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. 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.

Bremsstrahlung asymmetry, R caused by the angular spin momentum transfer of a bremsstrahlung particle to the photons of an emitted forward-backward peaking radiation pattern. Momentum transfer from charged particle to photon could be in the form of bremsstrahlung particle emitting a photon of higher momentum. Bremsstrahlung particle, following anticlockwise spiral particle trajectory, has bremsstrahlung spin in the clockwise direction

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. This extended work reports another novel asymmetry in the overall radiation pattern. 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 mathematical modeling of the bremsstrahlung process into different high-density mediums 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.

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.

Probability allows predicting the most and least probable outcomes. However, the probability of an outcome is affected by the physical quantities that describe the universe. The certainty of a single outcome and uncertainties of many outcomes are determined by how uniformly a scalar field (i.e. Potential field, entropy, mass) is distributed over an entity. It is known that an increase in entropy increases the likelihood. In this paper, this knowledge is taken one step further to understand the likelihood of the possible outcomes within an entity which have either a uniform or non-uniform scalar field. Uniform scalar fields over an entity have net-zero scalar field value. An example of Uniform scalar fields over an entity is rolling an unloaded dice where every individual six outcomes have an equal likelihood. Uniform scalar fields over an entity are where most uncertainty occurs as all outcomes have an equal likelihood. The non-uniform scalar field over an entity is where there is most certainty towards a single outcome. For example, a loaded dice has the highest probability for a single outcome. The theoretical model created in this paper is based on two square six by 6 cm dice, where one die is loaded non-uniformly with different chemical molecules of different entropy and mass value and represented with contour lines in a contour map. Another dice is loaded uniformly with the same chemical molecule of the same entropy and mass all over the dice. As the distribution of the chemical molecule is uniform, this configuration represents an unloaded die. Neither entropy nor mass scalar fields alone are capable of determining the outcome of the dice alone. The outcome is also determined by the type of external force, energy acting on the entity (i.e. dice), and the definition of probability. All in all, the Important result is that regardless of the definition of probability, type of external force, energy, or internal scalar field within the entity, the most probable outcome, and the least probable outcome are determined and connected by the gradient of the scalar field (i.e. Gradient of Entropy, ∇ S ) within the entity.

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. As Fibonacci numbers increase, ratio of two consecutive Fibonacci number approaches to the value of Golden ratio. New equation describing the value of Fibonacci number can be used to re-write eigen-frequency orders of Schumann resonances.

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.

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 method build on the previously stated idea of locating Schumann resonances on a single particle's radiation pattern using a Golden ratio. 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 Golden ratio. Moreover, extending the idea of ratios to a specific ratio called octaves used in standing waves that identify the identical sounding notes with different frequencies. Knowing the value of initial Schumann resonant frequency, this method allows us to predict the magnitude of other Schumann resonances on the radiation pattern of a single accelerated charged particle conveniently. In addition, it also allows us to find and match Schumann resonances that are on the same radiation lobe, which is named electromagnetic Schumann octaves. Furthermore, it is important to find Schumann octaves as they propagate in the same direction and have a higher likelihood of wave interference.

The forward peaking radiation pattern of a single particle with an increasing particle velocity is well-established knowledge. Further details of a single particle radiation pattern suggest that a particle also has a backward peaking radiation pattern and two associated asymmetries coming from the Doppler and spiral trajectory bremsstrahlung effects. Relativistic particle under periodic motion emits spiral radiation pattern which is measured as short pulses by the sensors. However, the transition from peaking to spiral radiation pattern as particle transits from discrete to continuous periodic motion is not clear. This paper reports a possible physical asymmetric effect caused by the bremsstrahlung spiral trajectory that could be responsible for the spiral radiation pattern emitted by the periodic particle motion. The bremsstrahlung asymmetry changes within each period that change the radiation intensity symmetry continuously, within a specific minimum and maximum range. This maximum and minimum range is defined by the limits of the bremsstrahlung asymmetry, R. This change in radiation intensity, independent of particle periodicity, emits circular waves of the varying radius that forms a spiral radiation pattern. Hence, the spiral of a periodic motion comes from a parameter, R, that is independent of periodicity. Hence, parameter R can change during a period by preserving the periodicity of the incoming particle motion. Overall, a continuous periodic motion is important in predicting the experimental observations as incoming particle interacts with multiple target particles meaning the same bremsstrahlung process repeats periodically.

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 method build on the previously stated idea of locating Schumann resonances on a single particle’s radiation pattern using a Golden ratio and their Octave 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 Golden ratio. Previous idea of 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 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. This contribution, introduces another property of Schumann resonant points on a relativistic radiation pattern that enables to predict the direction of the remaining Schumann resonant frequency points that are not Octave pairs. Previously, Schumann Octaves were introduced as a method to predict which Schumann resonant points exist on same radiation lobe, hence propagate in the same direction. This method of Triads is an additional method to Octaves in order to predict propagation direction of all Schumann points besides Octave pairs. Count of Schumann resonant frequency points starts with one as the first and minimum frequency Schumann point on a Golden ratio spiral. Count of Schumann resonant frequency points goes up to seven with increasing radius of Golden ratio spiral. Hence, the odd triad consists of Schumann resonant points 1, 3 and 5. Whereas, even triad consists of Schumann resonant points 2,4 and 6. First point in the triad is called “root” and final point is called “third”. Root and the third are always Octave apart from each other. Hence, exist on same radiation lobe and propagate in the same direction. Odd number triads distribute vertically and even number triads distribute horizontally on a relativistic radiation pattern plot. Hence, this causes Octave value of an odd triad to be bigger than the Octave value of even triad. There are three Octave pairs and odd triad is the one with the highest Octave value. Triads together with Octaves helps to predict magnitude and direction of Schumann resonant points without needing to refer to a radiation pattern plot.

The forward peaking radiation pattern of a single particle with an increasing particle velocity is well-established knowledge. Further details of a single particle radiation pattern suggest that a particle also has a backward peaking radiation pattern and two associated asymmetries coming from the Doppler and spiral trajectory bremsstrahlung effects. Relativistic particle under periodic motion emits spiral radiation pattern which is measured as short pulses by the sensors. However, the transition from peaking to spiral radiation pattern as particle transits from discrete to continuous periodic motion is not clear. This paper reports a possible physical asymmetric effect caused by the bremsstrahlung spiral trajectory that could be responsible for the spiral radiation pattern emitted by the periodic particle motion. The bremsstrahlung asymmetry changes within each period that change the radiation intensity symmetry continuously, within a specific minimum and maximum range. This maximum and minimum range is defined by the limits of the bremsstrahlung asymmetry, R. This change in radiation intensity, independent of particle periodicity, emits circular waves of the varying radius that forms a spiral radiation pattern. Hence, the spiral of a periodic motion comes from a parameter, R, that is independent of periodicity. Hence, parameter R can change during a period by preserving the periodicity of the incoming particle motion. Overall, a continuous periodic motion is important in predicting the experimental observations as incoming particle interacts with multiple target particles meaning the same bremsstrahlung process repeats periodically.

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. 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.