Space charge-limited emission studies using Coulomb's Law
Carr, Christopher G.
- Publisher: Monterey California. Naval Postgraduate School
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 non-linear differential equation. This approach can also be applied to cylindrical and spherical geometries, but only for one-dimensional 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 non-linear differential equation, and to limit the emission area to two-dimensional 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