“…Here P is the gun's perveance, defined by the geometry of the gun. However, the price, dimensions and complexity of DC electron guns and power supplies grow significantly with the voltage [44,48], (mostly, due to isolation and pulsed power system complexity), and in practice are preferred to be kept around 10-20 kV for compact medical accelerators, 30-50 kV for industrial accelerators and to 80-160 kV for large high-current facilities [15,21,44,[49][50][51]. Therefore, the injection usually occurs at lower velocities than β ph , which fundamentally limits the capture of the beam.…”