  Evidence of self-synchronization has been observed in multi-electrode corona
discharge systems, where the application of high negative DC voltages induces a
self-sustained mode of current pulse trains. These pulses, historically
referred to as Trichel pulses, characterize the operation of a two-electrode
system where the discharge electrode is subjected to a high negative DC
voltage. The numerical algorithm indicates that in a multi-electrode discharge
system, comprising multiple two-electrode discharges, each two-electrode system
independently produces pulse trains. These systems, each comprising a pair of
electrodes, operate in a pulsed mode, with synchronization emerging from weak
yet significant interactions among them. These interactions arise from the
mutual influence of electric fields and space charges generated by each
discharge pair. This influence extends beyond individual systems, leading to a
synchronization between both pairs, both in a pulsed mode. A three-species
model of discharge was employed to simulate this process and it was based on
the finite element method formulation. Two different numerical models were
investigated, a 2D model, consisting of two discharge electrodes and a third
grounded electrode, and two 1D-axisymmetric models, consisting dual and triple
pairs of discharge systems. Experiments show a multi-stable nature of the
coupled pulsed discharge systems, indicating that under appropriate conditions
the pulse trains exhibit two distinct modes of synchronization: in-phase
synchronization and anti-phase synchronization. The occurrence of each mode
depends on factors such as interaction strength, applied voltage level, and
various system parameters. Furthermore, variations in these factors can lead to
additional outcomes, including out of phase synchronization, as well as
scenarios involving near-harmonic oscillations and quenching.
