arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1305.7253physics.plasm-ph
收藏

活性等离子体共振光谱:动力学泛函分析描述

Active plasma resonance spectroscopy: A kinetic functional analytic description

Jens Oberrath, Ralf Peter Brinkmann

摘要:

术语“有源等离子体共振光谱”(APRS)表示一类相关技术,其出于诊断目的利用等离子体在电子等离子体频率$ω_{\rm pe}$上或附近共振的自然能力:无线电频率信号(在GHz范围内)通过天线或探针耦合到等离子体中,记录光谱响应,并且使用数学模型来确定等离子体参数,如电子密度或电子温度。这份手稿提供了一个动力学描述APRS有效的所有压力和探头的几何形状。描述的主题是探针与其影响域的等离子体的相互作用。在第一步骤中,建立该域的动能自由能,其相对于RF功率具有确定的时间导数。在没有射频激发的情况下,它具有李雅普诺夫泛函的性质;它的最小值提供了等离子体探针系统的稳定平衡。配备有由自由能的第二变分激发的标量积,平衡的所有扰动的集合形成希尔伯特空间。微扰的动力学可以用那个空间的演化方程来描述。等离子体探针系统的光谱响应函数由动力学算子的预解式的矩阵元组成。给出了一个等效电路模型的解释,并解释了在无碰撞制度的光谱的残留加宽。

英文摘要:

The term "Active Plasma Resonance Spectroscopy" (APRS) denotes a class of related techniques which utilize, for diagnostic purposes, the natural ability of plasmas to resonate on or near the electron plasma frequency $ω_{\rm pe}$: A radio frequent signal (in the GHz range) is coupled into the plasma via an antenna or probe, the spectral response is recorded, and a mathematical model is used to determine plasma parameters like the electron density or the electron temperature. This manuscript provides a kinetic description of APRS valid for all pressures and probe geometries. Subject of the description is the interaction of the probe with the plasma of its influence domain. In a first step, the kinetic free energy of that domain is established which has a definite time derivative with respect to the RF power. In the absence of RF excitation, it assumes the properties of a Lyapunov functional; its minimum provides the stable equilibrium of the plasma-probe system. Equipped with a scalar product motivated by the second variation of the free energy, the set of all perturbations of the equilibrium forms a Hilbert space. The dynamics of the perturbations can be cast in an evolution equation in that space. The spectral response function of the plasma-probe system consists of matrix elements of the resolvent of the dynamical operator. An interpretation in terms of an equivalent electric circuit model is given and the residual broadening of the spectrum in the collisionless regime is explained.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