The standing wave effect, which may lead to center-high density profiles in high frequency capacitive discharges, can be enhanced by nonlinearly excited harmonics. In this work, a nonlinear transmission line model, which solves for the electromagnetic fields in the time domain, is coupled to a two-dimensional bulk plasma fluid model to study nonlinear effects in asymmetric cylindrical capacitive argon discharges. An analytical collisional or collisionless (ion) sheath model is used to determine the stochastic and ohmic sheath heating and the nonlinear dependence of sheath voltage on sheath charge. We first examine a base case of a 20mTorr argon discharge driven with an electron power P _e = 40 W at a frequency f = 60 MHz, using collisionless and collisional sheath models. For the collisionless sheath model, the nonlinearly excited harmonics near the series and spatial resonance frequencies significantly enhance the on-axis power deposition and lead to a sharp peak of electron density at the discharge center. The collisional sheath model gives a smaller sheath width, leading to lower series and spatial resonance frequencies and a smaller source voltage for the fixed electron power. As a result, lower harmonics with broader spatial profiles and decreased magnitude are excited, reducing the center-high plasma nonuniformity. Then, we examine the discharge in a pressure range of 20–100mTorr at fixed P _e = 40 W and f = 60 MHz, using the collisional sheath model. As pressure increases, the harmonics gradually damp out, and the enhancement of on-axis power deposition becomes less significant. At the same time, more power is localized near the powered electrode edge due to decreased skin depth and smaller energy diffusion. As a result, the density peak shifts from the radial center to the powered electrode edge.

驻波效应可能会导致高频电容放电中的中心高密度分布，非线性激发的谐波可以增强驻波效应。在这项工作中，求解时域电磁场的非线性传输线模型与二维体等离子体流体模型耦合，以研究非对称圆柱电容氩气放电中的非线性效应。分析碰撞或无碰撞（离子）鞘模型用于确定随机和欧姆鞘加热以及鞘电压对鞘电荷的非线性依赖性。我们首先检查了一个 20mTorr 氩气放电的基本情况，该放电由电子功率P _e = 40 W驱动，频率为f= 60 MHz，使用无碰撞和碰撞鞘模型。对于无碰撞鞘模型，串联和空间共振频率附近的非线性激发谐波显着增强轴上功率沉积并导致放电中心电子密度的尖峰。碰撞鞘层模型给出了较小的鞘层宽度，导致较低的串联和空间共振频率以及固定电子功率的较小源电压。结果，具有更宽空间分布和减小幅度的低次谐波被激发，从而减少了中心高等离子体的不均匀性。然后，我们在固定P _e = 40 W 和f下检查 20–100 mTorr 压力范围内的放电= 60 MHz，使用碰撞鞘模型。随着压力的增加，谐波逐渐减弱，轴上功率沉积的增强变得不那么显着。同时，由于趋肤深度减小和能量扩散较小，更多的功率集中在通电电极边缘附近。结果，密度峰值从径向中心移动到通电电极边缘。