AI 中文总结
本文建立了helicon放电点火时从真空到稳态的波色散关系过渡演化解析理论，揭示了helicon与TG波分支的分离特性及密度依赖规律。
AI 中文摘要
在稳态、充分发展的磁化等离子体柱中，helicon波与Trivelpiece–Gould（TG）波的色散关系已得到充分确立，但放电并非从该状态开始。点火期间，电子密度上升5至7个数量级，电子-中性粒子碰撞频率下降2至3个数量级，因此色散关系本身是随时间变化的量，其存在性需得到证明。本文针对均匀轴向场中的圆柱柱，建立了该过渡过程的闭合解析理论，采用冷态、碰撞性的双粒子描述，该描述在真空极限下仍保持正则性。得出三个结构性结果：第一，真空极限是控制垂直波数的四次方程的简并二重根；helicon分支与TG分支并非在某阈值处出现的独立模式，而是单个真空根的两个分支，由介电张量的旋光性和各向异性部分分裂而成。判别式的主导阶贡献完全抵消，因此分支随密度线性分离，而非受扰重根常见的平方根行为；分离相应受到抑制，helicon根在电子密度达到约10¹⁵ m⁻³前始终固定在真空值，而TG根立即偏离。
英文摘要
The dispersion relations of the helicon and Trivelpiece--Gould (TG) waves in a steady, fully developed magnetised plasma column are well established, but the discharge does not begin in that state. During ignition the electron density rises through five to seven orders of magnitude and the electron--neutral collision frequency falls by two to three, so the dispersion relation is itself a time-dependent object whose very existence must be justified. This paper develops a closed analytical theory of that transition for a cylindrical column in a uniform axial field, using a cold, collisional, two-species description that remains regular in the vacuum limit. Three structural results emerge. First, the vacuum limit is a degenerate double root of the quartic governing the perpendicular wavenumber; the helicon and TG branches are not independent modes that appear at some threshold but the two lobes of a single vacuum root, split by the gyrotropic and anisotropic parts of the dielectric tensor. The leading-order contribution to the discriminant cancels identically, so the branches separate linearly in density rather than with the square-root behaviour generic to a perturbed repeated root; the separation is correspondingly suppressed, and the helicon root remains pinned at its vacuum value until the electron density reaches about 10$^{15}$ m$^{-3}$ while the TG root departs immediately.
Comments41 pages, 7 figures
