Streamer in air: Broadening and branching

The streamer in air starts from the stressed electrode tip under a critical electric field (E_cr) of 4. 5 kV/cm. This streamer filament assumes a minimum radius (r₀) of 30 μm value. This condition has been achieved at a critical low value of injected energy (U_cr). As the applied electric field (E) and energy (U) increase, the radius (r) and temperature (T) of initiated filament increase as well. New deduced equations govern the control of this increase. The streamer starts in broadening and branching when U/U_cr = 8, and E/E_cr = VS. The filament radius changes from a minimum value of 30 μm, at atmospheric temperature 300 K, to a maximum value of 120 μηι, at temperature 19200 K. This maximum temperature will be the arc temperature, and it occurs at electric field of 36 kV/cm for breakdown in air.