Abstract

We use the exponential parametrization of the nonextensive distribution to calculate the dielectric constant in an electron gas obeying the nonextensive statistics. As we show, the exponential parametrization allows us to make such calculations in a straightforward way, bypassing the use of intricate formulas obtained from integral tables and/or numerical methods. For illustrative purposes, we apply first the method to the calculation of the permittivity and the corresponding dispersion relation in the ultrarelativistic limit of the electron gas, and verify that it reproduces in a simple way the results that had been obtained previously by other authors using the standard parametrization of the nonextensive distribution. In the same spirit we revisit the calculation of the same quantities for a non-relativistic gas, in the high frequency limit, which has been previously carried out, first by Lima et al., and subsequently revised by Chen and Li. Our own results agree with those obtained by Chen and Li. For completeness, we also apply the method the low frequency limit in the non-relativistic case, which has been previously considered by Dai et al. in the context of the stream plasma instability. We discuss some features of the results obtained in each case and their interpretation of terms of generalized nonextensive quantities, such as the Debye length λ_D^(q), the plasma frequency ω_p^(q) and the ultra-relativistic frequency Ω_e,rel^(q). In the limit q → 1 such quantities reduce to their classical value and the classical result of the dispersion relations are reproduced.

Graphical abstract

中文翻译：

---

使用非扩展统计简化等离子体振荡的计算

摘要

我们使用非扩展分布的指数参数化来计算电子气体中的介电常数，服从非扩展统计。正如我们所展示的，指数参数化使我们能够以一种直接的方式进行此类计算，而无需使用从积分表和/或数值方法中获得的复杂公式。出于说明目的，我们首先将该方法应用于电子气体超相对论极限中的介电常数和相应的色散关系的计算，并验证它以简单的方式再现了其他作者先前使用该方法获得的结果。非广泛分布的标准参数化。本着同样的精神，我们重新审视了非相对论气体在高频范围内的相同数量的计算，首先由Lima等人进行，然后由Chen和Li进行修订。我们自己的结果与Chen和Li的结果一致。为了完整起见，我们还将该方法在非相对论情况下应用了低频极限，Dai等人先前已经考虑过。在流等离子体不稳定的情况下。我们讨论了在每种情况下获得的结果的一些特征以及它们对广义非广义量的解释，例如德拜长度λ 在流等离子体不稳定的情况下。我们讨论了在每种情况下获得的结果的一些特征以及它们对广义非广义量的解释，例如德拜长度λ 在流等离子体不稳定的情况下。我们讨论了在每种情况下获得的结果的一些特征以及它们对广义非广义量的解释，例如德拜长度λ_d ^（q）中，等离子体频率ω _p ^（Q）和超相对论频率Ω _E，相对^（Q） 。在极限q  →1中，这些量减少到其经典值，并且再现了色散关系的经典结果。

图形概要