Quantum Corrections to Classical BGK Modes in Phase Space

In this paper we study the quantum corrections to the Bernstein‐Greene‐Kruskal equilibria of plasma physics by using perturbation methods near the classical solution. We obtain the solution for the Wigner function and for the self‐consistent potential to first order in the smallness parameter, which is the square of Planck's constant (in dimensionless form), and investigate the structure of the quantum phase space.

Keywords:

• Vlasov‐Poisson system
• Wigner‐Poisson system
• BGK modes
• Quantum BGK modes
• Plasma waves
• Semiclassical limit

Acknowledgments

Work partially supported by the Italian Ministry for University and Research.