A coordinate system invariant formulation for space-charge limited current with nonzero injection velocity

Author:

Halpern Jacob MORCID,Darr Adam MORCID,Harsha N R SreeORCID,Garner Allen LORCID

Abstract

Abstract Recent studies have extended the classical space-charge limited current (SCLC) solution in a non-magnetic, planar diode with zero injection velocity to other geometries using variational calculus (VC). We further extend VC to solve for SCLC with a non-relativistic, monoenergetic injection velocity from first principles for nonplanar diodes. By extremizing either the current or a functional of the electric field (and not its derivative), we demonstrate that VC can find either the bifurcation or the SCLC solution, respectively. The bifurcation solution is characterized by the onset of particle reflection, resulting in a singularity in the derivative of the electric field at the virtual cathode, physically analogous to the singularity at the cathode in SCLC for zero injection velocity. Alternatively, using VC to extremize a functional of the potential and its gradient (electric field) yields the maximum current SCLC result. We then derive the SCLC solutions in cylindrical and spherical diodes; additionally, we develop a method to determine SCLC numerically and the bifurcation solution exactly for any orthogonal geometry. Implications for the potential profile and virtual cathode are discussed, especially the behavior for other geometries.

Funder

Purdue University Nuclear Engineering Undergraduate Research Scholarship

Purdue Doctoral Fellowship

Air Force Office of Scientific Research

Publisher

IOP Publishing

Subject

Condensed Matter Physics

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3