Relationship of mode transitions and standing waves in helicon plasmas

Abstract

The helicon wave plasma (HWP) sources have well-known advantages of high efficiency and high plasma density, with broad applications in many areas. The crucial mechanism lies on mode transitions, which has been an outstanding issue for years. We have built a fluid simulation model and further developed the Peking University Helicon Discharge (PHD) code. The mode transitions also known as density jumps of a single-loop antenna discharge are reproduced in simulations for the first time. It is found that large-amplitude SHWs are responsible for the mode transitions, similar to those of a resonant cavity for laser generation. This paper intends to give a complete and quantitative standing helicon wave (SHW) resonance theory to explain the relationship of the mode transitions and the SHWs. The SHW resonance theory reasonably explains several key questions in helicon plasmas, such as mode transition and efficient power absorption, and helps to improve future plasma generation methods.

The wave mode transition of argon helicon plasma

“…The approximate helicon wave dispersion relation of k z k = ωeµ 0 n e /B 0 (where k z and k are the axial wavenumber and total wavenumber, n e is the plasma density and µ 0 is magnetic permeability), which is valid for ω ce ≫ω, suggests linear dependence of density and the magnetic field for a given mode (at fixed ω and k z ) [18,30,31]. The stepwise increase in the density indicates the discharge operating in different helicon modes [19][20][21][22][23][24][25][26][27][28]. Most experimental and theoretical studies of multiple helicon modes have either been carried out in axially bounded systems (typically with a metal plate at the upper and/or lower end near the antenna), which are usually associated with the existence of standing helicon waves (SHWs) or cavity modes, determined by the geometry of the discharge cavity [19][20][21][22][23][24].…”

“…Generally, a simplified dispersion relation is satisfied when weakly damping helicon (H) waves are excited and penetrate into the central region at higher magnetic fields (typically B 0 > 200 G), while the strongly damping Trivelpiece-Gould (TG) waves can be strongly absorbed near the plasma edge (∼mm) or suppressed near the surface in the antiresonance region [11][12][13][14][15][16]. However, the relation between the density and the RF power or magnetic field in experiments is divided into several stages [16][17][18][19][20][21][22][23][24][25][26][27][28][29], indicating multiple helicon modes at increasing power or magnetic fields, which was characterized by an absolute jump in plasma density, the wavelength of the helicon wave and plasma potential, etc.…”

“…The stepwise increase in the density indicates the discharge operating in different helicon modes [19][20][21][22][23][24][25][26][27][28]. Most experimental and theoretical studies of multiple helicon modes have either been carried out in axially bounded systems (typically with a metal plate at the upper and/or lower end near the antenna), which are usually associated with the existence of standing helicon waves (SHWs) or cavity modes, determined by the geometry of the discharge cavity [19][20][21][22][23][24]. For example, Chi et al [19] reported the multiple density jumps of three wave modes using a DSF antenna under a lower magnetic field of B 0 = 55 G in a short system consisting of grounded aluminium endplates at both ends, which were considered cavity mode transitions.…”

“…They claimed that the density jump process is characterized by two temporal phases with the contribution of higher axial SHW modes. Wu et al [23] also provided a complete and quantitative SHW resonance theory to explain the relationship between the multiple helicon mode transitions of a single-loop antenna discharge and the SHWs using a fluid simulation model.…”

Effect of antenna helicity on discharge characteristics of helicon plasma under a divergent magnetic field

“…The different directions of antenna current will excite opposite azimuthal modes in the same magnetic field B 0 , as shown in figures 2(b) and (d). The optimal length of the helical antennas with m ±1 was determined based on equation (1) [28,29]…”