On the structure of relativistic hydrodynamics for hot plasmas

Andreev, Pavel A.

doi:10.1088/1402-4896/ac8028

Cited by 7 publications

(24 citation statements)

References 38 publications

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“…Approximate calculation of functions p ab , t ab , q, and M abcd gives the following representations (for more details see ref. [14])…”

Section: Electromagnetic Waves In the Relativistic Magnetized Plasmasmentioning

confidence: 99%

“…The final equation in this set of hydrodynamic equations is the equation of evolution of current of the reverse relativistic gamma factor (the hydrodynamic Theta function). [ 14 ] Actually it is equation for its thermal part

{t}^a

(see Equation 7 and text below):

\begin{matrix} centertrue \\ (\partial_{t} + v \cdot \nabla) t^{a} + \partial^{a} \overset{true˜}{t} + false(t \cdot \nabla false) v^{a} + t^{a} false(\nabla \cdot v false) \\ + Γ (\partial_{t} + v \cdot \nabla) v^{a} = \frac{e}{m} {italicnE}^{a} [1 - \frac{v^{2}}{c^{2}} - \frac{3 p}{{nc}^{2}}] \\ + \frac{e}{italicmc} ε^{italicabc} {italicnv}_{b} B_{c} [1 - \frac{v^{2}}{c^{2}} - \frac{5 p}{{nc}^{2}}] - \frac{2 e}{{mc}^{2}} E^{a} p [1 - \frac{v^{2}}{c^{2}}] \\ - \frac{e}{{mc}^{2}} {italicnv}^{a} v^{b} E_{b} [1 - \frac{v^{2}}{c^{2}} - \frac{9 p}{{nc}^{2}}] + \frac{10 e}{3 {italicmc}^{4}} \end{matrix}

…”

Section: Relativistic Hydrodynamic Modelmentioning

confidence: 99%

“…The model used in this paper is suggested in ref. [14], where the spectrum of the Langmuir waves is considered for the relativistically large temperatures. Fig.…”

Section: Electromagnetic Waves In the Relativistic Magnetized Plasmasmentioning

confidence: 99%

“…The z-projection of the velocity field together with the z-projection of the electric field and the concentration satisfying linearized continuity equation: 𝜕 t 𝛿n + n 0 𝜕 z 𝛿v z = 0 describe the longitudinal waves described in ref. [14] The dynamics of the x-and y-projections of the velocity and the x-and y-projections of the electric field requires the equations for the evolution of the x-and y-projections of the flux of the reverse relativistic factor:…”

Section: Electromagnetic Waves In the Relativistic Magnetized Plasmasmentioning

confidence: 99%

“…Necessary equations of state are obtained either. [14] Extended sets of hydrodynamic equations allows to calculate equations of state for the hydrodynamic models. However, to some extend, it is possible to avoid the derivation and the application of the extended hydrodynamic models.…”

Section: Introductionmentioning

confidence: 99%

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Waves propagating parallel to the magnetic field in relativistically hot plasmas: A hydrodynamic model with the average reverse gamma factor evolution

Andreev

2023

Contributions to Plasma Physics

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The high‐frequency part of the dispersion dependence of electromagnetic waves propagating parallel to the external magnetic field in the plasma is considered. The plasma is macroscopically motionless, but has relativistic temperatures T∼mec2$$ T\sim {m}_e{c}^2 $$, where me$$ {m}_e $$ is the electron rest mass and, c$$ c $$ is the speed of light. The analysis is based on a novel hydrodynamic model based on four equations for the recently developed material fields (Andreev, Phys. Scr., 2022, 97, 085602). These material fields are the concentration, velocity field, average reverse relativistic γ$$ \gamma $$ factor, and the flux of the reverse relativistic γ$$ \gamma $$ factor. In the nonrelativistic regime, there are three transverse waves (the ions are motionless). In this study, we trace the charge of these properties under the influence of relativistic effects. Strong thermal effects lead to a coefficient in front of the cyclotron frequency, which decreases its effective contribution of the cyclotron frequency. At T=0.1mec2$$ T=0.1{m}_e{c}^2 $$, we have a decrease in the existence area of the fast magneto‐sound wave from the area of large frequencies. However, the existence area of extraordinary waves becomes larger at smaller frequencies. In the strong magnetic field limit ∣Ωe∣>ωLe$$ \mid {\Omega}_e\mid >{\omega}_{Le} $$, an additional wave appears with a frequency below the thermally decreased cyclotron frequency, where ∣Ωe∣$$ \mid {\Omega}_e\mid $$ is the electron cyclotron frequency, and ωLe$$ {\omega}_{Le} $$ is the Langmuir frequency. A further increase in the temperature leads to the disappearance of fast magneto‐sound waves and to a considerable increase in the existence area of the extraordinary waves towards smaller frequencies.

