Patch model of a spherical cathode

In a dispenser cathode the surface is composed of many small regions having different and individual values of work functions called "patches". The non-uniform emission results in a gradual transition from space-charge (SC) region to temperature limited (TL) region. The emission of a planar cathode is modeled using a \´top-hat\´ model. In practice, the convergent guns are incorporated with a spherical cathode. The above model is applied to a spherical cathode-anode system. This model can also be extended to a gun geometry provided that the field distribution across the cathode cross section is uniform. In this paper the performance of three types of cathode, viz. B-Type, Alloy-coated, and Scandate cathodes are studied. In the present model the real cathode is replaced by a fictitious cathode, having a maximum current density at θ = 0° and a minimum at the rim. The analysis shows that there exists an analogy between a planar cathode and a spherical cathode, enabling the emission current to be modeled in a manner similar to a planar cathode.