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.Fireballs are a discharge phenomenon that can occur near electrodes biased above the plasma potential by an amount greater than the neutral gas ionization potential 1 . They are characterized by a secondary plasma whose plasma potential is near the electrode potential and at its boundary is separated from the bulk plasma by a double layer. Typically, the fireball plasma is several hundred Debye lengths, much larger than the initial sheath scale. Recent experimental studies of fireballs have focused on their stability 2-5 and properties as ion sources 6-8 . One of the most common observations is hysteresis in the current-voltage (I-V) traces between the upswing and downswing of the electrode bias 9,10 , see Fig. 1A. Upon increasing the electrode bias, the fireball onset is abrupt lasting on the order of a microsecond once a critical electrode bias is exceeded 9,11 . This critical bias is determined by the neutral gas pressure, electrode area, and the electron-impact ionization cross section of the neutral gas 12 . After onset, increased current collection is observed primarily due to the greater electron collection by the surface area of the fireball compared to that of the initial electron sheath, but also due to an increased ionization rate within the fireball. Upon decrementing the electrode bias below the critical bias, the fireball persists and the increased current collection relative to the prefireball formation value continues to be observed. The fireball eventually collapses after continued decrementation of the electrode bias and the electron current collection returns to pre-fireball levels.When the plasma chamber is small enough, fireball formation result in a state of global non-ambipolar flow where electrons are only lost to the fireball surface area 13 . In this state, the bulk plasma potential is locked to a fixed offset of the potential of the electrode due to the ...