2020/06/28 by Pavel A. Andreev
Earth and Planetary Sciences · Physics and Astronomy · #Classical mechanics #Condensed matter physics #Coulomb #Dust and Plasma Wave Phenomena #Electron #Euler equations #Geometry #High-pressure geophysics and materials #Ionosphere and magnetosphere dynamics #Physics #Plasma oscillation #Quantum #Quantum Mechanics and Applications #Quantum electrodynamics #Quantum fluid #Quantum hydrodynamics #Quantum mechanics #Solar and Space Plasma Dynamics #Spin (aerodynamics) #Statistical Mechanics and Entropy #Tensor (intrinsic definition) #physics.plasm-ph
paper · pdf · doi:10.1017/s002237782100101x
5+3 pages
arxiv created 2020/06/28 · openalex publication_date 2020/06/28 · arxiv updated 2021/11/17 · openalex created_date 2021/11/22 · openalex updated_date 2026/08/05
If we study the quantum effects in plasmas in terms of traditional hydrodynamics via the continuity and Euler equations we find the quantum Bohm potential and the force of spin-spin interaction. However, if we extend the set hydrodynamic equations beyond the 13-moments approximation, and include the third rank tensor evolution equation along with the pressure evolution equation, we obtain the quantum corrections to the Coulomb interaction. It is found in contrast with the fact that hydrodynamic equations for the higher rank tensors do not contain interaction in the classic plasmas studied in the selfconsistent (meanfield) approximation. Therefore, we present the quantum hydrodynamic model, where the quantum effects are studied beyond the quantum Bohm potential. Developed model is considered in two regimes: all electrons in plasmas are considered as the single fluid, and the separate spin evolution regime, where electrons with different spin projections are considered as two different fluids. To illustrate the fundamental meaning of found quantum effects we demonstrate their contribution in the spectrum of the Langmuir waves and the spin-electron-acoustic waves. It is worth to mention that the application of the pressure evolution equation ensures that the contribution of pressure in the Langmuir wave spectrum is proportional to (3/5)vFe2, unlike (1/3)vFe2 appearing from hydrodynamics based on the continuity and Euler equations, where vFe is the Fermi velocity. Same correction corresponds on other plasmas phenomena like the speed of sound for spin-electron-acoustic waves. Moreover, it is found that novel quantum effects provide the novel wave solutions.