A Introduction to the Classical Spiral Electrodynamics: The” Spiral-Spin”

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.

 https://rajpub.com/index.php/jap/article/view/8494