Full understanding of the basic physical mechanism behind the low magnetic field density peak phenomenon is crucial for realizing a simple, low-cost, and high-performance radio frequency helicon plasma source. Although research on this nonlinear phenomenon has continued for many years, there is still no unified explanation, and further theoretical and experimental research is needed.

As a further theoretical attempt to clarify the basic physical picture behind the low magnetic field density peak phenomenon, this paper investigates the influence of neutral gas pressure on Trivelpiece-Gould (TG) wave energy deposition characteristics in this context. Within the typical parameter range of low magnetic field density peak phenomenon, i.e. , wave frequency ω/(2π) = 13.56 MHz, low magnetic field (B₀ ≤ 100 G, 1 G = 10^–4 T), moderate plasma density (n₀ = 1 × 10¹² cm^–3), low neutral gas pressure (p ≤ 5 mTorr, 1 mTorr = 0.133 Pa), ratio of axial ion temperature to axial electron temperature (T_i,z /T_e,z = 0.1), by employing the general warm plasma dielectric tensor model and the eigenmode dispersion relationship of electromagnetic waves in magnetized plasma, the mode coupling characteristic between helicon and Trivelpiece-Gould (TG) waves, and the power deposition properties of helicon and TG waves for the first three azimuthal modes (m = 0, –1, +1) are theoretically analyzed. Analytical results suggest that: 1) The intensity of neutral gas pressure significantly impacts the mode coupling between the electromagnetic and electrostatic branches of Whistler waves, as well as between the helicon wave and TG wave. It also alters the position of the mode coupling surface (MCS) and the amplitude of the perpendicular wave numbers of helicon and TG waves. 2) For the first three azimuthal modes (m = 0, –1, +1) of helicon and TG waves, under low-pressure conditions, as pressure increases, energy deposition by the helicon wave gradually weakens while that by the TG wave increases; the m = +1 mode dominates energy deposition for the helicon wave, while the m = 0 mode dominates for the TG wave. As pressure increases, the peak energy deposition regions for both the m = +1 mode of the helicon wave and the m = 0 mode of the TG wave shift toward the edge of the plasma column. The m = 0 mode of TG wave plays a dominant role in overall energy deposition, with collisional and Landau damping dominating at different electron temperature ranges. As pressure increases, collisional damping induced energy deposition intensifies until a critical pressure threshold is exceeded beyond which collisional damping becomes the absolutely dominant mechanism. 3) For the m = 0 mode of the TG wave, under low neutral gas pressure conditions, energy deposition resulting from collisional and Landau damping peaks at a magnetic field of approximately 50 G and an electron temperature of a few electron-volts. These results provide theoretical support for understanding the low magnetic field density peak phenomenon and offer new evidence for a more comprehensive understanding of the helicon discharge process.