Vortex Solitons and Filamentation of Electromagnetic Beams in Relativistically Degenerate Plasmas
We study the propagation and stability of electromagnetic vortex beams in relativistically de generate plasmas. We show that such plasmas support localized vortex solitons carrying orbital angular momentum and analyze their linear and nonlinear stability. Vortex solitons undergo az imuthal symmetry-breaking instabilities whose growth rates depend on beam power, propagation constant, and topological charge, with the dominant mode determining the number of filaments formed during breakup. We further demonstrate that vortex solitons act as nonlinear attractors with a finite basin of attraction, while the vortex core remains topologically protected, maintaining a strictly zero field intensity at the beam center throughout the evolution. The results persist across a broad range of degeneracy parameters and are relevant to hard X-ray radiation propagating in dense astrophysical plasmas.