Space chargelimited emission studies using Coulomb's Law
Doctoral thesis
OPEN
Carr, Christopher G.
(2004)
 Publisher: Monterey California. Naval Postgraduate School

Subject:
Space charge  Electric fields  Differential equations, Nonlinear  Electrons  Emission
Approved for Public Release; Distribution is Unlimited
Child and Langmuir introduced a solution to space charge limited emission in an infinite area planar diode. The solution follows from starting with Poisson's equation, and requires solving a nonlinear differential equation. This approach can also be applied to cylindrical and spherical geometries, but only for onedimensional cases. By approaching the problem from Coulomb's law and applying the effect of an assumed charge distribution, it is possible to solve for space charge limited emission without solving a nonlinear differential equation, and to limit the emission area to twodimensional geometries. Using a Mathcad worksheet to evaluate Coulomb's law, it is possible to show correlation between the solution derived by Child and Langmuir and Coulomb's law.
Ensign, United States Navy