AI 中文总结
本研究针对真空二极管，证明过往认为的分岔解$J_{LD}$并非有效稳态解，明确真实分岔解为$J_{Jaff\acute{e}}$，并通过粒子模拟给出磁滞电流密度$J_{hys}$与$J_{Jaff\acute{e}}$的半经验关系。
AI 中文摘要
对于真空内具有非零初速度$u_0\ne0$的电子，空间电荷限制电流密度（SCLCD）由$J_{Jaff\acute{e}}$给出。当电流密度$J>J_{Jaff\acute{e}}$时，会发生电子反射并伴随虚阴极（VC）振荡。过往研究显示，该振荡可持续至$J=J_{hys}$时出现磁滞现象，通常声称$J_{hys}\approx J_{LD}<J_{Jaff\acute{e}}$，其中$J_{LD}$也称为分岔解，是虚阴极处电子速度为零的稳态电流密度。本研究证明$J_{LD}$并非有效稳态解，因为其对应的电荷密度高于真实SCLCD$J_{Jaff\acute{e}}$；进一步证明$J_{Jaff\acute{e}}$对应真实的数学分岔解。通过在不同间隙距离和电压下的粒子模拟，本研究证实$J_{hys}$始终与$J_{LD}$不同，且可通过一个简单的半经验关系表示为$J_{Jaff\acute{e}}/J_{CL}$的函数，其中$J_{CL}$是$u_0=0$时真空内的空间电荷限制电流密度。
英文摘要
For electrons with nonzero initial velocity $u_0\ne0$ in vacuum, the space-charge-limited current density (SCLCD) is given by $J_{Jaff\acute{e}}$. For current densities $J>J_{Jaff\acute{e}}$, electron reflections occur along with virtual cathode (VC) oscillations. Past studies have exhibited hysteresis by sustaining these oscillations until $J=J_{hys}$, often claiming $J_{hys}\approx J_{LD}<J_{Jaff\acute{e}}$, where $J_{LD}$, also called the bifurcation solution, represents the steady-state current density where the electron velocity is zero at the VC. In this study, we demonstrate that $J_{LD}$ is not a valid steady-state solution since it represents a higher charge density than $J_{Jaff\acute{e}}$, the true SCLCD. We further demonstrate that $J_{Jaff\acute{e}}$ also corresponds to the true, mathematical bifurcation solution. Using particle-in-cell simulations across various gap distances and voltages, we demonstrate that $J_{hys}$ consistently differs from $J_{LD}$ and can be represented by a simple semi-empirical relationship as a function of $J_{Jaff\acute{e}}/J_{CL}$, where $J_{CL}$ is the SCLCD in vacuum for $u_0=0$.
