Hydrodynamics of quantum corrections to the Coulomb interaction via the third rank tensor evolution equation: application to Langmuir waves and spin-electron acoustic waves

The quantum effects in plasmas can be described by the hydrodynamics containing the continuity and Euler equations. However, novel quantum phenomena are found via the extended set of hydrodynamic equations, where the pressure evolution equation and the pressure flux third-rank tensor evolution equat...

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Bibliographic Details
Published in:Journal of plasma physics 2021-10, Vol.87 (5), Article 905870511
Main Author: Andreev, Pavel A.
Format: Article
Language:English
Subjects:
Acoustic waves
Acoustics
Electron spin
Euler-Lagrange equation
Evolution
Fluid mechanics
Hydrodynamic equations
Hydrodynamics
Langmuir waves
Mathematical analysis
Plasma physics
Plasmas (physics)
Quantum phenomena
Tensors
Wave spectra
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Summary:The quantum effects in plasmas can be described by the hydrodynamics containing the continuity and Euler equations. However, novel quantum phenomena are found via the extended set of hydrodynamic equations, where the pressure evolution equation and the pressure flux third-rank tensor evolution equation are included. These give the quantum corrections to the Coulomb interaction. The spectra of the Langmuir waves and the spin-electron acoustic waves are calculated. The application of the pressure evolution equation ensures that the contribution of pressure in the Langmuir wave spectrum is proportional to $(3/5)v_{\textrm {Fe}}^{2}$ rather than $(1/3)v_{\textrm {Fe}}^{2}$, where $v_{\textrm {Fe}}$ is the Fermi velocity.
ISSN:0022-3778
1469-7807
DOI:10.1017/S002237782100101X