Local and nonlocal conditions for electron runaway in a gas gap with a conical cathode with a variable opening angle

The conditions for the generation of runaway electrons in an air gap are compared at different degrees of inhomogeneity of the electric field distribution provided by varying the opening angle of the conical cathode: in the range 40°–120° in experiments and 0°–180° in calculations. It is demonstrated that, in a weakly inhomogeneous electric field (according to the proposed classification, this corresponds to cones with angles greater than the Taylor angle of 98.6°), the runaway condition has a local character. The transition of free electrons into the runaway mode is determined by the local distribution of the electric field near their starting point—the tip of the cone. The local electric field strength must exceed a threshold value comparable to the strength critical for the runaway of electrons in a uniform field. In a strongly inhomogeneous field (cones with angles less than 98.6°), this condition is not sufficient for electrons to run away throughout the gap. Electrons accelerating in the near-cathode region may begin to slow down in a weak field at a distance from the cathode. In this case, the runaway condition becomes nonlocal. It is determined by the dynamics of electrons in the entire gap, primarily in the near-anode region, and reduces to the requirement that the potential difference applied to the gap exceeds a certain threshold value.