Theory of positive corona in SF6 due to a voltage impulse

A theoretical examination is made of the mechanism of corona formation for a positive point-plane gap in SF₆ at 100 kPa. The impulse voltage applied has a rise time of 15 ns and peak value of 200 kV. Seed electrons are released 1 ns after the start of the voltage rise. For a 0.5-cm diameter positive sphere located 6.5 cm from a negative plane, the calculated circuit current initially consists of subnanosecond corona onset pulses, and then the current steadily rises to a maximum, as the voltage reaches a maximum, followed by a rapid fall in current. During the current rise a streamer moves out into the gap along a 100-μm channel, with the electric field in the streamer trail E>E*, where E* is the critical field where ionization equals attachment. The light output during the discharge is predicted to be a maximum at the anode with only a minor pulse of light at the streamer head, making it hard to detect. After the current maximum, recombination rapidly reduces the numbers of positive ions, negative ions, and electrons, but the net charge density remains constant and thus so does the electric field. The electric field is E~E* in the streamer trail, but has a sharp maximum, E≫E* at the head of the streamer trail. The origin of mid-gap precursors, observed when the streamer channel reilluminates after some 100 ns, is attributed to this field maximum in the remnant electric field. The evolution of positive ions, negative ions, and electrons is described by one-dimensional continuity equations, with the space-charge electric fields determined by the disk method. The effects of ionization, attachment, recombination, electron diffusion, and photoionization are all included. New numerical methods allow resolution of the streamer head and the anode fall region to be obtained with a 1-μm mesh, while following the streamer propagation for ~2 cm