Coordinate System Invariant Formulation of Fractional-Dimensional Child-Langmuir Law for a Rough Cathode

被引：2

作者：

Zubair, Muhammad ^{[1
]}

Fatima, Adeela ^{[2
]}

Raheem, Noreen ^{[2
]}

Ang, Yee Sin ^{[3
]}

Mehmood, Muhammad Qasim ^{[1
,2
]}

Massoud, Yehia ^{[1
]}

机构：

[1] King Abdullah Univ Sci & Technol KAUST, Innovat Technol Labs ITL, Thuwal 239556900, Saudi Arabia

[2] Informat Technol Univ ITU Punjab, Dept Elect Engn, MicroNano Lab, Ferozepur Rd, Lahore 54600, Pakistan

[3] Singapore Univ Technol & Design SUTD, Sci Math & Technol SMT Cluster, Singapore 487372, Singapore

来源：

ADVANCED PHYSICS RESEARCH | 2023年 / 2卷 / 07期

关键词：

fractional dimensional spaces; Langmuir-Blodgett equations; space charge limited current; variational calculus; CHARGE-LIMITED CURRENTS; SPACE-CHARGE; CURRENT FLOW;

D O I：

10.1002/apxr.202200120

中图分类号：

O59 [应用物理学];

学科分类号：

摘要：

This work presents an exact closed-form analytical model of the space charge limited (SCL) current density for planar, cylindrical, and spherical geometries in fractional dimensional spaces (F-alpha) where alpha represents the fractional dimensions having a range 0 < alpha <= 1. Decreasing value of alpha shows an increasing degree of surface roughness. This analytical model approaches Langmuir-Blodgett equations for sufficiently close anode (R-a) and cathode (R-c) radii for integer dimensions (alpha = 1). To calculate SCL current density for any geometry, variational calculus (VC) is used to derive the differential equations in fractional (alpha) dimensions. The effect of electrode radius ratios on space charge limited current is investigated here considering the surface roughness.

引用

页数：8

共 16 条

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Zubair, M.
Ang, L. K.
PHYSICS OF PLASMAS, 2016, 23 (07)
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Ragan-Kelley, Benjamin
Verboncoeur, John
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Ragan-Kelley, Benjamin
Verboncoeur, John
Feng, Yang
PHYSICS OF PLASMAS, 2009, 16 (10)
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Lisovskiy, V. A.
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Pearlman, Marcus
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PHYSICS OF PLASMAS, 2021, 28 (12)
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Koh, WS
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PHYSICS OF PLASMAS, 2005, 12 (05) : 1 - 6
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Chen, S. H.
Tai, L. C.
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Koh, W. S.
PHYSICS OF PLASMAS, 2011, 18 (02)

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