An impedance model is formulated and tested for the ∼1 kV, 1 kA/cm2, arc-plasma cathode electron source used for local helicity injection tokamak startup. A double layer sheath is established between the high-density arc plasma (narc≈1021 m−3) within the electron source, and the less dense external tokamak edge plasma (nedge≈1018 m−3) into which current is injected at the applied injector voltage, Vinj. Experiments on the Pegasus spherical tokamak show that the injected current, Iinj, increases with Vinj according to the standard double layer scaling Iinj∼Vinj3/2 at low current and transitions to Iinj∼Vinj1/2 at high currents. In this high current regime, sheath expansion and/or space charge neutralization impose limits on the beam density nb∼Iinj/Vinj1/2. For low tokamak edge density nedge and high Iinj, the inferred beam density nb is consistent with the requirement nb≤nedge imposed by space-charge neutralization of the beam in the tokamak edge plasma. At sufficient edge density, nb∼narc is observed, consistent with a limit to nb imposed by expansion of the double layer sheath. These results suggest that narc is a viable control actuator for the source impedance.