TY - JOUR

T1 - Active plasma resonance spectroscopy: Eigenfunction solutions in spherical geometry

AU - Oberrath, Jens

AU - Brinkmann, Ralf P.

PY - 2014/12/1

Y1 - 2014/12/1

N2 - The term active plasma resonance spectroscopy 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 ωpe: 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. The mathematical model of an arbitrarily shaped probe-plasma system can be written in an abstract but very compact equation. It contains an appropriate operator, which describes the dynamical behavior and can be split into a conservative and a dissipative part. Based on the cold plasma model, this manuscript provides a solution strategy to determine the electrical admittance of a specific probe-plasma system derived from the abstract dynamical equation. Focusing on probes with a spherical-shaped probe tip the general admittance can be derived analytically. Therefore, the matrix representation of the resolvent of the dynamical operator is determined. This matrix representation is derived by means of the eigenfunctions and eigenvalues of the conservative operator. It can be shown that these eigenvalues represent the resonance frequencies of the probe-plasma system which are simply connected to the electron density. As an example, the result is applied to established probe designs: the spherical impedance probe and the multipole resonance probe.

AB - The term active plasma resonance spectroscopy 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 ωpe: 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. The mathematical model of an arbitrarily shaped probe-plasma system can be written in an abstract but very compact equation. It contains an appropriate operator, which describes the dynamical behavior and can be split into a conservative and a dissipative part. Based on the cold plasma model, this manuscript provides a solution strategy to determine the electrical admittance of a specific probe-plasma system derived from the abstract dynamical equation. Focusing on probes with a spherical-shaped probe tip the general admittance can be derived analytically. Therefore, the matrix representation of the resolvent of the dynamical operator is determined. This matrix representation is derived by means of the eigenfunctions and eigenvalues of the conservative operator. It can be shown that these eigenvalues represent the resonance frequencies of the probe-plasma system which are simply connected to the electron density. As an example, the result is applied to established probe designs: the spherical impedance probe and the multipole resonance probe.

KW - Engineering

KW - active plasma resonance spectroscopy

KW - eigenfunctions

KW - eigenvalues

KW - functional analytic

KW - impedance probe

KW - multipole resonance probe

KW - resonance frequencies

UR - http://www.scopus.com/inward/record.url?scp=84919384452&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/ce59afad-fbed-3a3b-93df-115e8cfa8854/

U2 - 10.1088/0963-0252/23/6/065025

DO - 10.1088/0963-0252/23/6/065025

M3 - Journal articles

AN - SCOPUS:84919384452

VL - 23

JO - Plasma Sources Science and Technology

JF - Plasma Sources Science and Technology

SN - 0963-0252

IS - 6

M1 - 065025

ER -