, symmetry of the magnitude of bremsstrahlung asymmetry, R differs between forward peaking radiation lobe pairs relative to backward peaking radiation lobe pairs. This is another novel asymmetry and it causes bremsstrahlung asymmetry, R to be larger in the forward peaking compared to backward peaking radiation. The outcome is the shrink in radiation length that occurs in the backward peaking lobes. This extended work reports, changes in the radiation pattern as the emitted wave propagates through different mediums. Two novel formulas are derived from Snell’s law for a particle entering the medium horizontally and from any other angle between \Pi/2 and -\Pi/2 radians. The novel outcome is the change in angle between forward peaking radiation lobe pair and backward peaking radiation lobe pair defined as bremsstrahlung angle, \theta_{brem}. When the bremsstrahlung particle crosses different mediums, change in angle between the forward and backward radiation lobe pairs, bremsstrahlung angle, \theta_{brem} breaks into its components as each lobe changes angle at different magnitudes from the particle’s velocity vector. Therefore, bremsstrahlung angle, \theta_{brem} between forward-backward peaking lobes transforms into individual angles \Omega_{1}, \Omega_{2}, \Omega_{3}. \Omega_{4} all measuring from the particle’s velocity vector.

Terrestrial Gamma-ray Flashes exhibit slopes of ionizing radiation associated with bremsstrahlung. Bremsstrahlung has a continuous spectrum of radiation from radio waves to ionizing radiation. The Poynting vector of the emitted radiation, i.e., the radiation pattern around a single particle under the external lightning electric field during interaction with other particles or atoms, is not quite well known. The overall radiation pattern arises from the combination of radiation of parallel and perpendicular motions of a particle caused by the acceleration from the lightning electric field and the bremsstrahlung. The calculations and displays of radiation patterns are generally limited to a low-frequency approximation for radio waves and separate parallel and perpendicular motions. Here we report the radiation patterns of combined parallel and perpendicular motions from accelerated relativistic particles at low and high frequencies of the bremsstrahlung process with an external lightning electric field. The primary outcome is that radiation patterns have four relative maxima with two forward peaking and two backward peaking lobes. The asymmetry of the radiation pattern, i.e., the different intensities of forward and backward peaking lobes, are caused by the Doppler effect. A novel outcome is that bremsstrahlung has an asymmetry of the four maxima around the velocity vector caused by the curvature of the particle's trajectory as it emits radiation. In addition, change in kinetic energy of bremsstrahlung electron and shrinking radiation lobe due to bremsstrahlung asymmetry were found to increase electron's energy concentration towards the outer regions of the curved trajectory. This mathematical modeling helps to better understand the physical processes of a single particle's radiation pattern, which might assist the interpretation of observations with networks of radio receivers and arrays of gamma-ray detectors.

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.