Abstract
In this paper, a numerical iteration approach to resolve the space charge limited (SCL) bipolar flow problem in cylindrical geometries has been developed. Such an approach is basis for the simultaneous determination of the unknown current densities and the potential distribution. We employed this method to study the characteristics of the SCL bipolar flow. By considering a cylindrical geometry with a cathode radius Rc and an anode radius Ra, the enhancement over the classical Langmuir-Blodgett (LB) law is investigated as a function of Rc/Ra. It is found that for the bipolar flow model, the SCL current density can be given by F×JLB, where F and JLB represent the enhancement factor on account of the influence of ions and the LB law, respectively. The enhancement factor F follows a Rc/Ra scaling and gradually converges to a constant with increasing Rc/Ra. The planar bipolar flow solution is recovered in the condition where the values of Rc and Ra are much greater than that of the gap spacing.
Highlights
SPACE-CHARGE-LIMITED (SCL) current flow has received lots of attention in vacuum electronic devices (VEDs), for it has an important effect on the modeling high power microwaves (HPM) and x-ray sources, heavy ion beams, compact high power THz sources, and free electron lasers [1], [2]
We proposed an iteration approach to numerically investigate the SCL bipolar flow problem in a cylindrical geometry without analytically solving the nonlinear Poisson’s
As the SCL bipolar flow problem in the 1D planar geometry, the parameter q and the limiting electron current density are strongly related to the boundary conditions
Summary
SPACE-CHARGE-LIMITED (SCL) current flow has received lots of attention in vacuum electronic devices (VEDs), for it has an important effect on the modeling high power microwaves (HPM) and x-ray sources, heavy ion beams, compact high power THz sources, and free electron lasers [1], [2]. In [9], an approximate current density scaling expressions for cylindrical bipolar diodes in positive and negative polarity for non-relativistic and relativistic regimes are provided. Such a bipolar flow problem is of fundamental interest since positive ions are commonly used to mitigate the space charge effect [45]. For the SCL bipolar flow problem in the cylindrical model, the exact analytical solutions are not easy to obtain. We proposed an iteration approach to numerically investigate the SCL bipolar flow problem in a cylindrical geometry without analytically solving the nonlinear Poisson’s. By discretely dividing the calculation area of the discharge space into grid points, and by applying the finite difference method and appropriate iteration algorithms, the SCL electron current density can be determined for a given injection ion current density
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
