Abstract
We develop a general electrostatic steady-state model to calculate the two-dimensional (2D) space-charge-limited current (SCLC) with an initial velocity v0 (i.e., kinetic energy e K V = m v 0 2 / 2 ) injected from a cathode into a vacuum diode with a spacing D and a potential difference of Vg. We consider two types of beam cross section: (a) a sheet beam with a width W and (b) a circular beam with a radius R, where both W and R are larger than D in the calculation. By introducing a parameter ϵ ≡ K V / V g ≥ 0 , we can tune the operating regime to be in between the accelerating diode ( ϵ ≪ 1 ) and drift space ( ϵ ≫ 1 ). Hence, we verify the 2D SCLC model by converging to some prior analytical findings such as the 2D Child-Langmuir law at ϵ = 0, 2D SCLC at drift space at ϵ ≫ 1 , and their 1D limits at W / D ≫ 1 or R / D ≫ 1 . Our 2D SCLC model indicates that there is a maximal value at ϵ ∼ 1 / 60 , which is independent of W/D or R/D. Furthermore, the hysteresis behavior is also studied when the injected current density is beyond the SCLC threshold and its dynamics are mainly influenced by ϵ instead of geometrical effect. This model is useful in high current electron beam emission with a finite emission area and with a non-negligible arbitrary injection kinetic energy.
Original language | English |
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Article number | 063105 |
Journal | Physics of Plasmas |
Volume | 31 |
Issue number | 6 |
DOIs | |
Publication status | Published - 2024 Jun 1 |
All Science Journal Classification (ASJC) codes
- Condensed Matter Physics