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arXiv physics/0410204physics.plasm-ph
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非广延相对论等离子体中的纵向振荡

Longitudinal oscillations in a nonextensive relativistic plasma

Victor Munoz

摘要:

在Tsallis [C. Tsallis,J. Stat. Phys.{ \bf 52},479(1988)],其中非扩展性由Tsallis熵中的参数$q$表征。$q=1$对应于通常的玻尔兹曼-吉布斯,广泛的统计形式主义。在非相对论区域,平衡分布函数的归一化意味着$-1\leq q\leq\infty$。我们表明,在相对论制度更严格的约束必须满足,即$0\leq q \leq 1+ k_B T/mc^2$,其中$k_B$是玻耳兹曼常量,$T$是等离子体的温度,和$m$是粒子质量。然后,我们研究质子-电子等离子体中的纵向振荡,假设不动的质子和电子的分布函数最大化Tsallis的熵。这些振荡的色散关系被写在积分形式的长波长限制。在超相对论性区域中,$q$的所有可能值都可以用广义超几何函数得到明确的表达式。

英文摘要:

The dispersion relation of longitudinal electrostatic oscillations in a relativistic plasma is studied in the context of the nonextensive statistics formalism proposed by Tsallis [C. Tsallis, J. Stat. Phys. {\bf 52}, 479 (1988)], where nonextensivity is characterized by a parameter $q$ in Tsallis's entropy. $q=1$ corresponds to the usual Boltzmann-Gibbs, extensive statistics formalism. In the nonrelativistic regime, normalizability of the equilibrium distribution function implies that $-1\leq q\leq\infty$. We show that in the relativistic regime much tighter constraints must be satisfied, namely $0\leq q \leq 1+ k_B T/mc^2$, where $k_B$ is the Boltzmann constant, $T$ is the temperature of the plasma, and $m$ is the particle mass. Then we study longitudinal oscillations in a proton-electron plasma, assuming immobile protons, and electrons whose distribution function maximizes Tsallis's entropy. The dispersion relation of these oscillations is written in integral form for the long wavelength limit. Explicit expressions in terms of generalized hypergeometric functions can be found for all possibles values of $q$ in the ultra-relativistic regime.

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