Development of Basic Science Relativistic Effects on the Dispersion and Stability of Orbital Angular Momentum (OAM) Plasmons in Degenerate Quantum Plasmas

This paper presents a comprehensive theoretical investigation into the relativistic effects on the dispersion characteristics and modulational stability of Orbital Angular Momentum (OAM) plasmons in degenerate quantum plasmas. Utilizing a relativistic quantum hydrodynamic (QHD) model, we analyze the collective electron dynamics by incorporating Fermi pressure, the Bohm quantum potential, and relativistic mass corrections. By transitioning from traditional plane-wave solutions to helical/vortex modes characterized by the topological charge l, we derive a modified dispersion relation that explicitly accounts for the OAM-dependent wave number. Our results demonstrate that the inclusion of the OAM index significantly shifts the dispersion curves and interacts non-linearly with quantum diffraction effects. Furthermore, through the derivation of the Nonlinear Schrödinger Equation (NLSE), we examine the Modulational Instability (MI) of these waves. The analysis reveals that increasing the OAM index l expands the stability regions, thereby suppressing the growth rate of instability in certain density regimes. We identify specific parametric regions—characterized by the PQ criterion—where the plasma supports the formation of bright and dark solitons. These findings provide a theoretical framework for understanding complex wave phenomena in high-density environments, such as laser-produced plasmas and the dense interiors of astrophysical white dwarfs, where both relativistic and OAM effects are non-negligible.

کلیدواژه ها:

Orbital Angular Momentum (OAM) plasmons ، Nonlinear Schrödinger equation (NLSE) ، Relativistic quantum hydrodynamics (QHD) ، Bright and dark solitons ، Modulational instability (MI)