Trojan Wave Packets in the Circularly Polarized  and the Magnetic Fields on the  multi-electron multi-layer Helium planar circular trajectories with the  scaled regular polygon nesting

Upon the discovery of the single electron Trojan Wave Packets in an atom of  Hydrogen driven by the 

Circularly Polarized (C.P.) electromagnetic field [1] we have formulated the theorem stating that the 

number of a distinct classically rotating frozen $N$-electron 

configurations in the external magnetic field, the nuclear ion 

field and the co-rotating electric field may be at least the

product of all naturally defined foldings of total force surfaces  (the maximal number

any straight  line may cut the surface which nontrivially is 2) obtained 

by putting each of the $3N$-dimensional  gradient component of 

the Zero Velocity Surface to zero. Consistently with it 

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 discrete 

rotational symmetry $C_{nv}$ distortion by the polarizing Circularly Polarized 

electromagnetic field without the loss of its nature.

Those were the multi-electron atom trajectories consisting 

of many layers of electrons moving in phase on 

circles with electron configurations placed at the 

vertexes of angles of identical or different by type by type or mutually twisted but only scaled 

regular polygons.

We have also recently  discovered the multi-electron trajectories 

which have the genetic origin of the two-electron non-Langmuir planar circular trajectories [1]

when all electrons in one plane are placed at the vertices of the identical scaled and nested regular polygons. 

Here for the first time we consider the multi-electron trajectories consisting of many 

layers of those which behave collectively as large charges compressed by the strong magnetic field to thick flakes

upon the rotation in the longitudinal equilibrium between the mutual repulsion and 

the nuclear attraction with the embedding planes being slightly curved to reach the equilibrium. 

The classical stabilization of the trajectories by the combination of 

fields further leads to the existence of non-dispersing 

localized Trojan-like wave packets moving around the trajectories. 

The time dependent Hartree simulations of such Wave Packets 

as well as those with the Time Dependent Quantum Diffusion 

Monte Carlo Method are conducted. [1] M. Kalinski, et al., 

Phys. Rev. Lett. {bf 95}, 103001, (2005).