General scaling laws of space charge effects in field emission

Space charge effects in field emission: One dimensional theory

The current associated with field emission is greatly dependent on the electric field at the emitting electrode. This field is a combination of the electric field in vacuum and the space charge created by the current. The latter becomes more important as the current density increases. Here, a study is performed using a modified classical one dimensional 1D Child–Langmuir description that allows...

Space charge effects in field emission: Three dimensional theory

Field emitters rely on high gradients on microfabricated structures to enable substantial levels of emitted current, which can in turn act to reduce the field at the emission site of a single emitter. An account of that effect is obtained in the following steps: a model of the emitter geometry based on the point charge model that allows for the determination of the apex radius and field enhance...

Discrete space charge affected field emission: Flat and hemisphere emitters

Conservation laws of scaling-invariant field equations

A simple conservation law formula for field equations with a scaling symmetry is presented. The formula uses adjoint-symmetries of the given field equation and directly generates all local conservation laws for any conserved quantities having non-zero scaling weight. Applications to several soliton equations, fluid flow and nonlinear wave equations, Yang-Mills equations and the Einstein gravita...

Space charge and quantum effects on electron emission

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