Hydrodynamic and kinetic models for spin-1/2 electron-positron quantum plasmas: Annihilation interaction, helicity conservation, and wave dispersion in magnetized plasmas

Abstract

We discuss complete theory of spin-1/2 electron-positron quantum plasmas, when electrons and positrons move with velocities mach smaller than the speed of light. We derive a set of two fluid quantum hydrodynamic equations consisting of the continuity, Euler, spin (magnetic moment) evolution equations for each species. We explicitly include the Coulomb, spin-spin, Darwin and annihilation interactions. The annihilation interaction is the main topic of the paper. We consider contribution of the annihilation interaction in the quantum hydrodynamic equations and in spectrum of waves in magnetized electron-positron plasmas. We consider propagation of waves parallel and perpendicular to an external magnetic field. We also consider oblique propagation of longitudinal waves. We derive set of quantum kinetic equations for electron-positron plasmas with the Darwin and annihilation interactions. We apply the kinetic theory for the linear wave behavior in absence of external fields. We calculate contribution of the Darwin and annihilation interactions in the Landau damping of the Langmuir waves. We should mention that the annihilation interaction does not change number of particles in the system. It does not related to annihilation itself, but it exists as a result of interaction of an electron-positron pair via conversion of the pair into virtual photon. A pair of the non-linear Schrodinger equations for electron-positron plasmas including the Darwin and annihilation interactions. Existence of conserving helicity in electron-positron quantum plasmas of spinning particles with the Darwin and annihilation interactions is demonstrated. We show that annihilation interaction plays an important role in quantum electron-positron plasmas giving contribution of the same magnitude as the spin-spin interaction.

On the equation of state for the “thermal” part of the spin current: The Pauli principle contribution in the spin wave spectrum in a cold fermion system

“…It is similar to the spinless case when the continuity and Euler equations can be represented as the single fluid effective non-linear Schrodinger equation [53]. Even spin-orbit interaction [19] and other relativistic effects [22], [58] can be included in non-linear effective equations. Nonlinearity is caused by different factors: the many-particle interaction effect and the pressure, particularly the Fermi pressure.…”

Spin-electron acoustic soliton and exchange interaction in separate spin evolution quantum plasmas

“…Among them we find the appearance of the spinplasma waves with frequencies near the cyclotron frequency [3], [4], [5], [6]. Later it was demonstrated that the quantum Bohm potential existing in the magnetic moment evolution equation shifts the frequency of the spin-plasma waves [7], [8]. This shift is proportional to the square of the wave vector.…”

“…Spin parts of the vorticity and helicity for spin-1/2 electron-positron plasmas were obtained in Ref. [8]. These phenomena appear along with the change of properties of well-known plasma phenomena (see for instance Refs.…”

“…This shift is proportional to the square of the wave vector. The annihilation interaction between electrons and positrons gives a shift of the spin-plasma wave frequency on a constant proportional to the magnetic moment density of the spin-1/2 quantum electron-positron plasmas [8]. Generation of waves in magnetized plasmas by neutron beams via the spinspin and spin-current interactions of the neutron spins with the spins and electric currents of the electrons and ions of the plasmas was considered in Ref.…”

Rich eight-branch spectrum of the oblique propagating longitudinal waves in partially spin-polarized electron-positron-ion plasmas

“…A hydrodynamic and kinetic models for spin-1/2 electron-positron quantum plasmas has been developed in Ref. [37] which incorporates the Coulomb, spin-spin, Darwin and annihilation interactions. There was concluded that the contributions of the annihilation interactions shifts the eigenfrequencies of the transverse electromagnetic plane polarized waves and transverse spin-plasma waves.…”