  A model is proposed to explain hysteresis observed in fireball formation and
extinction as electrode bias is varied in partially ionized plasmas. Formation
is predicted after a sufficiently deep potential well is established in the
electron sheath of the electrode. Under the experimental conditions considered,
once the fireball forms the plasma potential rapidly increases, resulting in
electrons being only lost to the electrode.Previous predictions suggest that
once formed the fireball double layer must maintain a potential close to the
ionization potential of the neutral gas to remain in a steady state. In this
paper, it is predicted that changes in electrode bias after formation results
in a corresponding change in fireball size and plasma potential. This change in
plasma potential allows the double layer potential to be maintained at biases
both above and below the electrode bias at onset. The fireball extinguishes
when the required double layer potential can no longer be maintained with
balance of current loss of the bulk plasma. These predictions are tested
experimentally and are found to be in good agreement with the measurements.
