Effect of cathode microprotrusion shape on its thermal instability

In order to study the effect of the cathode microprotrusion shape on its thermal instability, the evolution process of the thermal instability has been numerically investigated with the microprotrusion shape chosen as column, truncated cone and cone under different applied electric field. There is an obvious difference in temperature distribution in the microprotrusion with different shapes when the temperature at the microprotrusion peak reaches melting point of the cathode material. While the shape of microprotrusion is changed from column, truncated cone to cone, the region where temperature is close to the melting point reduces. At a given applied electric field, the smaller the ratio of top radius to bottom radius of the microprotrusion is, the larger the time delay of explosive electron emission is; the time delay of explosive electron emission increases exponentially with the decrease of the ratio of top radius to bottom radius of the microprotrusion or strength of the cathode surface electric field when the cathode surface electric field is larger than 11 GV/m.