The diagram of a 1D drift space of gap spacing in (a) a single electron sheet model, and (b) an equivalent drift space model with a short electron pulse having a width of and a potential of at the beam-vacuum interfaces, propagating inside the gap. The solid line corresponds to the potential profile distributed in the gap for a given value of injected current density .
The normalized short-pulse space-charge-limited (SCL) current density in a drift space, as a function of the normalized injection pulse duration . The analytical results for the equivalent drift space model with [Eq. (11)] and without [Eq. (9a)] pulse expansion are plotted in solid lines, respectively (bottom and top). The single-sheet model [Eq. (4)] is plotted in dashed line. The symbols corresponds to the PIC simulation results (circles for and ; crosses for and ; squares for and ).
The normalized short-pulse relativistic SCL current density in drift space , as a function of (a) the normalized pulse injection duration for to 100 (top to bottom), and (b) the normalized electron beam voltage for to 1 (long pulse). The solid and dashed lines represent, respectively, the results with and without pulse expansion. The symbols in (b) illustrate the PIC simulation results in the electrostatic mode: (×) is with no adjustment, (△) is with , and (◇) is with adjustment to have the same transit time to the theoretical value.
The comparison between the transit time of a single particle in a gap obtained from PIC simulation (symbols) and calculations (lines) as a function of to 1000.
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