# 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 the 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 the contribution of the annihilation interaction in the quantum hydrodynamic equations and in the spectrum of waves in magnetized electron-positron plasmas. We consider the propagation of waves parallel and perpendicular to an external magnetic field. We also consider the oblique propagation of longitudinal waves. We derive the set of quantum kinetic equations for electron-positron plasmas with the Darwin and annihilation interactions. We apply the kinetic theory to the linear wave behavior in absence of external fields. We calculate the 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 conversionmore »

- Authors:

- Faculty of Physics, Lomonosov Moscow State University, Moscow (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22490926

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physics of Plasmas; Journal Volume: 22; Journal Issue: 6; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ANNIHILATION; ELECTRON-POSITRON INTERACTIONS; HELICITY; HYDRODYNAMICS; J-J COUPLING; KINETIC EQUATIONS; LANDAU DAMPING; MAGNETIC FIELDS; MAGNETIC MOMENTS; NONLINEAR PROBLEMS; PARTICLES; PHOTONS; QUANTUM PLASMA; SCHROEDINGER EQUATION; SPECTRA; SPIN; VISIBLE RADIATION

### Citation Formats

```
Andreev, Pavel A., E-mail: andreevpa@physics.msu.ru.
```*Hydrodynamic and kinetic models for spin-1/2 electron-positron quantum plasmas: Annihilation interaction, helicity conservation, and wave dispersion in magnetized plasmas*. United States: N. p., 2015.
Web. doi:10.1063/1.4922662.

```
Andreev, Pavel A., E-mail: andreevpa@physics.msu.ru.
```*Hydrodynamic and kinetic models for spin-1/2 electron-positron quantum plasmas: Annihilation interaction, helicity conservation, and wave dispersion in magnetized plasmas*. United States. doi:10.1063/1.4922662.

```
Andreev, Pavel A., E-mail: andreevpa@physics.msu.ru. Mon .
"Hydrodynamic and kinetic models for spin-1/2 electron-positron quantum plasmas: Annihilation interaction, helicity conservation, and wave dispersion in magnetized plasmas". United States.
doi:10.1063/1.4922662.
```

```
@article{osti_22490926,
```

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

author = {Andreev, Pavel A., E-mail: andreevpa@physics.msu.ru},

abstractNote = {We discuss the 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 the contribution of the annihilation interaction in the quantum hydrodynamic equations and in the spectrum of waves in magnetized electron-positron plasmas. We consider the propagation of waves parallel and perpendicular to an external magnetic field. We also consider the oblique propagation of longitudinal waves. We derive the set of quantum kinetic equations for electron-positron plasmas with the Darwin and annihilation interactions. We apply the kinetic theory to the linear wave behavior in absence of external fields. We calculate the 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 the electron-positron plasmas including the Darwin and annihilation interactions is derived. Existence of the conserving helicity in electron-positron quantum plasmas of spinning particles with the Darwin and annihilation interactions is demonstrated. We show that the annihilation interaction plays an important role in the quantum electron-positron plasmas giving the contribution of the same magnitude as the spin-spin interaction.},

doi = {10.1063/1.4922662},

journal = {Physics of Plasmas},

number = 6,

volume = 22,

place = {United States},

year = {Mon Jun 15 00:00:00 EDT 2015},

month = {Mon Jun 15 00:00:00 EDT 2015}

}