Abstract
The axisymmetric steady-state electron flow emitted from an electrified semi-infinite perfectly-conducting filament in vacuum is theoretically analyzed using an Eulerian model. The high symmetry allows for a solution in terms of self-similar functions, with radial dependence described by power-laws, leading to an eigenvalue problem for the angular dependence, which is numerically solved.Our results show a unique eigenvalue compatible with the boundary conditions, leading to a r−1.6308 dependence for the electron number density, r0.3692 for the electric potential, r0.1846 for the velocity field. Hence, for an infinitely thin filament, space charge limited emission is not compatible with our boundary conditions.
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