旨在揭示含双频周期激励的不同尺度Filippov系统的非光滑簇发振荡模式及分岔机制.以Duffing和Van der Pol耦合振子作为动力系统模型,引入周期变化的双频激励项,当两激励频率与固有频率存在量级差时,将两周期激励项表示为可以作为一慢变...旨在揭示含双频周期激励的不同尺度Filippov系统的非光滑簇发振荡模式及分岔机制.以Duffing和Van der Pol耦合振子作为动力系统模型,引入周期变化的双频激励项,当两激励频率与固有频率存在量级差时,将两周期激励项表示为可以作为一慢变参数的单一周期激励项的代数表达式,给出了当保持外部激励频率不变,改变参数激励频率的情况下,快子系统随慢变参数变化的平衡曲线及因系统出现的fold分岔或Hopf分岔导致的系统分岔行为的演化机制.结合转换相图和由Hopf分岔产生稳定极限环的演化过程,得到了由慢变参数确定的同宿分岔、多滑分岔的临界情形及因慢变参数改变而出现的混合振荡模式,并详细阐述了系统的簇发振荡机制和非光滑动力学行为特性.通过对比两种不同情形下的平衡曲线及分岔图,指出虽然系统有相似的平衡曲线结构,却因参数激励频率取值的不同,致使平衡曲线发生了更多的曲折,对应的极值点的个数也有所改变,并通过数值模拟,对结果进行了验证.展开更多
The deposition layer on the discharge channel wall of a Hall thruster after long-term operation occasionally detaches from the wall and interferes with the plasma inside the channel,resulting in current pulse and thre...The deposition layer on the discharge channel wall of a Hall thruster after long-term operation occasionally detaches from the wall and interferes with the plasma inside the channel,resulting in current pulse and threatening the power supply.To understand the generation mechanism of the current pulse,the interaction between the peeling material and the channel plasma was studied by the particle-in-cell and Monte Carlo collision(PIC/MCC)method.The plasma evolution and distribution in the Hall thruster channel when peeling material existed were simulated.Simulation results show that the peeling material changes the electron transportation and ionization,and the effects are related to the position of the peeling material.When the peeling material invades the zone where the ionization rate is originally the highest without peeling material,the ionization process is almost terminated.The ionization suppression by the peeling material will cause the propellant gas to refill the channel exit.As the peeling material moves away,gas discharge is induced near the channel exit,resulting in anode current pulse.展开更多
文摘旨在揭示含双频周期激励的不同尺度Filippov系统的非光滑簇发振荡模式及分岔机制.以Duffing和Van der Pol耦合振子作为动力系统模型,引入周期变化的双频激励项,当两激励频率与固有频率存在量级差时,将两周期激励项表示为可以作为一慢变参数的单一周期激励项的代数表达式,给出了当保持外部激励频率不变,改变参数激励频率的情况下,快子系统随慢变参数变化的平衡曲线及因系统出现的fold分岔或Hopf分岔导致的系统分岔行为的演化机制.结合转换相图和由Hopf分岔产生稳定极限环的演化过程,得到了由慢变参数确定的同宿分岔、多滑分岔的临界情形及因慢变参数改变而出现的混合振荡模式,并详细阐述了系统的簇发振荡机制和非光滑动力学行为特性.通过对比两种不同情形下的平衡曲线及分岔图,指出虽然系统有相似的平衡曲线结构,却因参数激励频率取值的不同,致使平衡曲线发生了更多的曲折,对应的极值点的个数也有所改变,并通过数值模拟,对结果进行了验证.
基金supported by National Natural Science Foundation of China(No.U23B20152).
文摘The deposition layer on the discharge channel wall of a Hall thruster after long-term operation occasionally detaches from the wall and interferes with the plasma inside the channel,resulting in current pulse and threatening the power supply.To understand the generation mechanism of the current pulse,the interaction between the peeling material and the channel plasma was studied by the particle-in-cell and Monte Carlo collision(PIC/MCC)method.The plasma evolution and distribution in the Hall thruster channel when peeling material existed were simulated.Simulation results show that the peeling material changes the electron transportation and ionization,and the effects are related to the position of the peeling material.When the peeling material invades the zone where the ionization rate is originally the highest without peeling material,the ionization process is almost terminated.The ionization suppression by the peeling material will cause the propellant gas to refill the channel exit.As the peeling material moves away,gas discharge is induced near the channel exit,resulting in anode current pulse.
