How and Why Do Lightning Sferics have Unstructured Wavefronts

Extending on the complete radiation patterns of the bremsstrahlung process involving bremsstrahlung asymmetry and Doppler shift. The mathematical model is simplified, preserving the forward-backward peaking radiation properties and involved asymmetries to help model the tendency of rotation in the wavefront of the emitted wave. Results show that the curl of the gradient of the radiation intensity is non-zero, and the wavefront of the bremsstrahlung radiation follows a tapered spiral wavefront in 2D and a tapered helical wavefront in 3D. The radius of the backward rotational wavefront was found to decrease as the wave propagates. Spiral geometry has different magnitudes of radius as the wavefront rotates as a result of the involved bremsstrahlung and Doppler asymmetries. This is further supported diagrammatically by applying Huygen's principle on a relativistic radiation pattern. Outcomes describe why the lightning discharges display a partial temporal and spatial coherence, hence why lightning sferics are not known to produce structured wavefronts. Bremsstrahlung emissions start with a backward rotating and irregularly shrinking radius wavefront. Therefore, spatial coherency degrades as their tapered helical structure breaks down due to the irregular shrinkage of radius, leaving the bremsstrahlung radiation with partial temporal coherency. Rotation always starts from the shorter, bremsstrahlung symmetric lobe.

Momentum transfer from particle to rotating wavefront photon, quantized via conservation of momentum,  p_f - p_i = - ΔP_field , and ΔP_field = (n' - n) ℏ k = Δn ℏ k, hence p_f = p_i - Δn ℏ k  where p_i, and p_f are initial and final particle momentum. Hence, the relationship between bremsstrahlung asymmetry, R, as a function of the whole-number multiple of the quantum of action "n", R(n), is found. A whole multiple of the quantum of action "n" is tuned, until the correct scale of the graph, for the bremsstrahlung asymmetry quantity, R, matches the classical prediction describing the asymmetry in radiation lobes due to the particle's curved trajectory. This allowed predicting the whole number multiple of the quantum of action "n", which is n ≅ 6.3 × 10¹⁰, following the Bohr correspondence principle. Since tuning is performed with the parameter whole multiple of the quantum of action "n", which only comes with the photon orbital angular momentum, this gives the traits of a rotating wavefront.

Position vector, r, is a function of bremsstrahlung asymmetry, R, which does not include the Doppler shift in its formulation. The results demonstrate the discovery of the Doppler asymmetry within the equation that relates the bremsstrahlung asymmetry, R, to the multiples of the quantum of action, n. This indicates that the two asymmetries are related to each other, which is explained using the idea that once there is an asymmetry about one axis of symmetry of an object, automatically, there are asymmetries about the other remaining axes of symmetry of the same object. Unless the center of what is causing asymmetry does not lie exactly on the symmetry axes (Otherwise, everything would be symmetric again), which is not the case with Bremsstrahlung radiation patterns.