Development of a Method for Evaluating Electron Temperature from Electron Cyclotron Emission Spectra in Optically Thin Magnetized Plasmas

Yuan-Yao Chang^1*, Eiichirou Kawamori¹

¹Institute of Space and Plasma Sciences, National Cheng Kung University, Tainan, Taiwan

* Presenter:Yuan-Yao Chang, email:gundanoovs@gmail.com

Electron cyclotron emission (ECE) is a well-established diagnostic for measuring electron temperature in optically thick magnetized plasmas, including tokamaks. However, its conventional application is limited under optically thin conditions, and a reliable method for such cases has yet to be established.
In this study, we propose a new calibration approach to determine the electron temperature in optically thin plasmas using the intensity ratio of ECE harmonics. Based on the Schott–Trubnikov formula [1], we demonstrate a one-to-one relationship between temperature and the intensity ratio of the second and third harmonics. Theoretical calculations show that this ratio is weakly dependent on background parameters such as magnetic field and density within the range of 0.05–0.1 T and 10^15–10^17m⁻³ during the low temperature regime.
To verify this concept, laboratory experiments were conducted on the Magnetized Plasma eXperiment (MPX) device at National Cheng Kung University. The MPX is a linear mirror machine that generates magnetized plasma using a LaB₆-coated cathode and five confinement coils. Electron temperature was measured simultaneously using a Langmuir probe and an ECE radiometer. The lenses were employed as collection optics to improve the intensity of the detected signals. The radiometer, consisting of a heterodyne circuit and band-pass filters, measured the 2nd and 3rd harmonic intensities for comparison with theoretical predictions.
The experimental results show noticeable differences from the theoretical predictions, especially in the low-temperature range, where the measured intensity ratios deviate significantly from the expected curve. These discrepancies may come from several factors, such as imperfect calibration, the mixture of X- and O-mode emissions, and stray reflections from the chamber walls. To address these issues, we plan to improve the calibration accuracy and perform FDTD simulations to better understand the correction terms. In addition, placing a metallic mesh in front of the antenna may help achieve pure X-mode detection, and adding a viewing dump could effectively reduce unwanted stray radiation inside the chamber.
The ECE system and calibration method are intended for application in Taiwan’s first spherical tokamak experiment, conducted under the ongoing FIRST project.

Reference
[1] I.H. Hutchinson and K. Kato, Nucl. Fusion, 26, 179 (1986).

Keywords: Plasma Diagnostics, Electron Cyclotron Emission, Nuclear Fusion