k-means Clustering Waveform Analysis for Phase-resolved Electron Energy Gain in Inductively Coupled Plasma under Confronting Divergent Magnetic Fields

We have performed Monte Carlo simulations of a low-pressure ICP under the confronting divergent magnetic fields, which have a separatrix that confines electrons, to investigate the mechanism of the electron heating in a magnetized plasma by the partial resonance [1, 2]. The partial resonance (a temporary and local ECR), which occurs in the resonant region near |B| = 2π(m/e)f, is notable mechanism as energy deposition to electrons in these plasmas. Here, B, m/e, and f are magnetic field, the electronic mass-to-charge ratio, and driving frequency, respectively. The phase-resolved electron energy gain (EEG, the energy gained by an electron per unit time during free flight) was observed as a key quantity to evaluate the partial resonance. EEG waveforms were characterized using the k-means clustering technique. Some of the EEG waveforms have an asymmetry that their amplitudes are larger in the first half period than in the second. We investigated the position-dependent features of the asymmetry by the k-means clustering for them.

The result shows that the specific asymmetry are characterized by the sampling location relative to the separatrix and contours of |B|. The EEG waveforms in the resonant region have a form of sin²2πft approximately, where t is time. The efficient energy deposition to electrons by the electric field E [3] was reconfirmed. The stronger B becomes, the more the phase of EEG leads relative to that in the resonant region. The phase lead would be caused by the higher electron gyrofrequency. In addition, the asymmetry of the EEG waveforms enhances, possibly because of the alternation of E×B drift direction. Under the separatrix, the EEG waveforms have a simple form of sin2πft unlike those in the resonant region. This characteristic is thought to be due to the low E and the strong B. The k-means clustering for the EEG waveforms would be a useful tool for identifying the physical factor causing the asymmetry.

[1] R. Okazaki and H. Sugawara: Japan. J. Appl. Phys. 62, SL1003 (2023). [2] R. Okazaki and H. Sugawara: Japan. J. Appl. Phys. 63, 126001 (2024). [3] K. Nakashima, H. Takahashi and H. Sugawara, Japan. J. Appl. Phys. 58, No.11, Art. No. 116001 (2019).