Automated electron temperature fitting of Langmuir probe I–V trace in plasmas with multiple Maxwellian EEDFs

Abstract

An algorithm for automated fitting of the effective electron temperature from a planar Langmuir probe I-V trace taken in a plasma with multiple Maxwellian electron populations is developed through MATLAB coding. The code automatically finds a fitting range suitable for analyzing the temperatures of each of the electron populations. The algorithm is used to analyze I-V traces from both the Institute of Plasma Physics Chinese Academy of Sciences's Diagnostic Test Source device and a similar multi-dipole chamber at the University of Wisconsin-Madison. I-V traces reconstructed from the parameters fitted by the algorithm not only agree with the measured I-V trace but also reveal physical properties consistent with those found in previous studies. Cylindrical probe traces are also analyzed with the algorithm and it is shown that the major source of error in such attempts is the disruption of the inflection point due to both decreased signal-to-noise ratio and greater sheath expansion. It is thus recommended to use planar probes with radii much greater than the plasma Debye length when signal-to-noise ratio is poor.

Instability enhanced thermalization of bi-Maxwellian EEDF in multi-dipole confined hot cathode discharge: an experimental observation

“…Figures 3 and 4 illustrate the current-voltage (I-V) characteristics obtained through Langmuir probe measurements, with identical neutral gas pressure conditions (8.9 × 10 −2 Pa), but varying plasma discharge currents. To automate the process of determining the effective electron temperature from a planar Langmuir probe I-V trace acquired in a plasma containing multiple Maxwellian electron populations, an algorithm has been developed using MATLAB coding [29]. This algorithm automatically identifies an appropriate fitting range for analyzing the temperatures associated with each electron population.…”

“…After each fitting is completed, the high-temperature electrons need to be subtracted from the I-V trace. Otherwise the hotter electrons become 'double-counted' for the lower temperature fittings [8,29]. Figures 3 and 4 also depict the fitting process for plasma currents of 1 A and 8 A.…”

Parametrization of electron sheath expansion for Langmuir probe I-V traces

“…The electron sheath expansion is also commonly approximated as a linear effect [17]. This is because electron sheath is expected to have a much smaller sheath thickness compared to that of an ion sheath, leading to a less pronounced sheath expansion effect.…”

“…The fitting algorithm in this work is based on the previous work by Yip et al [17]. The fitting method of ion current 𝐼 𝑖 and electron current 𝐼 𝑒 is modified using the Sheridan's model except that the fitting In this work, the ion current fitting range is chosen to be −85 V < 𝑉 bias < −55 V. We assumed cold and non-drifting ions which implies that when 𝑉 bias ≥ 𝑉 𝑝 , the ion current 𝐼 𝑖 = 0.…”

“…The ion current 𝐼 𝑖 is then subtracted from the 𝐼-𝑉 trace and multiple Maxwellian fitting is performed, the process of which is shown in detail in reference [17]. The device where the experiments were conducted is a multi-dipole confined hot cathode source, which would be introduced in detail in the following section, and generally has several electron species due to the complicated processes of formation of the bulk electron energy distribution function (EEDF) including primary electrons injected into the device from the hot cathode, primary electrons degraded by collisions with the neutrals, secondary electrons produced by primary electrons colliding with the device's chamber wall, plasma electrons produced via impact ionization, and electron loss to the walls [18].…”