The planar Multipole Resonance Probe: a functional analytic approach
The planar Multipole Resonance Probe: a functional analytic approach
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DOI：
10.1140/epjti/s40485-018-0049-x
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发表时间：
2018-08-09
影响因子：
1
通讯作者：
Oberrath, J.
中科院分区：
文献类型：
--
作者：
Friedrichs, M.;Oberrath, J.
主动等离子体共振光谱（APRS）是一种众所周知的诊断方法，其中射频探针浸入等离子体并激发等离子体振荡。等离子体的响应被记录为频率依赖谱，其中出现共振峰。通过数学模型，可以从探测到的共振中确定电子密度或电子温度等等离子体参数。大多数APRS探针都有一个共同点，即它们浸入等离子体中，并且由于探针的物理存在而干扰等离子体。因此，它们是侵入性的，至少可以影响血浆的均匀性。为了解决这一问题，我们发明了一种可集成到等离子体反应器腔壁上的平面多极共振探头（pMRP）。本文提出了pMRP的第一个解析模型，该模型基于电子的冷等离子体描述。利用泛函解析方法和完备的标准正交基函数集，导出了探针等离子体系统的一般导纳。给出了含收敛性研究的近似导纳的显式谱。所确定的谐振频率与以往的仿真结果吻合较好。
Active Plasma Resonance Spectroscopy (APRS) is a well known diagnostic method, where a radio frequency probe is immersed into a plasma and excites plasma oscillations. The response of the plasma is recorded as frequency dependent spectrum, in which resonance peaks occur. By means of a mathematical model plasma parameters like the electron density or the electron temperature can be determined from the detected resonances.The majority of all APRS probes have in common, that they are immersed into the plasma and perturb the plasma due to the physical presence of the probe. Thus, they are invasive and can at least influence the homogeneity of the plasma. To overcome this problem, the planar Multipole Resonance Probe (pMRP) was invented, which can be integrated into the chamber wall of a plasma reactor.Within this paper, the first analytic model of the pMRP is presented, which is based on a cold plasma description of the electrons. The general admittance of the probe-plasma system is derived by means of functional analytic methods and a complete orthonormal set of basis functions. Explicit spectra for an approximated admittance including a convergence study are shown. The determined resonance frequencies are in good agreement with former simulation results.