Kinetic Simulation of the Ideal Multipole Resonance Probe

TL;DR

This paper develops a kinetic simulation model for the ideal multipole resonance probe in plasma diagnostics, capturing kinetic effects beyond the Drude model to improve understanding of resonance behavior at low pressures.

Contribution

It introduces a gridless spectral kinetic simulation method for the MRP, addressing limitations of the Drude model by including collisionless damping effects.

Findings

Kinetic effects significantly influence resonance structures.

The model accurately predicts collisionless damping.

A new formula for electron temperature estimation is proposed.

Abstract

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 is proposed.