TY - JOUR

T1 - The planar Multipole Resonance Probe

T2 - a functional analytic approach

AU - Friedrichs, Michael

AU - Oberrath, Jens

N1 - The authors acknowledge support by the internal funding of the Leuphana University Lüneburg and the German Research Foundation via the project OB 469/1-1. Gratitude is expressed to J. Gong, D.-B. Grys, M. Lapke, M. Oberberg, D. Pohle, C. Schulz, J. Runkel, R. Storch, T. Styrnoll, S. Wilczek, T. Mussenbrock, P. Awakowicz, T. Musch, and I. Rolfes, who are or were part of the MRP-Team at Ruhr University Bochum. Explicit gratitude is expressed to R.P. Brinkmann for fruitful discussions.

PY - 2018/8/9

Y1 - 2018/8/9

N2 - 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.

AB - 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.

KW - Active Plasma Resonance Spectroscopy

KW - Multipole Resonance Probe

KW - non-invasive Plasma Process Monitoring

KW - Plasma Diagnostic

KW - Functional analysis

KW - planar Multipole Resonance Probe

KW - Engineering

UR - https://www.mendeley.com/catalogue/5d179906-f7b6-35c6-a0f4-b84083e1e56f/

U2 - 10.1140/epjti/s40485-018-0049-x

DO - 10.1140/epjti/s40485-018-0049-x

M3 - Journal articles

VL - 5

JO - EPJ Techniques and Instrumentation

JF - EPJ Techniques and Instrumentation

SN - 2195-7045

IS - 1

M1 - 7

ER -