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“…Approximate calculation of functions p ab , t ab , q, and M abcd gives the following representations (for more details see ref. [14])…”

Section: Electromagnetic Waves In the Relativistic Magnetized Plasmasmentioning

confidence: 99%

{t}^a

(see Equation 7 and text below):

\begin{matrix} centertrue \\ (\partial_{t} + v \cdot \nabla) t^{a} + \partial^{a} \overset{true˜}{t} + false(t \cdot \nabla false) v^{a} + t^{a} false(\nabla \cdot v false) \\ + Γ (\partial_{t} + v \cdot \nabla) v^{a} = \frac{e}{m} {italicnE}^{a} [1 - \frac{v^{2}}{c^{2}} - \frac{3 p}{{nc}^{2}}] \\ + \frac{e}{italicmc} ε^{italicabc} {italicnv}_{b} B_{c} [1 - \frac{v^{2}}{c^{2}} - \frac{5 p}{{nc}^{2}}] - \frac{2 e}{{mc}^{2}} E^{a} p [1 - \frac{v^{2}}{c^{2}}] \\ - \frac{e}{{mc}^{2}} {italicnv}^{a} v^{b} E_{b} [1 - \frac{v^{2}}{c^{2}} - \frac{9 p}{{nc}^{2}}] + \frac{10 e}{3 {italicmc}^{4}} \end{matrix}

…”

Section: Relativistic Hydrodynamic Modelmentioning

confidence: 99%

“…The model used in this paper is suggested in ref. [14], where the spectrum of the Langmuir waves is considered for the relativistically large temperatures. Fig.…”

Section: Electromagnetic Waves In the Relativistic Magnetized Plasmasmentioning

confidence: 99%

Section: Electromagnetic Waves In the Relativistic Magnetized Plasmasmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Waves propagating parallel to the magnetic field in relativistically hot plasmas: A hydrodynamic model with the average reverse gamma factor evolution

Andreev

2023

Contributions to Plasma Physics

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Hydrodynamic and kinetic representation of the microscopic classic dynamics at the transition on the macroscopic scale

Andreev

2024

J. Plasma Phys.

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An open problem of the derivation of the relativistic Vlasov equation for systems of charged particles moving with velocities up to the speed of light and creating the electromagnetic field in accordance with the full set of the Maxwell equations is considered. Moreover, the method of derivation is illustrated on the non-relativistic kinetic model. Independent derivation of the relativistic hydrodynamics is also demonstrated. The key role of these derivations of the hydrodynamic and kinetic equations includes the explicit operator of averaging on the physically infinitesimal volume suggested by L.S. Kuzmenkov.

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Relativistic hydrodynamic model with the average reverse gamma factor evolution for the degenerate plasmas: High-density ion-acoustic solitons

Andreev

2022

Physics of Plasmas

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High-density low-temperature plasmas with degenerate species are considered in the limit of high Fermi velocities close to the speed of light. The small amplitude ion-acoustic solitons are studied in this regime. The analysis presented here is based on a relativistic hydrodynamic model with the average reverse gamma factor evolution consisting of the equations for the evolution of the functions such as the concentration, the velocity field, the average reverse relativistic gamma factor, and the flux of the reverse relativistic gamma factor, which are considered as main hydrodynamic variables. Justification of the suggested model via comparison of the hydrodynamic results with the result of application of the relativistic Vlasov kinetic equation is made in the linear approximation.

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On the structure of relativistic hydrodynamics for hot plasmas

Cited by 7 publications

References 38 publications

Waves propagating parallel to the magnetic field in relativistically hot plasmas: A hydrodynamic model with the average reverse gamma factor evolution

Waves propagating parallel to the magnetic field in relativistically hot plasmas: A hydrodynamic model with the average reverse gamma factor evolution

Hydrodynamic and kinetic representation of the microscopic classic dynamics at the transition on the macroscopic scale

Relativistic hydrodynamic model with the average reverse gamma factor evolution for the degenerate plasmas: High-density ion-acoustic solitons

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