On relaxation processes in a completely ionized plasma
On relaxation processes in a completely ionized plasma
复制标题
完全电离等离子体中的弛豫过程
DOI：
10.26565/2312-4334-2020-3-03
复制
发表时间：
2020
影响因子：
5.2
通讯作者：
O. Hrinishyn
中科院分区：
文献类型：
--
作者：
A. Sokolovsky;S. Sokolovsky;O. Hrinishyn
本文研究了在空间均匀的完全电离等离子体中，外加恒定的空间均匀小电场时，电子能量和动量密度的弛豫。等离子体被认为是在一个广义的洛伦兹模型，相反，标准的一个假设，离子形成一个平衡系统。在洛伦兹之后，它被电子-电子和离子-离子相互作用所忽略。研究是基于我们早期从朗道动力学方程得到的线性动力学方程。因此，长程电子-离子库仑相互作用必然被描述。该模型的研究是基于碰撞积分算子的谱理论。该算子是对称的，正定的。其特征向量的形式选择的对称不可约张量描述动力学模式的系统。相应的本征值是弛豫系数，并定义了系统的弛豫时间。建立了描述电子能量和动量密度演化的标量和矢量本征函数（矢量和标量系统模式）。本文用这种方法得到了对任何时候都有效的密度的精确封闭方程组。此外，它被假定为它们的弛豫时间远远超过所有其他模式的弛豫时间。在这种情况下，存在一个特征时间，使得在相应的更大的时间，系统的演化减少描述的渐近值的密度。在约化描述下，电子分布函数仅通过渐近密度依赖于时间，并且满足一组封闭方程。在我们以前的文章中，我们在没有外电场的情况下证明了这个结果，并找到了精确的非平衡分布函数，这里证明了这种简化的描述也适用于小的均匀外电场。这可以被认为是Bogolyubov关于等离子体弛豫过程的泛函假设的一个证明，证明是在场的微扰理论的一级近似下进行的。然而，它的想法在该领域的所有订单中都是真实的。对等离子体中的电子迁移率、电导率以及电子与离子的平衡温差现象进行了严格的理论讨论和近似分析。为此，在前一篇文章的基础上，本文用Sonine多项式的本征函数级数截断展开法讨论了谱问题的近似解。在一次多项式近似下，弛豫过程结束时的非平衡电子分布函数可用麦克斯韦分布函数近似。这一结果证明了Lorentz-Landau等离子体非平衡过程理论中的假设是正确的。温度和速度弛豫系数的计算，我们早在一个和两个多项式近似。
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.