Maximal charge injection of consecutive electron pulses with uniform temporal pulse separation

Abstract

A charge sheet model is proposed for the study of the space-charge limited density of consecutive electron pulses injected to in a diode with uniform temporal pulse separation. Based on the model, an analytical formula is derived for expressing the dependency of the charge density limit on the gap spacing, gap voltage, and pulse separation. The theoretical results are verified by numerical solutions up to electron energy of a few MeV, including relativistic effects. The model can be applied to the design of multiple-pulse electron beams for time resolved electron microscopy and free electron lasers. V

Space-charge effect of the time-varying electron injection in a diode: Classical and relativistic regimes

“…This is when the SC limit dominates the electron flow process and the virtual diode forms. It is also speculated that the zero cathode field E C ¼ 0 is not a critical condition for the space charge limit for time-varying 2017) injection cases, as previous work 6,22 consider so. We speculate that the time-dependent space-charge limit may involve a more dynamic process of the virtual cathode than a static zero cathode field.…”

“…For example, a recent work based on the 1D charge sheet model investigated how the temporal interval becomes distorted due to the space-charge effect. 22 Another recent work 13 used a characteristic method to solve the 1D pressureless Euler-Poisson equations and achieved an over-classical limit by varying the anode boundary voltage with time although the relevant characteristics are not solvable in a closed form for arbitrary temporal profiles of injection. Therefore, a general treatment for time-varying flow of electrons is demanded.…”

Maximal charge injection of a uniform separated electron pulse train in a drift space

“…In this paper, we extend our previous work [24] of calculating the maximum charge density for a uniform electron pulse train in a diode to a drift space. In Ref.…”

“…In past years, the studies of SCLC in a diode and a drift space have been revised extensively to consider various effects such as finite emission area [12][13][14][15][16], short pulse length and relativistic (and quantum) effects [17][18][19][20][21][22][23][24], semianalytical scaling for cylindrical and spherical diodes [25,26].…”

“…In Ref. [24], a 1D model to study the space charge limited charge injection of a train of multiple electron pulse into a diode were presented. The charge sheet model was used to obtain an analytical formula, which can quickly provide such upper limit of charge density injection once the values of gap spacing, gap voltage, and the initial time separation between the pulses are provided.…”