Measurement of Electron Entropy via Electron Cyclotron Emission in Laboratory Plasmas

Tzu-Chi Liu^1*, Eiichirou Kawamori¹

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

* Presenter:Tzu-Chi Liu, email:aragorn0402@hotmail.com

Confinement of high temperature plasmas has been a major physics issue for the realization of fusion power plants [1]. It is widely recognized that turbulence transport dominates the loss of energy and particles in magnetically confined plasmas [2]. One important characteristic feature of turbulence is that energy is irreversibly carried from large spatial scales where it is input, to small scales where the dissipation into heat takes place. As a result, a cascade of entropy is formed in the phase space. Such cascades has been observed numerically [3] and experimentally for ion-scale turbulence [4], but so far no experimental evidence exists for electron-scale turbulence.

To verify the cascade of entropy for electron-scale turbulence, a novel method has been proposed [5] for the measurement of the electron entropy utilizing electron cyclotron emission (ECE) from optically thin plasmas. At low density and temperatures, the radiation carries detailed information regarding the motion of the electrons in phase space, with each harmonics being coupled differently to the velocity distribution function. Viewing the relationships between the ECE spectra of multiple harmonics and the distribution function as constraints under which the entropy should be maximized, an application of the method of maximum entropy then yields both the fluctuation part of the distribution function and the associated entropy in phase space.

Here we report about the experimental verification of this method conducted in a linear mirror device, where the plasma is of low density (n_e ≦ 10¹⁸} [m^-3]) and low temperature (T_e ≦ 10 [eV]) so that the optically thin condition applies. The ECE radiation is collected by a heterodyne receiver, where the frequency of the emission is downconverted and then directly digitized via a high sampling rate oscilloscope. Fourier analysis then gives the spatially-resolved radiation spectrum with much higher spatial resolution than that of measured by bandpass filter banks in conventional radiometry. After application of the method, the electron velocity distribution function measured by Langmuir probes is used to cross-check with the reconstruction result.

[1] M. Shimada et al, Nucl. Fusion 47, S1 (2007)
[2] P. C. Liewer, Nucl. Fusion 25, 543 (1985)
[3] T. Tatsuno, et al., Phys. Rev. Lett. 103, 015003 (2009)
[4] E. Kawamori and Y. T. Lin, Commun. Phys. 5(1), 338 (2022)
[5] E. Kawamori, Nucl. Fusion 65, 026024 (2025)

Keywords: Plasma diagnostics, Plasma turbulence, Electron entropy