The spherical multipole resonance probe: kinetic damping in its spectrum

Oberrath, Jens

doi:10.1088/1361-6595/ab759f

Cited by 10 publications

(15 citation statements)

References 44 publications

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“…However, in the kinetic spectral response, residual damping appears in the vanishing pressure limit. This collisionless damping can only be interpreted as kinetic effects, which have been verified in further studies [16,[26][27][28]. A brief comparison of the Drude model and kinetic model is shown in Tab.…”

Section: Introductionsupporting

confidence: 54%

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Kinetic investigation of the planar Multipole Resonance Probe under arbitrary pressure

Wang¹,

Friedrichs²,

Oberrath³

et al. 2021

Preprint

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Active plasma resonance spectroscopy (APRS) refers to a class of plasma diagnostic methods that use the ability of plasma to resonate at or near the electron plasma frequency for diagnostic purposes. The planar multipole resonance probe (pMRP) is an optimized realization of APRS.It has a non-invasive structure and allows simultaneous measurement of electron density, electron temperature, and electron-neutral collision frequency. Previous work has investigated the pMRP through the Drude model and collision-less kinetic model. The Drude model misses important kinetic effects such as collision-less kinetic damping. The collision-less kinetic model is able to capture pure kinetic effects. However, it is only applicable to the low-pressure plasma. To further study the behavior of the pMRP, we develop a collisional kinetic model in this paper, which applies to arbitrary pressure. In this model, the kinetic equation is coupled to the Poisson equation under the electrostatic approximation. The real part of the general admittance is calculated to describe the spectral response of the probe-plasma system. Both collision-less kinetic damping and collisional damping appear in the spectrum. This model provides a possibility to calculate the electron density, electron temperature, and electron-neutral collision frequency from the measurements.

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Section: Introductionsupporting

confidence: 54%

“…The pMRP is developed from the spherical multipole resonance probe (MRP) [23][24][25][26]. It consists of two semi-disc electrodes covered by a thin dielectric layer, which maintains a high degree of geometric and electrical symmetry.…”

Section: Introductionmentioning

confidence: 99%

Kinetic investigation of the planar Multipole Resonance Probe under arbitrary pressure

Wang¹,

Friedrichs²,

Oberrath³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…To overcome the limitation, a kinetic investigation is required. In [24][25][26][27], a general kinetic model of the probe-plasma system is discussed, and the functional analytic solutions of its specific geometries are determined. Unfortunately, it remains challenging for the collisionless case, which appears to be greatly relevant to reveal the pure kinetic effects.…”

Section: Introductionmentioning

confidence: 99%

Kinetic Simulation of the Ideal Multipole Resonance Probe

Gong,

Friedrichs,

Oberrath

et al. 2021

Preprint

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Active plasma resonance spectroscopy (APRS) is a process-compatible plasma diagnostic method which utilizes the natural ability of plasmas to resonate on or near the electron plasma frequency.The Multipole Resonance Probe (MRP) is a particular design of APRS that has a high degree of geometric and electric symmetry. The principle of the MRP can be described on the basis of an idealized geometry that is particularly suited for theoretical investigations. In a pressure regime of a few Pa or lower, kinetic effects become important, which can not be predicted by the Drude model. Therefore, in this paper a dynamic model of the interaction of the idealized MRP with a plasma is established. The proposed scheme reveals the kinetic behavior of the plasma that is able to explain the influence of kinetic effects on the resonance structure. Similar to particle-in-cell, the spectral kinetic method iteratively determines the electric field at each particle position, however, without employing any numerical grids. The optimized analytical model ensures the high efficiency of the simulation. Eventually, the presented work is expected to cover the limitation of the Drude model, especially for the determination of the pure collisionless damping caused by kinetic effects.A formula to determine the electron temperature from the half-width ∆ω is proposed.

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“…Here, we only focus on active plasma resonance spectroscopy (APRS) [2,3]: RF signals are fed into the plasma via a probe or antenna, the plasma is excited to oscillate, and the spectral response is recorded. The plasma parameters, such as electron density and temperature, can be obtained from the measured spectra through a specific mathematical model [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

“…Based on the concept of APRS, a variety of probes have been invented, such as the plasma resonance probe [4,5,17], curling probe [6,7,18], hairpin probe [8,9,19,20], and Multipole Resonance Probe (MRP) [1,[10][11][12]21]. As an optimized realization of APRS, the MRP allows a unique resonance peak in its spectrum and a simple relation between the resonance and the electron plasma frequency.…”

Section: Introductionmentioning

confidence: 99%

Kinetic investigation of the planar Multipole Resonance Probe in the low-pressure plasma

Wang,

Friedrichs,

Oberrath

et al. 2021

Preprint

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Active Plasma Resonance Spectroscopy (APRS) is a well-established plasma diagnostic method: a radio frequency signal is coupled into the plasma via a probe or antenna, excites it to oscillate, and the response is evaluated through a mathematical model. The majority of APRS probes are invasive and perturb the plasma by their physical presence. The planar Multipole Resonance Probe (pMRP) solves this problem: it can be integrated into the chamber wall and minimizes the perturbation. Previous work has studied the pMRP in the frame of the Drude model, but it misses important effects like collision-less damping. In this work, a collision-less kinetic model is developed to further investigate the behavior of the pMRP. This model consists of the Vlasov equation, which is coupled with the Poisson equation under electrostatic approximation. The spectral response of the probe-plasma system is found by calculating the complex admittance. This model covers the kinetic effects and overcomes the limitations of the Drude model.

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The spherical multipole resonance probe: kinetic damping in its spectrum

Cited by 10 publications

References 44 publications

Kinetic investigation of the planar Multipole Resonance Probe under arbitrary pressure

Kinetic investigation of the planar Multipole Resonance Probe under arbitrary pressure

Kinetic Simulation of the Ideal Multipole Resonance Probe

Kinetic investigation of the planar Multipole Resonance Probe in the low-pressure plasma

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