Charge transport and mode transition in dual-energy electron beam diodes

Abstract

This Letter uncovers five distinct charge transport modes and their transitions in dual-energy electron beam diodes. We via first-principle particle-in-cell (PIC) simulations establish that the specific mode (e.g., space charge oscillations) and the current transport characteristics are essentially governed by the interplay between the electron beam energy and injected current density. A generalized analysis is conducted for n-component electron beams, and a theoretical piecewise function is for the transmitted current density proposed, which agrees well with the PIC results under designed conditions. The discovery provides a mechanistic picture of multiple electron beam transport in diodes, paving the way for novel designs of high-performance modern vacuum electronic devices.

Figures (4)

• Figure 1: Schematic of the dual-energy electron beam driven diode, in which the cathode injection current consists of low-energy and high-energy electrons. Low-energy electrons tend to be reflected mostly, whereas high-energy electrons can be transmitted predominantly to the anode. $x_\text{c}=0$ is the cathode, and $x_\text{a}=d_\text{gap}$ is the anode. Note that the cathode-to-virtual cathode region is enlarged and $x_\text{ref,1}<x_\text{ref,2}<x_\text{vc}\ll d_\text{gap}$, where $x_\text{ref,1}$ and $x_\text{ref,2}$ are the reflection points, and $x_\text{vc}$ is the virtual cathode position.
• Figure 2: Five operation modes in the dual-energy electron beam driven diode. The panels from left to right correspond to (a1)--(a5) $\phi$--$x$, (b1)--(b5) $E_\text{s}$--$t$, and (c1)--(c5) $\bar{n}_e$--$E_\text{s}$. The combinations of the emitted electrons (e$_1$ and e$_2$) result in five operation modes, i.e., M1 (both e$_1$ and e$_2$ transmitted), M2 (e$_1$ oscillated and e$_2$ transmitted), M3 (e$_1$ reflected and e$_2$ transmitted), M4 (e$_1$ reflected and e$_2$ oscillated), and M5 (both e$_1$ and e$_2$ oscillated).
• Figure 3: Total transmitted current $J_\text{tran}$ ($J_\text{tran} = J_\text{tran,1} + J_\text{tran,2}$ with $J_\text{tran,1}$ for low-energy electron $\text{e}_1$ and $J_\text{tran,2}$ for high-energy electron $\text{e}_2$) and reflected current $J_\text{ref}$ ($J_\text{ref} = J_\text{ref,1} + J_\text{ref,2}$ with $J_\text{ref,1}$ for $\text{e}_1$ and $J_\text{tran,2}$ for $\text{e}_2$) as a function of the injected current $J_0$ ($J_0 = J_1 + J_2$ with $J_1$ for $\text{e}_1$ and $J_2$ for $\text{e}_2$) under different conditions. Governing parameters ($\beta_1/\beta_2,\ J_1/J_2$)= (0.1, 1) for (a), (0.5, 4) for (b), (0.5, 0.25) for (c), and (0.95, 1) for (d). (e) Schematic of the operation mode transition for panel (a). (f)--(g) Illustrations of the transmitted current for panels (b) and (c). (h) Schematic of the operation mode transition for panel (d).
• Figure 4: Transmitted current density $J_\text{tran}$ versus the total injected current density $J_0$. The prediction from the proposed theoretical formula [Eq. \ref{['EQ3']}] agrees well with PIC simulation results, for example, with the electron beam number $n = 3$.