Theory for two dimensional electron emission between parallel flat electrodes

Torres-Cordoba, Rafael
December 2009
Physics of Plasmas;Dec2009, Vol. 16 Issue 12, p123106
Academic Journal
The electron emission in space charge is limited for the case of a planar cathode; such emission is generated by using an approximation that models electric field formation by a dipole, which generates an oscillatory symmetrical density current j(x), minimum value is moved around the origin and calculated throughout the Poisson equation. Such value has been previously calculated based upon the already stated conditions for the two dimensional (2D) case. In our matter under study, it is stated that a symmetric oscillatory potential, namely, μ(x,y) is invariably generated; because of that the boundary conditions represented by both a barrier potential and a square potential will satisfy this potential as well. For the case of the square potential, it is taking into account either a potential is attractive or repulsive. In this study one of the principal problems is discussed. It is when the space charge creates a potential barrier that prohibits steady-state beam propagation. In this paper it is claimed to have found the boundary conditions that fully satisfy the potential, and the potential satisfies approximately the Poisson equation for the 2D case, and the electron emission is generated through a finite strip due to electrical dipole formation.


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