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We simulate and characterize positive streamers in ambient air in homogeneousbackground electric fields from 4.5 to 26 kV/cm in a 4 cm gap. They canaccelerate or decelerate depending on the background electric field. Manyexperiments have shown that a streamer keeps propagating in a stable manner inthe so-called stability field of 4.5 to 5 kV/cm. Our fluid streamer simulationsin STP air show that: (1) In a homogeneous field larger than 4.675 kV/cm, asingle streamer accelerates, and in a lower field, it decelerates andeventually stagnates with a small radius and very high field enhancement. (2)In a field of 4.675 kV/cm, the streamer head propagates with an approximatelyconstant velocity of 6.7 x 10$^4$ m/s and an optical radius of 55 $\mu$m overdistances of several centimeters as a stable coherent structure. These valuesfor the radius and velocity agree well with measurements of so-called minimalstreamers. (3) Behind the uniformly translating streamer head, the channelconductivity decreases due to electron attachment and recombination, and theelectric field returns to its background value about 1 cm behind the head. Thepropagation behavior of the solitary streamer agrees with the originaldefinition of the stability field, which is the homogeneous field in which astreamer can propagate with a constant speed and shape.

Simulations of positive streamers in air in different electric fields: steady motion of solitary streamer heads and the stability field