  Self-organized spatial plasma structures exhibit many similarities with
Turing structures obtained in biology and chemistry. Using an analytical
mesoscopic approach it is shown that plasma balls of fire belong to the same
class of Turing structures like the Brusselator. It is also mathematically
proved that the existence of these self-organized plasma structures is related
with a negative differential resistance. There are also established the
mathematical conditions which the negative differential resistance must satisfy
for obtaining a stationary ball of fire at the anode of a plasma diode.
