A Introduction to the Classical Spiral Electrodynamics: The” Spiral-Spin”
DOI:
https://doi.org/10.24297/jap.v17i.8494Keywords:
Larmor Frequency, Lorentz Equation, Maxwell Equations, Chandrasekhar Equation, Newton’s Laws, Schwarz-Christoffel Conformal Mapping, Spiral Coordinates, Wentzel-Kramers-Brillouin (WKB) MethodAbstract
This paper demonstrates the existence of analytical solutions of the Lorentz equation for charged particles in “uniform pilot time-varying magnetic fields". These analytical solutions represent a temporal generalization of the Larmor's orbits and are expressed through a Schwarz-Christoffel spiral mapping or in spiral coordinates.
The concepts of "spiral-spin” moment and "polar-spiral" angular momentum are then presented, the existence of a subclass of solutions for which these two angular moments are conserved is demonstrated.
It is also shown that under the action of the "pilot fields," there exist particular trajectories for which the charged particles have a "spiral-spin" momentum constant proportional to +1/2 (solution named "spiral-spin-up ") and -1/2 (solution named "spiral-spin-down "), respectively.
The results are in full agreement with the ideas of L.DeBroglie and A. Einstein on the possible existence of pilot fields able to describe the physical reality deterministically.
Finally, the solution of the Lorentz equation is discussed with the WKB (Wentzel-Kramers-Brillouin) method for a superposition of two uniform magnetic fields with the same direction, the first constant and the second time-varying.
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