Langmuir waves in semi-relativistic spinless quantum plasmas

jeff madura;

Many-particle quantum hydrodynamics based on the Darwin Hamiltonian (the Hamiltonian corresponding to the Darwin Lagrangian) is considered. A force field appearing in the corresponding Euler equation is considered in detail. Contributions from different terms of the Darwin Hamiltonian in the Euler equation are traced. For example, the relativistic correction to the kinetic energy of particles leads to several terms in the Euler equation; these terms have different form. One of them has a formsimilar to a termappearing from the Darwin term. Hence, the two different mechanisms give analogous contributions in wave dispersion. A microscopic analog of the Biot–Savart law, called the current–current interaction, describing an interaction of moving charges via the magnetic field, is also included in our description. The semi-relativistic generalization of the quantum Bohm potential is obtained. Contribution of the relativistic effects
in the spectrum of plasma collective excitations is considered. The contributions of the spin–spin, spin–current, and spin–orbit interactions in this model are considered. The contribution of the spin evolution in the Langmuir wave spectrum is calculated at the propagation of wave perpendicular to the external magnetic field.