An impedance model has been developed for the arc-plasma cathode electron current source used in localized helicity injection tokamak startup. According to this model, a potential double layer (DL) is established between the high-density arc plasma (n_arc~10^21 m^−3) in the electron source, and the less-dense external tokamak edge plasma (n_edge~10^18 m^−3) into which current is injected. The DL launches an electron beam at the applied voltage with cross-sectional area close to that of the source aperture: A_inj ~ 2 cm^2. The injected current, I_inj, increases with applied voltage, V_inj, according to the standard DL scaling, I_inj~V_inj^3/2, until the more restrictive of two limits to beam density n_b arises, producing I_inj~V_inj^1/2, a scaling with beam drift velocity. For low external tokamak edge density n_edge, space-charge neutralization of the intense electron beam restricts the injected beam density to n_b~n_edge. At high J_inj and sufficient edge density, the injected current is limited by expansion of the DL sheath, which leads to n_b~n_arc. Measurements of n_arc, I_inj , n_edge, V_inj, support these predicted scalings, and suggest n_arc as a viable control actuator for the source impedance. Magnetic probe signals 300 degrees toroidally from the injection location are consistent with expectations for a gyrating, coherent electron beam with a compact areal cross-section. Technological development of the source has allowed an extension of the favorable I~V^1/2 to higher power without electrical breakdown.