Trojan Wave Packets in the Circularly Polarized and the Magnetic Fields on the multi-layer Langmuir type $(1)$ Helium trajectories with the inter-layer twist

Consistently with our recently discovered theorem stating that the number of distinct classically shape-invariantly rotating electron configurations in the external magnetic field and the nuclear ion field may be at least the product of all foldings of surfaces obtained by putting each of the multi-dimensional gradient component of the Zero Velocity Surface to zero we have discovered a several highly symmetric configurations originated from the Langmuir type $(1)$ ``Hoop Earrings" rotating Helium-like model trajectories [1] with further small symmetry distortion by the Circularly Polarized electromagnetic field without the loss of its nature. Those were the $2N$ or $2N+1$ electron Helium trajectories consisting of two or many layers of electrons moving in phase on circles with electron configurations placed at the vertexes of angles of identical by type but only scaled regular polygons parallel in space. Here we extend the case to the situation when the neighboring layer polygnons are phase-shifted by the half of their external angle. The classical stabilization of the trajectories by the combination of fields further leads to the existence of non-dispersing localized wave packets moving around the trajectories. [1] M. Kalinski, et al., Phys. Rev. Lett. {bf 95}, 103001, (2005).