Temperature and velocity relaxation in plasma. Spectral theory approach

Sokolovsky, S. А.; Sokolovsky, A. I.; Kravchuk, І. S.; Grinishin, O. A.

doi:10.15421/331919

Cited by 2 publications

(6 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As a result, relaxation coefficients are written in the one-polynomial approximation but exactly in small electron-to-ion mass ratio 2  . Details of these calculations with consideration of the two-polynomial approximation are discussed in our paper [18]. These results show that commonly used the Maxwell distribution function with electron component temperature and velocity as the electron distribution function in the presence of relaxation processes (see [5,9,10,12]) is true only in one-polynomial approximation and for small n u and 0 T T  .…”

Section: Eejp 3 (2020)mentioning

confidence: 67%

“…This is possible because the plasma is considered in the generalized Lorentz model [7] in which kinetic equation for electrons is a linear one and ions form an equilibrium system. In this approach the relaxation phenomena in plasma are discussed for spatially uniform states in our papers [17,18] and exact distribution function is found in the terms of scalar and vector eigenfunction p A , p n B p of the collision integral operator. These eigenfunction are calculated by the method of truncated expansion in the Sonine polynomial series.…”

Section: According This One Plasma Component Distribution Functions Fmentioning

confidence: 99%

“…Let us derive time equations for the densities  , n  . Kinetic equation (3) and definitions (9), (12), (15), (16), (18) after integration by parts give the next time equations for the momentum density l…”

Section: Evolution Of Energy and Momentum Densities Of The Electron Smentioning

confidence: 99%

See 2 more Smart Citations

On relaxation processes in a completely ionized plasma

Sokolovsky

Hrinishyn

2020

EEJP

View full text Add to dashboard Cite

Relaxation of the electron energy and momentum densities is investigated in spatially uniform states of completely ionized plasma in the presence of small constant and spatially homogeneous external electric field. The plasma is considered in a generalized Lorentz model which contrary to standard one assumes that ions form an equilibrium system. Following to Lorentz it is neglected by electron-electron and ion-ion interactions. The investigation is based on linear kinetic equation obtained by us early from the Landau kinetic equation. Therefore long-range electron-ion Coulomb interaction is consequentially described. The research of the model is based on spectral theory of the collision integral operator. This operator is symmetric and positively defined one. Its eigenvectors are chosen in the form of symmetric irreducible tensors which describe kinetic modes of the system. The corresponding eigenvalues are relaxation coefficients and define the relaxation times of the system. It is established that scalar and vector eigenfunctions describe evolution of electron energy and momentum densities (vector and scalar system modes). By this way in the present paper exact close set of equations for the densities valid for all times is obtained. Further, it is assumed that their relaxation times are much more than relaxation times of all other modes. In this case there exists a characteristic time such that at corresponding larger times the evolution of the system is reduced described by asymptotic values of the densities. At the reduced description electron distribution function depends on time only through asymptotic densities and they satisfy a closed set of equations. In our previous paper this result was proved in the absence of an external electric field and exact nonequilibrium distribution function was found. Here it is proved that this reduced description takes also place for small homogeneous external electric field. This can be considered as a justification of the Bogolyubov idea of the functional hypothesis for the relaxation processes in the plasma. The proof is done in the first approximation of the perturbation theory in the field. However, its idea is true in all orders in the field. Electron mobility in the plasma, its conductivity and phenomenon of equilibrium temperature difference of electrons and ions are discussed in exact theory and approximately analyzed. With this end in view, following our previous paper, approximate solution of the spectral problem is discussed by the method of truncated expansion of the eigenfunctions in series of the Sonine polynomials. In one-polynomial approximation it is shown that nonequilibrium electron distribution function at the end of relaxation processes can be approximated by the Maxwell distribution function. This result is a justification of Lorentz–Landau assumption in their theory of nonequilibrium processes in plasma. The temperature and velocity relaxation coefficients were calculated by us early in one- and two-polynomial approximation.

show abstract

Section: Eejp 3 (2020)mentioning

confidence: 67%

Section: According This One Plasma Component Distribution Functions Fmentioning

confidence: 99%

See 1 more Smart Citation

On relaxation processes in a completely ionized plasma

Sokolovsky

Hrinishyn

2020

EEJP

View full text Add to dashboard Cite

show abstract

“…where the following identity was taken into account is the collision integral). To equation (6) the conditions that define the hydrodynamic variables should be added 3 (1)…”

Section: Real Liquid Approximationmentioning

confidence: 99%

“…The solution of equation (6) n , because the Maxwell distribution is proportional to the density and the collision integral depends linearly on the distribution function [2]. Substitution (9) in (6) with account for (7) gives the relation, which must be an identity.…”

Section: Real Liquid Approximationmentioning

confidence: 99%

Relaxation phenomena in electron plasma of semiconductors

Sokolovsky¹,

Sokolovsky²,

Hrinishyn³

2020

JPhysElectron

Self Cite

View full text Add to dashboard Cite

The hydrodynamics of the electron subsystems of semiconductors is studied in the approximations of the ideal and real liquid, taking into account processes of relaxation of temperatures and macroscopic velocities of electrons and phonons without assuming the local equilibrium of the system. A set of integral equations for the electron distribution function of the first order in gradients is obtained, which determines the sources in the hydrodynamic equations of the ideal liquid approximation and the dissipative flows of energy and momentum of electrons. The steady states of the system in the ideal liquid approximation are investigated. The exact formulas for the electron mobility of the semiconductor and its conductivity are derived and kinetic coefficients that determine current in a spatially inhomogeneous state are calculated. In the presence of an electric field, the phenomenon of difference of temperatures of the electron and phonon subsystems is predicted. The obtained expressions are specified for the case of temperatures much higher the Debye temperature.

show abstract

Temperature and velocity relaxation in plasma. Spectral theory approach

Cited by 2 publications

References 0 publications

On relaxation processes in a completely ionized plasma

On relaxation processes in a completely ionized plasma

Relaxation phenomena in electron plasma of semiconductors

Contact Info

Product

Resources

About