On relaxation processes in a completely ionized plasma
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.
D. Jou, J. Casas-Vazques, and G. Lebon, Extended Irreversible Thermodynamics, (Springer, 2010).
S.V. Peletminskii, Yu.V. Slyusarenko, and A.I. Sokolovsky, Physica A. 326(3-4), 412-429 (2003), https://doi.org/10.1016/S0378-4371(03)00255-3.
V.N. Gorev, A.I. Sokolovsky, in: Actual Problems of Mathematical Physics and its Applications. Proceedings of Institute of Mathematics NASU, 11(1), (IM, Kyiv, 2014), pp. 67-92.
H.A. Lorentz, Proc. Acad. Sci. Amsterdam, 7, 438, 585 (1905).
L.D. Landau, ZhETF, 7, 203-209 (1936). (in Russian).
A.I. Akhiezer, S.V. Peletminsky, Methods of Statistical Physics, (Pergamon Press, Oxford, 1981).
S.A. Sokolovsky, A.I. Sokolovsky, I.S. Kravchuk, and O.A. Grinishin, Journal of Physics and Electronics, 26(2), 17-28 (2018), https://doi.org/10.15421/331818.
B.M. Smirnov, UFN, 172(12), 1411-1445 (2002). (in Russian).
A.F. Aleksandrov, L.S. Bogdankevich, and A.A. Rukhadze, Principles of Plasma Electrodynamics, (URSS, Moscow, 2013), pp. 504.
E.M. Lifshitz, and L.P. Pitaevskii, Physical kinetics, (Pergamon Press, Oxford, 1981).
I.S. Braginsky, ZhETF, 33, 459 (1957).
N.N. Bogolyubov, and N.N. Bogolyubov (Jr.), Аспекты теории полярона [Aspects of polaron theory], (Fizmatlit, Moscow, 2004), pp. 175. (in Russian).
V.N. Gorev, and A.I. Sokolovsky, Ukr. J. Phys. 60(3), 232-246 (2015), https://doi.org/10.15407/ujpe60.03.0232.
V. N. Gorev, S.A. Sokolovsky, and A.I. Sokolovsky, Vìsnik Dnìpropetrovs’kogo unìversitetu. Serìâ Fìzika, radìoelektronika, 24(23/2), 83-93 (2016).
S.A. Sokolovsky, A.I. Sokolovsky, І.S. Kravchuk, O.A. Grinishin, Journal of Physics and Electronics, 26(2), 17-28 (2018), https://doi.org/10.15421/331818.
S.A. Sokolovsky, A.I. Sokolovsky, І.S. Kravchuk, O.A. Grinishin, in: Proceedings of IEEE 40th International Conference on Electronics and Nanotechnology (ELNANO-2020), ISBN: 978-1-7281-9712-8, (Kyiv, Ukraine, 2020), pp. 284-287.
S.A. Sokolovsky, and A.I. Sokolovsky, in: Proceedings of IEEE 2nd Ukraine Conference on Electrical and Computer Engineering, (UKRCON-2019), ISBN: 978-1-7281-3882-4, (Lviv, Ukraine, 2019), pp. 783-787.
S.A. Sokolovsky, A.I. Sokolovsky, І.S. Kravchuk, and O.A. Grinishin, Journal of Physics and Electronics, 27(2), 29-36 (2019), https://doi.org/10.15421/3919/9.
S.A. Sokolovsky, Theoretical and Mathematical Physics, 168(2), 1150-1164 (2011), https://doi.org/10.1007/s11232-011-0093-z.
Gorev V., Gusev A., Korniienko V. & Aleksieiev M. (2021)
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).